U.S. patent application number 13/767851 was filed with the patent office on 2016-06-09 for determining a polarization-related characteristic of an optical link.
This patent application is currently assigned to EXFO Inc.. The applicant listed for this patent is EXFO Inc.. Invention is credited to Hongxin Chen, Normand Cyr, Gregory Walter Schinn.
Application Number | 20160161397 13/767851 |
Document ID | / |
Family ID | 50232988 |
Filed Date | 2016-06-09 |
United States Patent
Application |
20160161397 |
Kind Code |
A9 |
Cyr; Normand ; et
al. |
June 9, 2016 |
DETERMINING A POLARIZATION-RELATED CHARACTERISTIC OF AN OPTICAL
LINK
Abstract
A polarization-related characteristic of an optical path is
determined from a predetermined function of the mean-square of a
plurality of differences between polarization-analyzed optical
power parameters corresponding to pairs of wavelengths mutually
spaced about a midpoint wavelength by a small optical frequency
difference. At least some of the said differences correspond to
wavelength pairs measured under conditions where at least one of
midpoint wavelength, input state of polarization (I-SOP) or
analyzed state of polarization (A-SOP) of a pair is different.
Inventors: |
Cyr; Normand; (Quebec,
CA) ; Chen; Hongxin; (Chino Hills, CA) ;
Schinn; Gregory Walter; (Quebec, CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
EXFO Inc. |
Quebec |
|
CA |
|
|
Assignee: |
EXFO Inc.
Quebec
CA
|
Prior
Publication: |
|
Document Identifier |
Publication Date |
|
US 20140071436 A1 |
March 13, 2014 |
|
|
Family ID: |
50232988 |
Appl. No.: |
13/767851 |
Filed: |
February 14, 2013 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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12568554 |
Sep 28, 2009 |
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13767851 |
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11992797 |
Mar 28, 2008 |
7920253 |
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PCT/CA2006/001610 |
Sep 29, 2006 |
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12568554 |
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PCT/CA2008/000577 |
Mar 28, 2008 |
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12568554 |
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60721532 |
Sep 29, 2005 |
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60907313 |
Mar 28, 2007 |
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Current U.S.
Class: |
356/73.1 |
Current CPC
Class: |
G01M 11/335 20130101;
G01N 21/21 20130101; G06F 17/18 20130101; G01M 11/3163 20130101;
G01M 11/3181 20130101; G01M 11/336 20130101 |
International
Class: |
G01N 21/21 20060101
G01N021/21; G06F 17/18 20060101 G06F017/18 |
Claims
1. A method of measuring a polarization-related characteristic of
an optical path (18) wherein light comprising polarized light is
propagated, the method comprising the steps of using:
polarization-controller-and-analyzer means
(14,20A;14A,14B,20;14A,14B,20A; 14,20; 14,20C; 14A,45) connected to
the optical path at or adjacent either the proximal end thereof or
a distal end thereof to control at least one of state of
polarization (I-SOP) of light launched in the optical path and
state of polarization (A-SOP) used to analyze light leaving the
optical path, detecting means (22; 22A,22B; 22D) to detect the
analyzed light and provide corresponding detection signals, and
processing means (40) to process the detection signals to derive
said polarization-related characteristic, wherein said light
leaving the optical path is analyzed to provide transmitted
coherent optical power at each wavelength of light in each of at
least two groups of wavelengths, and wherein the lowermost
(.lamda..sub.L) and uppermost (.lamda..sub.U) said wavelengths in
each said group of wavelengths are separated by a first small
optical frequency difference; and wherein each of the said at least
two groups comprises a wavelength pair, said pair in each group
defining a midpoint wavelength therebetween, and being mutually
spaced by a second small optical-frequency difference, the second
small optical-frequency difference being equal to or less than the
first optical-frequency difference, said second small
optical-frequency difference (.delta..nu.) being the same for
corresponding wavelength pairs in different groups, and wherein the
I-SOP and A-SOP are substantially constant for each coherent
optical power at each said wavelength in each said group, and
wherein at least one of the midpoint wavelength, I-SOP and A-SOP is
different between the respective said groups, the processing step
including the steps of: (i) computing at least one difference
between a pair of measured power parameters each corresponding to a
respective one of the wavelengths in said wavelength pair for each
of the said at least two groups, each said measured power parameter
being proportional to transmitted coherent optical power of the
said analyzed and subsequently detected light, thereby defining for
said at least two groups a set of at least two measured power
parameter differences; (ii) computing a mean-square value of said
set of at least two measured power parameter differences; and (iii)
calculating the polarization-related optical path characteristic as
a predetermined function of said mean-square value, said
predetermined function being dependent upon the said second small
optical-frequency difference between the wavelengths corresponding
to the said each of at least said two pairs of wavelengths.
2. A method according to claim 1, further comprising using light
source means connected to the optical path at or adjacent a
proximal end thereof to launch light comprising polarized light
into the optical path, and wherein the said
polarization-controller-and-analyzer means comprises input
controller means connected to the optical path at or adjacent a
proximal end thereof and polarization-controller-and-analyzer means
connected to the optical path at or adjacent a distal end
thereof.
3. A method according to claim 2, wherein: (a) corresponding
wavelength pairs in different groups have substantially the same
midpoint wavelength, (b) the second small optical frequency
difference (.delta..nu.) multiplied by differential group delay
(DGD) is less than 0.5, and (c) the said polarization-related
optical path characteristic comprises a differential group delay
(DGD) at the said midpoint wavelength.
4. A method according to claim 3, wherein the said measured power
parameter is normalized power T(.nu.), and the limit of said
predetermined function as said second small optical-frequency
difference (.delta..nu.) tends to zero may be expressed according
to the following differential formula: DGD ( v ) = .alpha. ds
.pi..delta. v .DELTA. T 2 ( v ) SOP ##EQU00175## where the constant
.alpha. ds = 9 2 , ##EQU00176## .nu. is the optical frequency
corresponding to the said midpoint wavelength, and .DELTA.T(.nu.)
is the difference in the normalized power obtained for a particular
I-SOP and A-SOP couple.
5. A method according to claim 3, wherein the said measured power
parameter is normalized power T(.nu.), and the mean-square value
computing step (ii) further comprises computation of relative
variance (.sigma..sub.r.sup.2(.nu.)) of normalized powers T(.nu.)
according to the expression: .sigma. r 2 ( v ) = ( 1 .sigma. 20 ) 2
[ T 2 ( v ) SOP - T ( v ) SOP 2 ] ##EQU00177## where a reference
variance .sigma..sub.20.sup.2= 1/12, .DELTA.T(.nu.) is the
difference in the normalized power obtained for a particular I-SOP
and A-SOP couple, and the limit of said predetermined function as
the second small optical-frequency difference .delta..nu. tends to
zero may be expressed according to the following differential
formula: DGD ( v ) = .alpha. ds .pi..delta. v .DELTA. T 2 ( v ) SOP
.sigma. r 2 ( v ) ##EQU00178## where the constant .alpha. ds = 9 2
, ##EQU00179## and .nu. is the optical frequency corresponding to
the said midpoint wavelength.
6. A method according to claim 3, wherein a) the said polarized
light is launched using light source means connected to the optical
path at or adjacent a proximal end thereof, said light source means
comprising broadband light having a spectral width encompassing the
said second small optical-frequency difference; b) the said
polarization-controller-and-analyzer means comprises spectral
filter means having a filter width sufficiently less than the said
second small optical-frequency difference as to allow each
wavelength in said wavelength pair to be spectrally resolved,
thereby rendering coherent the light selected from the light source
means; and c) the said spectral filter means is operable to select
for detection each of the wavelengths corresponding to the said
groups comprising the said wavelength pair.
7. A method according to claim 2, wherein: a) corresponding
wavelength pairs in at least two different groups have midpoint
wavelengths that are different, and a maximum difference between
corresponding midpoint wavelengths defines a prescribed wavelength
range; b) said second small optical-frequency difference
(.delta..nu.) multiplied by rms DGD is approximately equal to or
less than 0.2; and c) the said at least one polarization-related
optical path characteristic is rms DGD of the optical path measured
over said prescribed wavelength range.
8. A method according to claim 2, wherein: in the step of providing
transmitted coherent optical power at each wavelength of light in
each of at least two groups of wavelengths, at least one
quasi-continuum of transmitted coherent optical powers as a
function of optical frequency are detected and stored for further
analysis in said step (i), said optical frequency spanning a
prescribed wavelength range, a) said measured power parameters are
computed from said transmitted coherent optical powers; b) the
degree of any variation of I-SOP and A-SOP with respect to the
optical frequency is low, such that both of I-SOP and A-SOP,
respectively, are substantially the same for the coherent optical
powers at each of the wavelengths composing each of said wavelength
pairs.
9. A method according to claim 8, wherein the step of detecting and
storing at least one quasi-continuum detects and stores first and
second quasi-continua, wherein either or both of the I-SOP and
A-SOP corresponding to at least some of the coherent optical powers
at wavelengths in said first quasi-continuum are substantially
different than the either or both of the I-SOP and A-SOP,
respectively, for the corresponding said coherent optical powers in
said second quasi-continuum, said polarization-related optical-path
characteristic comprising at least one of a) rms DGD value over a
prescribed wavelength range; and b) when the said at least some of
stored measured power parameters correspond to a particular
midpoint wavelength, DGD at said particular midpoint
wavelength.
10. A method according to claim 8, wherein a) the polarized light
launched by said light source means comprises broadband light
encompassing the prescribed wavelength range; b) the said
polarization-controller-and-analyzer means includes spectral filter
means having a filter width sufficiently less than the said second
small optical-frequency difference as to allow each wavelength in
said wavelength pair to be spectrally resolved, such that the light
selected from the broadband light is coherent; and c) the said
spectral filter means is operable to sweep substantially
continuously to sequentially select for detection each of the
wavelengths corresponding to the said groups comprising the said
wavelength pairs, said sweep enabling said detection and storage of
a quasi-continuum of transmitted coherent optical powers as a
function of optical frequency.
11. A method according to claim 10, wherein d) said spectral filter
means comprises a polarization-diverse dual-channel scanning
monochromator; and e) said measured power parameters comprise pairs
of orthogonally-analyzed power parameters measured with said
polarization-diverse dual-channel scanning monochromator.
12. A method according to claim 1, wherein the said light
polarization-controller-and-analyzer means is connected to the
optical path at or adjacent the proximal end of the optical path
and there is provided a localized reflection at or adjacent the
distal end of the optical path.
13. A method according to claim 12, wherein: a) corresponding
wavelength pairs in at least two different groups have midpoint
wavelengths that are different, and a maximum difference between
corresponding midpoint wavelengths defines a prescribed wavelength
range, b) said second small optical-frequency difference
(.delta..nu.) multiplied by rms DGD is approximately equal to or
less than 0.15 and c) the said at least one polarization-related
optical path characteristic is the rms DGD over a prescribed
wavelength range.
14. A method according to claim 13, wherein the said measured power
parameter is normalized transmitted coherent power T(.nu.), and the
limit of said predetermined function as said second small
optical-frequency difference .delta..nu. tends to zero may be
expressed according to the following differential formula: rmsDGD (
v ) = .alpha. rt .alpha. ds .pi..delta. v .DELTA. T 2 ( v ) SOP ; v
##EQU00180## where the roundtrip factor .alpha. rt = 3 8
##EQU00181## and the constant .alpha..sub.ds= {square root over
(9/2)} if changes in I-SOP and A-SOP are not correlated, and
.alpha..sub.ds= {square root over (15/4)} if said changes are
correlated.
15. A method according to claim 13, wherein the said measured power
parameter is normalized transmitted coherent optical power T(.nu.),
and the mean square value computing step (ii) compensates for the
possible presence of unpolarized noise in the detected power
parameters, by the steps of: a) computing relative variance
(.sigma..sub.r.sup.2) of the normalized transmitted optical powers
at wavelengths corresponding to respective ones of a wavelength
pair centered about said midpoint wavelength; and b) computing the
ratio of the mean-square difference over said relative variance,
said rms DGD computed as a predetermined function of said ratio,
and the limit of said predetermined function as said second small
optical-frequency difference .delta..nu. tends to zero may be
expressed according to the following differential formula: rmsDGD (
v ) = .alpha. rt .alpha. ds .pi..delta. v .DELTA. T 2 ( v ) SOP ; v
.sigma. r 2 ##EQU00182## where the roundtrip factor .alpha. rt = 3
8 , ##EQU00183## the relative variance of the normalized powers is
defined as, .sigma. r 2 = ( 1 .sigma. 10 ) 2 [ T 2 ( v ) SOP ; v -
T ( v ) SOP ; v 2 ] ##EQU00184## where the constant
.sigma..sub.10.sup.2= 4/45, the roundtrip factor .alpha. rt = 3 8 ,
##EQU00185## and the constant .alpha..sub.ds= {square root over
(9/2)} if changes in I-SOP and A-SOP are not correlated, and
.alpha..sub.ds= {square root over (15/4)} if said changes are
correlated.
16. A method according to claim 1, wherein: a) the said
polarization-controller-and-analyzer means is connected to the
optical path at or adjacent the proximal end and used to analyze
said light leaving the optical path at the proximal end; b) each
group comprises at least one wavelength pair of series of light
pulses, each pair of series having both a common I-SOP of the
launched light and a common A-SOP used to analyze the light leaving
the optical path; c) the light pulses in each of the two series
composing the pair have substantially the same wavelengths; d)
corresponding wavelength pairs in at least two different groups
have midpoint wavelengths that are different, and a maximum
difference between corresponding midpoint wavelengths defines a
prescribed wavelength range; e) said second small optical-frequency
difference (.delta..nu.) multiplied by rms DGD is approximately
equal to or less than 0.15; f) the analyzed light comprises
resulting backreflected light caused by either or both of Rayleigh
scattering and discrete reflections along the optical path; g) the
said measured power parameter is backreflected power of the
analyzed backreflected light as a function of distance along the
optical path, and the said polarization-related characteristic of
the optical path is cumulative PMD value over the prescribed
wavelength range corresponding to a distance z along the optical
path, this said cumulative PMD value being estimated from
cumulative rms round-trip DGD for the same said prescribed
wavelength range; wherein said measured power parameter is
determined by: I) for each of at least some of the light pulses in
each series of light pulses in each said group, analyzing and
subsequently detecting the resulting backreflected light to provide
a corresponding impulse-response, said state of polarization
(A-SOP) used to analyze the backreflected light being the same for
each of the said series in said group, and converting each of the
impulse-responses into a corresponding electrical impulse-response
signal; II) for each said series of light pulses in each said
group, sampling and averaging the electrical impulse-response
signals of said at least some of the light pulses to provide an
OTDR trace as a function of time delay; and III) converting said
OTDR trace as a function of time delay to an OTDR trace
representing backreflected power as a function of distance.
17. A method according to claim 16, wherein detected coherent light
is substantially fully polarized, the said measured power parameter
is the computed normalized power T(.nu.,z) as a function of
distance z along the optical path (18), and the limit of said
predetermined function as the small second optical-frequency
difference .delta..upsilon. tends to zero may be expressed
according to the differential formula: PMD ( z ) = .alpha. rt
.alpha. ds .pi..delta. v .DELTA. T 2 ( v , z ) SOP ; v ##EQU00186##
where the roundtrip factor .alpha. rt = 3 8 , ##EQU00187## and
where the constant .alpha..sub.ds= {square root over (9/2)} if
changes in I-SOP and A-SOP are not correlated, and .alpha..sub.ds=
{square root over (15/4)} if said changes are correlated.
18. A method according to claim 16, wherein the said measured power
parameter is the computed relative power P.sub.R(.nu.,z) and the
mean square value computing step (ii) comprises the steps of: a)
computing relative variance (.sigma..sub.R.sup.2(z)) of said set of
at least two measured power parameter differences; and b) computing
the ratio of the mean-square difference of said set of at least two
measured power parameter differences over said relative variance,
said rms DGD being computed as said predetermined function of said
ratio, and the limit of said predetermined function as the small
second optical-frequency difference .delta..upsilon. tends to zero
may be expressed according to the differential formula: PMD ( z ) =
.alpha. rt .alpha. ds .pi..delta. v .DELTA. T 2 ( v , z ) SOP ; v
.sigma. R 2 ( z ) ##EQU00188## where the roundtrip factor .alpha.
rt = 3 8 , ##EQU00189## the relative variance of the normalized
powers is defined as, .sigma. r 2 ( z ) = ( 1 .sigma. 10 ) 2 [ P R
( z , v ) P R '' ( z , v ) SOP , v - T R ( z , v ) SOP , v 2 ]
##EQU00190## where the constant .sigma..sub.10.sup.2= 4/45, and the
constant .alpha..sub.ds= {square root over (9/2)} if changes in
changes in I-SOP and A-SOP are not correlated, and .alpha..sub.ds=
{square root over (15/4)} if said changes are correlated.
19. A method according to claim 1, wherein each said group of
wavelengths comprises at least one repeated said wavelength pair,
corresponding to an initial first wavelength pair, wherein the
I-SOP and A-SOP for each of these repeated wavelength pairs are
substantially the same within each said group, the computation of
the at least one said polarization-related optical path
characteristic including the measured power parameters at
wavelengths corresponding to these repeated wavelength pairs.
20. A method according to claim 1, wherein the measured power
parameter of step (i) is a normalized power T proportional to the
transmitted coherent optical power, determined by one of the
following steps: a) a power corresponding to one polarization
component composing the transmitted coherent optical power is
measured using one detector, and then the normalized power (T) is
obtained by dividing said measured power corresponding to one
polarization component by the average of at least some of said
measured powers corresponding to one polarization component at the
same corresponding wavelength in the different groups; b) two
powers corresponding to respective orthogonal polarization
components composing the transmitted coherent optical power are
measured simultaneously and each of the normalized powers (T) is
obtained by either (I) dividing at least one of the measured said
two powers by the sum of the measured said two powers; or (II)
dividing a weighted difference of the measured said two powers by
the sum of the measured said two powers; c) a first optical power
corresponding to one polarization component of the transmitted
coherent optical power and a second optical power directly
proportional to the output of light from the optical path are
measured, using respective first and second detectors, and the
normalized power (T) is obtained by dividing said first optical
power by said second optical power to obtain the relative power of
said first power at said wavelength, and then dividing said
relative power by the average of at least some of the relative
powers at the same wavelength in the different groups; d) using one
detector and one optical switch, two powers corresponding to
respective orthogonal polarization components composing the
transmitted coherent optical power are detected at different times
by the same detector where the optical switch is used to route said
two powers to the same detector, and then the normalized power T
for each wavelength of said powers is obtained by either (I)
dividing at least one of said two powers by the sum of said two
powers; or (II) dividing a weighted difference of said two powers
by the sum of said two powers; e) using one detector and one
optical switch, a first optical power corresponding to one
polarization component of the transmitted coherent optical power
and a second optical power directly proportional to the output of
light from the optical path are measured at different times by the
same detector, the optical switch being operable to route
successively the first optical power and the second optical power
to the same detector, and the normalized power (T) is obtained by
first dividing said first power by said second power to obtain a
ratio representing the relative power of said first power, and
dividing said relative power by the average of at least some of the
relative powers at the same wavelength in the different groups.
21. A method according to claim 1, wherein the measured power
parameter of step (i) is a relative power P.sub.R proportional to
the detected transmitted coherent optical power, determined by one
of the following methods: a) a power corresponding to one
polarization component composing the transmitted coherent optical
power is measured using one detector, and then the relative power
(P.sub.R) is obtained for each wavelength by dividing said power
corresponding to one polarization component by the average of at
least some of respective said powers in the different groups; b)
two powers corresponding to respective orthogonal polarization
components composing the transmitted coherent optical power are
detected simultaneously, and the relative power (P.sub.R) is
obtained by either (I) dividing at least one of said two powers by
the sum of said two powers; or (II) dividing a weighted difference
of said two powers by the sum of said two powers; c) a first
optical power corresponding to one polarization component composing
the transmitted coherent optical power and a second optical power
directly proportional to the output light from the optical path are
measured using respective first and second detectors and the
relative power (P.sub.R) corresponding to each wavelength of
coherent light is obtained by dividing said first optical power by
said second optical power; d) using one detector and one optical
switch, two powers corresponding to respective orthogonal
polarization components of the light are measured at different
times by the same detector, the optical switch being operable to
route successively said two powers to said same detector, and the
relative power (P.sub.R) for said powers is obtained by either (I)
dividing at least one of said two powers corresponding to the two
detected different polarization components for that coherent light
by the sum of said two powers; or (II) dividing a weighted
difference of said two powers by the sum of said two powers; e)
using one detector and one optical switch, a first optical power
corresponding to one polarization component composing the
transmitted coherent optical power and a second optical power
directly proportional to the output light from the optical path are
measured at different times by said one detector, the optical
switch being operable to route successively said first and second
optical powers to said one detector, and the relative power
(P.sub.R) is obtained by dividing said first power by said second
power.
22. A method according to claim 1, wherein: (a) said
polarization-controller-and-analyzer means comprises at least two
polarization discriminators for analyzing light leaving the optical
path, said at least two polarization discriminators having mutually
linearly-independent state-of-polarization conditions (A-SOPs); and
(b) respective transmitted coherent optical powers from said
polarization discriminators are detected substantially
simultaneously by corresponding detectors in the said detecting
means.
23. A method according to claim 22, wherein said
polarization-controller-and-analyzer means comprises a polarimetric
head, said polarimetric head comprising at least three said
polarization discriminators having mutually linearly-independent
state-of-polarization conditions (A-SOPs).
24. A method according to claim 1, wherein said
polarization-controller-and-analyzer means combines said light
leaving the optical path with a polarized coherent local oscillator
beam having a respective local-oscillator state of polarization
(SOP.sub.LO), thereby producing a corresponding heterodyne signal
at the detecting means, which is indicative of the transmitted
coherent optical power of said analyzed light according to a state
of polarization (A-SOP) corresponding to said SOP.sub.LO.
25. A method according to claim 1, wherein said light propagating
in said optical path comprises light from at least one
data-carrying Signal-Under-Test (SUT) connected to the optical path
at or adjacent a proximal end thereof, and launching light
comprising polarized light into the optical path, and wherein the
said polarization-controller-and-analyzer means connected to the
optical path at or adjacent a distal end thereof.
26. A method according to claim 25, wherein said
polarization-related characteristic comprises a partial DGD
imparted upon said at least one SUT.
27. A method according to claim 25, wherein said at least one
data-carrying SUT comprises at least two data-carrying SUTs; at
least one partial DGD value is measured for each of said
data-carrying SUTs; and said polarization-related characteristic
comprises polarization mode dispersion (PMD) of said optical path
and is calculated from the measured partial DGD values.
28. A method according to claim 26, wherein the said measured power
parameter is a normalized power T(.nu.), and the limit of said
predetermined function as said second small optical-frequency
difference (.delta..nu.) tends to zero may be expressed according
to the following differential formula: DGD p ( v ) = .alpha. ds
.pi..delta. v .DELTA. T 2 ( v ) SOP ##EQU00191## where the constant
.alpha..sub.ds= {square root over (3)}, .nu. is the optical
frequency corresponding to the said midpoint wavelength, and
.DELTA.T(.nu.) is the difference in the normalized power obtained
for a particular analyzer state-of-polarization (A-SOP).
29. A method according to claim 26, wherein the said measured power
parameter is a normalized power T(.nu.), and the mean-square value
computing step (ii) further comprises computation of relative
variance (.sigma..sub.r.sup.2(.nu.)) of normalized powers T(.nu.)
according to the expression: .sigma. r 2 ( v ) = ( 1 .sigma. 20 ) 2
[ T 2 ( v ) SOP - T ( v ) SOP 2 ] ##EQU00192## where a reference
variance .sigma..sub.20.sup.2= 1/12, .DELTA.T(.nu.) is the
difference in the normalized power obtained for a particular
analyzer state-of-polarization (A-SOP), and the limit of said
predetermined function as the second small optical-frequency
difference .delta..nu. tends to zero may be expressed according to
the following differential formula: DGD P ( v ) = .alpha. ds
.pi..delta. v .DELTA. T 2 ( v ) SOP .sigma. r 2 ( v ) ##EQU00193##
where the constant .alpha..sub.ds= {square root over (3)}, and .nu.
is the optical frequency corresponding to the said midpoint
wavelength.
30. A method according to claim 26, wherein said
polarization-controller-and-analyzer means comprises spectral
filter means having a filter width sufficiently less than the said
second small optical-frequency difference as to allow each
wavelength in said wavelength pair to be spectrally resolved.
31. A method according to claim 25, wherein said
polarization-controller-and-analyzer means comprises a polarimetric
head.
32. A method according to claim 25, wherein said distal end of said
optical path corresponds to a monitoring port tapped from an
optical fiber link and from which a portion of said signal under
test is extracted from the optical fiber link.
33. A method according to claim 1, wherein the distal end of the
optical path is terminated reflectively and the
polarization-controller-and-analyzer means comprises polarization
control means (14) connected to the proximal end of the optical
path and used both to control state of polarization (I-SOP) of the
launched light and state of polarization (A-SOP) used to analyze
the light leaving the proximal end of the optical path.
34. A method according to claim 16, wherein the said measured power
parameter is normalized transmitted coherent optical power
T(.nu.,z) as a function of distance z along the optical path (18),
and the mean-square value computing step (ii) compensates for the
possible contribution of unpolarized light to the detected power
parameters, by the steps of: a) computing relative variance
(.sigma..sub.r.sup.2(z)) of the normalized transmitted optical
powers corresponding to respective ones of a wavelength pair
centered about said midpoint wavelength as a function of distance z
along the optical path (18); and b) computing the ratio of the
mean-square difference over said relative variance, said rms DGD
computed as a function of said ratio as said predetermined function
being determined for small optical-frequency differences
.delta..nu. as a function of distance z along the optical path
(18), according to the following differential formula: PMD ( z ) =
.alpha. rt .alpha. ds .pi..delta. v .DELTA. T 2 ( v , z ) SOP ; v
.sigma. r 2 ( z ) ##EQU00194## where the roundtrip factor .alpha.
rt = 3 8 , ##EQU00195## the relative variance of the normalized
powers is defined as, .sigma. r 2 ( z ) = ( 1 .sigma. 10 ) 2 [ T (
z , v ) T '' ( z , v ) SOP , v - T ( z , v ) SOP , v 2 ]
##EQU00196## where the constant .sigma..sub.10.sup.2= 4/45, and the
constant .alpha..sub.ds= {square root over (9/2)} if changes in
I-SOP and A-SOP are not correlated, and .alpha..sub.ds= {square
root over (15/4)} if said changes are correlated.
35. A method according to claim 5, wherein said mean-square value
is computed in accordance with one of:
.DELTA.T.sup.2(.nu.).sub.SOP=.DELTA.T(.nu.).DELTA.T(.nu.).sub.SOP,
where .DELTA.T(.nu.) is the difference in the normalized
transmitted coherent optical powers measured for a particular I-SOP
and A-SOP couple;
.DELTA.T.sup.2(.nu.).sub.SOP=.DELTA.T(.nu.).DELTA.T''(.nu.).sub.SOP,
where .DELTA.T''(.nu.) is a normalized power difference calculated
from repeated measurements of transmitted coherent optical powers
measured under the same I-SOP and A-SOP conditions as those of
.DELTA.T(.nu.); and
.DELTA.T.sup.2(.nu.).sub.SOP=.DELTA.T(.nu.).DELTA.T''(.nu.).sub.SOP,
where .DELTA.T''(.nu.) is a normalized power difference calculated
from transmitted coherent optical powers for which A-SOP for
.DELTA.T(.nu.) is orthogonal to A-SOP for .DELTA.T''(.nu.).
36. A method according to claim 15, wherein said mean-square value
is computed in accordance with one of:
.DELTA.T.sup.2(.nu.).sub.SOP=.DELTA.T(.nu.).DELTA.T(.nu.).sub.SOP,
where .DELTA.T(.nu.) is the difference in the normalized
transmitted coherent optical power obtained for a particular I-SOP
and A-SOP couple;
.DELTA.T.sup.2(.nu.).sub.SOP=.DELTA.T(.nu.).DELTA.T''(.nu.).sub.SOP
where .DELTA.T(.nu.) is the difference in the normalized
transmitted coherent optical power obtained for a particular I-SOP
and A-SOP couple, and .DELTA.T''(.nu.) is a normalized transmitted
coherent optical power difference calculated from repeated
measurements of transmitted coherent optical powers measured under
the same I-SOP and A-SOP conditions as those of .DELTA.T(.nu.); and
.DELTA.T.sup.2(.nu.).sub.SOP=.DELTA.T(.nu.).DELTA.T''(.nu.).sub.SOP,
where .DELTA.T(.nu.) is the difference in the normalized
transmitted coherent optical power obtained for a particular I-SOP
and A-SOP couple, where .DELTA.T''(.nu.) is a normalized
transmitted coherent optical power difference calculated from
transmitted coherent optical powers for which A-SOP for
.DELTA.T(.nu.) is orthogonal to A-SOP for .DELTA.T''(.nu.).
37. A method according to claim 18, wherein said mean-square value
is computed in accordance with one of:
.DELTA.P.sub.R.sup.2(.nu.).sub.SOP=.DELTA.P.sub.R(.nu.).DELTA.P.sub.R(.nu-
.).sub.SOP, where .DELTA.P.sub.R(.nu.) is the difference in the
relative powers obtained for a particular I-SOP and A-SOP couple;
.DELTA.P.sub.R.sup.2(.nu.)=.DELTA.P.sub.R(.nu.).DELTA.P.sub.R''(.nu.).sub-
.SOP, where .DELTA.P.sub.R(.nu.) is the difference in the relative
power obtained for a particular I-SOP and A-SOP couple, and where
.DELTA.P.sub.R''(.nu.) is a relative power difference calculated
from repeated measurements of transmitted coherent optical powers
under the same I-SOP and A-SOP conditions as those of
.DELTA.P(.nu.); and
.DELTA.P.sub.R.sup.2(.nu.).sub.SOP=.DELTA.P.sub.R(.nu.).DELTA.P.sub.R''(.-
nu.).sub.SOP, where .DELTA.P.sub.R(.nu.) is the difference in the
relative power obtained for a particular I-SOP and A-SOP couple,
where .DELTA.P.sub.R''(.nu.) is a power difference calculated from
transmitted coherent optical powers for which A-SOP for
.DELTA.P.sub.R(.nu.) is orthogonal to A-SOP for
.DELTA.P.sub.R''(.nu.).
38. A method according to claim 29, wherein said mean-square value
is computed in accordance with one of:
.DELTA.T.sup.2(.nu.).sub.SOP=.DELTA.T(.nu.).DELTA.T(.nu.).sub.SOP;
.DELTA.T.sup.2(.nu.).sub.SOP=.DELTA.T(.nu.).DELTA.T''(.nu.).sub.SOP,
where .DELTA.T''(.nu.) is a normalized power difference calculated
from repeated measurements of transmitted coherent optical powers
under the same I-SOP and A-SOP conditions as those of
.DELTA.T(.nu.); and
.DELTA.T.sup.2(.nu.).sub.SOP=.DELTA.T(.nu.).DELTA.T''(.nu.).sub.SOP,
where .DELTA.T''(.nu.) is a normalized power difference calculated
from transmitted coherent optical powers for which A-SOP for
.DELTA.T(.nu.) is orthogonal to A-SOP for .DELTA.T''(.nu.).
39. Measurement instrumentation for measuring a
polarization-related characteristic of an optical path (18) wherein
light comprising polarized light is propagated, the measurement
instrumentation comprising: polarization-controller-and-analyzer
means (14,20A; 14A,14B,20; 14A,14B,20A; 14,20; 14,20C; 14A,45) for
connection to the optical path at or adjacent either the proximal
end thereof or a distal end thereof and operable to control at
least one of a state of polarization (I-SOP) of light launched in
the optical path and a state of polarization (A-SOP) used to
analyze light leaving the optical path, detecting means (22;
22A,22B; 22D) for detecting the analyzed light corresponding to at
least one analyzer SOP (A-SOP) and providing corresponding
detection signals, and processing means (40) for processing the
detection signals to derive said polarization-related
characteristic, wherein said light leaving the optical path is
analyzed to provide transmitted coherent optical power at each
wavelength of light in each of at least two groups of wavelengths,
and wherein the lowermost (.lamda..sub.L) and uppermost
(.lamda..sub.U) said wavelengths in each said group of wavelengths
are separated by a first small optical frequency difference; and
wherein each of the said at least two groups comprises a wavelength
pair, said pair in each group defining a midpoint wavelength
therebetween, and being mutually spaced by a second small
optical-frequency difference, the second small optical-frequency
difference being equal to or less than the first small
optical-frequency difference, and defining a midpoint wavelength
therebetween, said second small optical-frequency difference
(.delta..nu.) being the same for corresponding wavelength pairs in
different groups, and wherein the I-SOP and A-SOP are substantially
constant for each said wavelength in each said group, and wherein
at least one of the midpoint wavelength, I-SOP and A-SOP is
different between the respective said groups, the measurement
instrumentation being operable to: i) compute at least one
difference between a pair of measured power parameters each
corresponding to either or an average of the measured optical power
parameters at wavelengths corresponding to respective ones of a
wavelength pair centered about said midpoint wavelength, said
wavelength pair comprised within each of the said at least two
groups, each said measured power parameter being proportional to
transmitted coherent optical power of the said analyzed and
subsequently detected light, thereby defining for said at least two
groups a set of at least two measured power parameter differences;
ii) compute a mean-square value of said set of at least two
measured power parameter differences; and iii) calculate the
polarization-related optical path characteristic as a predetermined
function of said mean-square value, said predetermined function
being dependent upon the said second small optical-frequency
difference between the wavelengths corresponding to the said each
of at least said two pairs of wavelengths.
40. A method of measuring a polarization-related characteristic of
an optical path wherein light comprising polarized light is
propagated, the method comprising: polarization analyzing light
having propagated in the optical path according to at least two
different analyzer states of polarization (A-SOP); for each said at
least two different analyzer states of polarization: detecting
transmitted coherent optical power of the analyzed light at each
wavelength of light in a group of wavelengths, wherein said group
comprises at least one wavelength pair, said pair defining a
midpoint wavelength therebetween and being mutually spaced by a
small optical-frequency difference, and computing a difference
between a pair of measured power parameters each corresponding to a
respective one of the wavelengths in said wavelength pair, each
said measured power parameter being proportional to transmitted
coherent optical power of the said analyzed and subsequently
detected light, thereby defining a set of corresponding at least
two measured power parameter differences; computing a mean-square
value of said set of measured power parameter differences; and
calculating the polarization-related optical path characteristic as
a predetermined function of said mean-square value.
Description
CROSS-REFERENCE TO RELATED DOCUMENTS
[0001] This application is a Continuation-in-Part of U.S. patent
application Ser. No. 12/568,554 filed Sep. 28, 2009, published as
United States Patent Publication number US2010/0073667 A1 claiming
priority from U.S. Provisional patent application No. 60/907,313
filed 28 Mar. 2007 and also a Continuation-in-Part of U.S. patent
application Ser. No. 11/727,759 filed 28 Mar. 2007, now abandoned,
and a Continuation-in-Part of U.S. patent application Ser. No.
11/992,797 having an effective filing date Mar. 28, 2008. The
entire contents of each of these patent documents are incorporated
herein by reference and the reader is directed to them for further
reference.
TECHNICAL FIELD
[0002] This invention relates to a method and system for measuring
polarization-related characteristics of optical paths, which may
lead to impairments of a data-carrying signal propagating
therealong. The optical path normally comprises mostly optical
waveguide, such as an optical fiber link in a telecommunications
network
[0003] Preferred embodiments of the inventive concept are
especially applicable to the measurement of differential group
delay (DGD) of an optical path at a particular wavelength, or
root-mean-square or mean DGD over a specified wavelength range.
When the specified wavelength range is sufficiently wide, the
root-mean-square or mean DGD measurement closely approximates the
polarization mode dispersion (PMD) behavior of the optical
path.
[0004] Other preferred embodiments are especially applicable to the
monitoring of temporal pulse spreading of data-carrying optical
signals induced by DGD-related polarization characteristics of the
optical path along which the signals are propagating.
DEFINITIONS
[0005] Within this specification, certain terms are accorded the
following meanings:
[0006] "Optical frequency" (.upsilon.) and "wavelength" (.lamda.)
are used interchangeably, the two being related by
.lamda.=c/.upsilon., where c represents the speed of light in
vacuum. Note that wavelength, as used hereinbelow, corresponds to
that which would be measured in a vacuum.
[0007] "Fiber-Under-Test" (FUT) designates a guided optical
propagation medium for which one wishes to measure at least one
polarization-related characteristic. The FUT comprises primarily
optical fiber for which the guiding properties are "single mode" at
the optical frequencies of interest, but it may also include
intervening optical elements such as optical amplifiers, optical
switches and routers, etc. FUT is a special case of "optical link",
since the latter does not necessarily imply that measurements of
polarization-related characteristics will be taken thereof. Note
that FUT does not necessarily correspond to a link connecting
network nodes, but may be a portion of such a link for which access
may be gained via "tap" or monitor ports for "in-service"
measurements, or by temporarily breaking into the fiber path for
"dark fiber" measurements.
[0008] "Lightpath" refers to a particular restricted spectral
region of an optical link within which a particular data-carrying
signal normally propagates (often termed optical "channel"),
whether or not said spectral width is delimited by intervening
optical filtering.
[0009] "Dark channel" refers to an optical channel within which no
optical signals are propagating.
[0010] "DWDM" refers to Dense Wavelength-Division Multiplexing,
whereby multiple SUTs, each corresponding to a distinct central
wavelength, may be propagated along the same optical fiber link,
such the central wavelengths of respective adjacent SUTs may be
mutually spaced by optical-frequency differences typically of 100
GHz or less.
[0011] "Signal-Under-Test" (SUT) designates a normally
data-carrying optical signal traversing an optical link, such as
may be employed in an active telecom optical network. In this
specification, "live" signal and "data-carrying" signal will be
used interchangeably with SUT.
[0012] "State of Polarization" (SOP) defines the polarization
properties of a light beam (i.e. the relative amplitude and phases
of the electric field) within a particular short time interval and
at a particular location.
[0013] "Differential Group Delay" (DGD) is a parameter quantifying,
for a given optical frequency .upsilon. and within a particular
short time interval, the maximum difference in optical propagation
time along a guided propagation medium (primarily a single-mode
optical fiber), for all possible SOPs launched into the propagation
medium.
[0014] "Input Principal States of Polarization" (Input-PSPs) are,
for a given optical frequency and at a particular time, the two
SOPs of the light launched into the guided propagation medium
corresponding, respectively, to the slowest and fastest propagation
times in the medium.
[0015] "Output Principal States of Polarization" (Output-PSPs) are
the two SOPs of light exiting the propagation medium corresponding
to, respectively, the two Input-PSPs.
[0016] "Analyzer" refers to an element that permits detection of
only that fraction of the incident light corresponding to an SOP
aligned with its low-loss ("maximum-transmission") axis. This
element may be highly polarization-dependent (e.g. a linear
polarizer, or polarization beam splitter PBS), having
mutually-orthogonal low-loss and high-loss axes. Alternatively, it
may comprise other means, such as optical combining means to
combine polarized highly-coherent local oscillator light (e.g. from
a tunable laser) with the light under test to interfere at
subsequent heterodyne-detection means, the degree of detected
heterodyne signal depending upon the relative alignment of the
local oscillator SOP with the SOP of the light under test.
[0017] "Analyzer SOP" ("A-SOP") refers to the SOP of light
corresponding to maximum subsequent detection as it enters a
combination of a polarization-controller and an analyzer. Although
A-SOP varies as the polarization controller is varied, in some
variants it may be fixed (e.g. to act as a quarter-wave plate), as
is the case for a polarimeter having three analyzers, the (fixed)
A-SOPs of the analyzers being normally mutually orthogonal.
[0018] "Polarimetric head" refers to the optical portion of a
polarimeter, comprising at least three analyzers having mutually
linearly-independent A-SOPs and associated optical elements (e.g.
optical fiber, beam splitters, attenuators, lenses, etc.), and
means to propagate the resulting analyzed light to optical
detectors external thereto.
[0019] "Input SOP" ("I-SOP") refers to the state of polarization of
light as it is launched into the FUT.
[0020] "Polarization Mode Dispersion" (PMD) is the
polarization-related physical phenomenon giving rise to
polarization-dependent temporal spreading of an optical pulse.
Although in theory it is defined as an average of the
DGD(.upsilon.) values over all possible optical frequencies, in
practice it is normally estimated from an average of DGD(.upsilon.)
over a significantly wide prescribed spectral range encompassing
wavelengths of interest (e.g., the telecom C or C+L bands of
minimal-loss transmission). In telecom optical fiber, moderate to
high PMD may cause DGD(.upsilon.) to vary significantly over the
prescribed spectral range. PMD is usually defined as the
root-mean-square (rms) average of DGD(.upsilon.) over the
prescribed spectral range ("rms PMD", or simply "PMD"), but,
alternatively, may be defined as the arithmetic mean of
DGD(.upsilon.) over this same spectral range ("mean PMD").
[0021] "Overall PMD" is the PMD measured over the full length L of
an FUT (whether or not that fiber spans the full distance between
two nodes in the network).
[0022] "Cumulative PMD" is the value of the PMD from the input end
of the FUT up to a distance z along the FUT, where z.ltoreq.L.
[0023] "Partial DGD" (DGD.sub.P) is a parameter quantifying the
degree to which the DGD of the guided propagation medium (e.g.
optical fiber), for a given optical frequency .upsilon. and within
a particular short time interval, will induce temporal pulse
spreading of an SUT launched therein with a particular input SOP.
This parameter is thus a polarization-dependent characteristic of
the optical lightpath, manifest by its effect upon the SUT. For a
given optical frequency and at a particular time, the DGD will have
a value less than or equal to the corresponding DGD value--hence
the terminology "partial DGD".
[0024] "Degree of polarization" (DOP) of a light beam is defined as
the relative difference between the maximum and minimum power of a
light beam that traverses an adjustable polarization controller and
analyzer combination disposed in the physical light path. In other
words, if, upon suitable adjustment of the polarization controller,
the light power in the beam may be extinguished by 90% from its
maximum transmission value by the analyzer, the DOP=90%.
[0025] "In-service link" refers to an optical link, comprising
primarily optical fiber, within which at least one data-carrying
signal (i.e. which is not light from a test source) "test" signal)
normally propagates.
[0026] "OTDR" is an abbreviation for Optical Time Domain
Reflectometer, a test instrument that launches optical pulses into
an optical fiber and detects the resulting backreflected light to
provide distance-resolved information characterizing a FUT.
[0027] "Monitoring" and "measurement" are used interchangeably,
unless otherwise clearly specified. Although "monitoring" generally
implies a collection of measurements taken over a long period of
time from particular fixed locations in a network, and
"measurement" generally refers to sporadic or ad hoc acquisitions,
often with portable apparatus in the context of maintenance or
troubleshooting, the underlying method and apparatus as described
herein are identical.
MOTIVATION AND BACKGROUND ART
[0028] Polarization mode dispersion (PMD) is a polarization-related
physical phenomenon that often limits the bandwidth-distance
product of a fiber-optic-based telecom transmission link. In other
words, PMD may be the primary impairment limiting the reach (i.e.
maximum propagation distance) of high bit-/symbol-rate signals, and
PMD may limit the bandwidth that may be carried in a single optical
channel along a "long-haul" (i.e. long-distance) optical link.
[0029] Thus, it is desirable to be able to characterize one or more
PMD-related parameters of an optical link, or of lightpaths thereof
or of which they form a part.
[0030] Embodiments of aspects of the present invention enable
characterization of different PMD-related parameters, and are
particularly well suited to particular monitoring or measurement
needs associated with optical networks. To facilitate detailed
discussion and provide context for these embodiments, exemplary
applications now will be presented.
1.1 Manifestation of PMD as a Function of Wavelength
DGD and "Partial DGD"
[0031] New optical networks will increasingly be based on a "mesh"
topology or variants thereof, comprising multiple nodes connected
by a corresponding multiplicity of fiber links. Such mesh networks
may also employ Reconfigurable Optical Add-Drop Multiplexers
(ROADMs) at the nodes to individually route any particular signal
wavelength along a lightpath made up of different combinations of
fiber links than the paths traversed by some of the other signal
wavelengths. Signals at different wavelengths may carry payload at
different bandwidths (e.g. 40 Gb/s instead of 10 Gb/s). The
particular choice of route in the mesh may be determined by
high-level control plane software, based on criteria such as:
[0032] (i) avoiding blocking or interference from other lightpaths
having the same wavelength along certain node-to-node links in the
network; [0033] (ii) restoring a network after a cable cut along
one or more such links; and [0034] (iii) capacity of a particular
lightpath to propagate the particular signal bandwidth without
introducing an unacceptable level of impairments, e.g. arising from
PMD.
[0035] To this end, it may be advantageous to verify, using light
from a test source, the differential group delay (DGD) at the
wavelength of the particular lightpath shortly beforehand in order
to ensure that the lightpath is suitable, i.e. there would not be
excessive PMD-related impairment of the re-routed high-bandwidth
data-carrying signal. Furthermore, the test source itself should
not unduly perturb the network, e.g. affect the automatic gain
control of the optical amplifiers, etc., or otherwise affect
network operations.
[0036] The extent to which the PMD phenomenon induces temporal
spreading of the symbols constituting a particular data-carrying
signal (i.e. digital time slots, or "unit intervals") at a given
time is termed "partial DGD" (DGD.sub.P). DGD.sub.P is dependent
upon both the wavelength and the SOP of the signal being launched
into the optical fiber, in contrast to DGD, whose value is
independent of the launched SOP. For a given optical frequency, the
"worst-case" partial DGD corresponds to the DGD at that same
optical frequency, which obtains when the magnitudes of the
projection of the SOP of the signal onto each of the two
(orthogonal) principal states of polarization (PSPs) at the input
to the fiber are equal. In general, however, the signal SOP at the
fiber input is not well controlled (and often may change
unpredictably over time), and consequently the level of signal DGD
at a particular wavelength is less than the corresponding DGD at
that same wavelength.
[0037] Measurement of partial DGD may prove advantageous in optical
network troubleshooting, where an operator may need to determine
whether sudden observed "bursts" in bit error rate (BER) may be
PMD-related, rather than having been caused by other phenomena such
as optical amplifier instabilities, self-phase modulation,
intermittent connections, etc. As described by Boroditsky et al (US
patent publication number 2005/0232640 A1), a correlation of the
observed BER bursts with a sudden increase in DGD.sub.P, as
monitored in real- or near-real time would indicate that PMD is
indeed the likely cause of the problem. Furthermore, by carrying
out such a DGD.sub.P measurement at points along the signal
lightpath through the network (e.g. not necessarily limited to a
particular optical link between two nodes of a mesh network), one
may be able to approximately isolate the section primarily
responsible for the PMD impairment.
1.2 PMD Determination of an In-Service Optical Link
[0038] If a telecom operator wishes to upgrade one or more channels
of an existing in-service DWDM link by increasing the signal
bandwidth (i.e. bitrate, including possibly a concomitant increase
of the symbol rate), he may need to first verify whether the PMD of
the existing optical link is sufficiently low to support
transmission at this higher bandwidth. If measurements of the link
PMD had been taken at some earlier date (e.g. during installation
of the fiber plant), the documentation of these measurements may
have been lost or misplaced, for instance following acquisition of
existing fiber plant purchased from a third party. Furthermore, PMD
values taken several years earlier may no longer be indicative of
current PMD behavior, due to fiber ageing, etc.
[0039] Measurement methods and apparatus suitable for field
characterization of fiber plant during initial installation, such
as widely-used fixed-analyzer (or "wavelength scanning") [1] and
interferometric [2,3] methods, generally require a polarized
broadband light source to launch test light, encompassing the
spectral region of interest, into one end of the FUT and suitable
receiver instrumentation at the opposite end. Obviously, the launch
of a continuous spectrum of broadband light from a test source
would likely disrupt network operations and, hence, would be
incompatible with the concurrent transmission of active
data-carrying signals in the same FUT.
[0040] It would thus be desirable to be able to characterize PMD of
an in-service optical link without disrupting the data-carrying
signals.
[0041] In-service PMD may be determined by two approaches known in
the art: [0042] (i) DGD measurements in "dark channels" using test
source(s): Polarized light from a test sources (e.g. broadband
light, light from a tunable laser source) is launched into one end
of the FUT, preferably at a multiplicity of wavelengths
corresponding to respective "dark-channel" lightpaths, the
wavelengths being distributed over a wide spectral region. At each
wavelength, the test light is preferably launched with a
multiplicity of substantially different SOPs. The resulting light
is detected at the opposite end of the FUT--hence, this approach is
classified as being "two-ended". In this way, the DGD(.upsilon.)
may be determined for each lightpath wavelength. As will be
described in detail hereinbelow, this approach advantageously
offers good accuracy; [0043] (ii) DGD.sub.P measurements using
"live" signal(s): In place of "test sources", at least one, and
preferably a multiplicity of widely-spaced data-carrying signals of
the in-service network are used, the launched SOPs of which
generally do not vary substantially with time. In this way, the
DGD.sub.P(.upsilon.) or DGD.sub.P(.upsilon.,t) may be measured for
each lightpath wavelength. As will be discussed hereinbelow,
advantages are that test equipment need be placed only at one
location (i.e. no test source is required) and that the measurement
is completely "non-intrusive", since light may be detected via
existing tap couplers along the link. (Although a dedicated test
source is not required in this approach, since the live
data-carrying signals serve as "test sources", it is convenient
also to classify this approach as being "two-ended", in opposition
to "single-ended" OTDR-based to be described hereinbelow.)
1.3 Single-Ended Measurement of Overall PMD of an Inactive Optical
Link
[0044] Prior art approaches for measurement of overall (i.e.
"end-to-end") PMD in an (unlit) optical link usually involve
launching polarized light from a test source into one end of the
FUT, detecting and analyzing the light exiting the FUT, and
deducing the PMD therefrom using suitable analysis. However, there
are significant additional operational costs involved with placing
a dedicated source at one end and the measurement equipment at the
other, in addition to the difficulties often associated with
providing regular communication between the equipment placed at the
opposing ends.
[0045] There is, firstly, therefore a need for a single-ended
measurement approach necessitating minimal intervention at the
opposite end of the FUT, and which furthermore would be capable of
measurement over the often 80 km or longer spans between optical
amplifiers or ROADMs, etc.
1.4 Measurement of Cumulative PMD Along an Inactive Optical
Link
[0046] As explained in commonly-owned U.S. Pat. No. 6,724,469
(Leblanc), in optical communication systems, an unacceptable
overall polarization mode dispersion (PMD) level for a particular
long optical fiber may be caused by one or more short sections of
the optical fiber link. Where, for example, a network service
provider wishes to increase the bit rate carried by an installed
optical fiber link, say up to 40 Gb/s, it is important to be able
to obtain a distributed measurement of PMD, i.e., obtain the PMD
information against distance along the fiber, and locate the
singularly bad fiber section(s) so that it/they can be
replaced--rather than replace the whole cable.
[0047] Accordingly, Leblanc discloses a method of measuring
distributed PMD which uses a polarization OTDR, to identify high or
low PMD fiber sections, but does not provide a truly quantitative
PMD value for the FUT. Consequently, because of its inherently
"qualitative" nature, Leblanc's technique is not entirely suitable
for development as a commercial single-ended overall PMD testing
instrument that may measure the total PMD value for the entire of
fiber link.
[0048] It is known to employ a so-called polarization-sensitive
optical time domain reflectometer (POTDR; also commonly referred to
as a "Polarization optical time domain reflectometer") to try to
locate such "bad" sections. Basically, a POTDR is an OTDR that is
sensitive to the state of polarization (SOP) of the backreflected
light. Whereas conventional OTDRs measure only the power of
backreflected light to determine variation of attenuation along the
length of an optical path, e.g., an installed optical fiber, POTDRs
utilize the fact that the backreflected light also exhibits
polarization dependency in order to monitor polarization dependent
characteristics of the transmission path. Thus, the simplest POTDR
comprises an OTDR having a polarizer between its output and the
fiber-under-test (FUT) and an analyzer in the return path, between
its photodetector and the FUT. (It should be appreciated that,
although a typical optical transmission path will comprise mostly
optical fiber, there will often be other components, such as
couplers, connectors, etc., in the path. For convenience of
description, however, such other components will be ignored, it
being understood, however, that the term "FUT" used herein will
embrace both an optical fiber and the overall transmission path to
be characterized, according to context.)
[0049] A detailed review of the relevant prior art is provided in
United States patent publication number US2010/0073667 A1)
supra.
[0050] In order that the cumulative PMD may be characterized along
fiber lengths commonly used in installed systems, typically
spanning the 60-80 km distances between optical amplifiers, ROADMs,
etc. in optical networks, the POTDR should have a dynamic range
sufficient to characterize at least half the end-to-end fiber
length. The other half may then be characterized by repeating the
measurement process from the other end of the link, and the data
from each end may be "stitched" together to provide a full
cumulative PMD profile along the link.
[0051] (In this specification, the term "cumulative PMD" is used to
distinguish from the aforementioned "overall" PMD that is
traditionally measured from end-to-end. Because PMD is not a
localized quantity, PMD(z) is an integral from 0 to z, bearing
resemblance to a cumulative probability rather than the probability
distribution. When distance z is equal to the overall length of the
FUT, of course, the cumulative PMD is equal to the overall
PMD.)
SUMMARY OF THE INVENTION
[0052] The present invention seeks to eliminate, or at least
mitigate, the disadvantages of the prior art discussed above, or at
least provide an alternative.
[0053] According to one aspect of the present invention there is
provided a method of measuring a polarization-related
characteristic of an optical path (18) wherein light comprising
polarized light is propagated, the method comprising the steps of
using:
[0054] polarization-controller-and-analyzer means
(14,20A;14A,14B,20;14A,14B,20A; 14,20; 14,20C; 14A,45) connected to
the optical path at or adjacent either the proximal end thereof or
a distal end thereof to control at least one of state of
polarization (I-SOP) of light launched in the optical path and
state of polarization (A-SOP) used to analyze light leaving the
optical path,
[0055] detecting means (22; 22A,22B; 22D) to detect the analyzed
light and provide corresponding detection signals, and
[0056] processing means (40) to process the detection signals to
derive said polarization-related characteristic,
[0057] wherein said light leaving the optical path is analyzed to
provide transmitted coherent optical power at each wavelength of
light in each of at least two groups of wavelengths,
[0058] and wherein the lowermost (.lamda..sub.L) and uppermost
(.lamda..sub.U) said wavelengths in each said group of wavelengths
are separated by a first small optical frequency difference;
[0059] and wherein each of the said at least two groups comprises a
wavelength pair, said pair in each group defining a midpoint
wavelength therebetween, and being mutually spaced by a second
small optical-frequency difference, the second small
optical-frequency difference being equal to or less than the first
optical-frequency difference, said second small optical-frequency
difference (.delta..nu.) being the same for corresponding
wavelength pairs in different groups, and wherein the I-SOP and
A-SOP are substantially constant for each coherent optical power at
each said wavelength in each said group, and wherein at least one
of the midpoint wavelength, I-SOP and A-SOP is different between
the respective said groups, the processing step including the steps
of: [0060] (i) computing at least one difference between a pair of
measured power parameters each corresponding to a respective one of
the wavelengths in said wavelength pair for each of the said at
least two groups, each said measured power parameter being
proportional to transmitted coherent optical power of the said
analyzed and subsequently detected light, thereby defining for said
at least two groups a set of at least two measured power parameter
differences; [0061] (ii) computing a mean-square value of said set
of at least two measured power parameter differences; and [0062]
(iii) calculating the polarization-related optical path
characteristic as a predetermined function of said mean-square
value, said predetermined function being dependent upon the said
second small optical-frequency difference between the wavelengths
corresponding to the said each of at least said two pairs of
wavelengths.
[0063] According to a second aspect of the invention, there is
provided measurement instrumentation for measuring a
polarization-related characteristic of an optical path (18) wherein
light comprising polarized light is propagated, the measurement
instrumentation comprising:
[0064] polarization-controller-and-analyzer means (14,20A;
14A,14B,20; 14A,14B,20A; 14,20; 14,20C; 14A,45) for connection to
the optical path at or adjacent either the proximal end thereof or
a distal end thereof and operable to control at least one of a
state of polarization (I-SOP) of light launched in the optical path
and a state of polarization (A-SOP) used to analyze light leaving
the optical path,
[0065] detecting means (22; 22A,22B; 22D) for detecting the
analyzed light corresponding to at least one analyzer SOP (A-SOP)
and providing corresponding detection signals, and
[0066] processing means (40) for processing the detection signals
to derive said polarization-related characteristic,
[0067] wherein said light leaving the optical path is analyzed to
provide transmitted coherent optical power at each wavelength of
light in each of at least two groups of wavelengths,
[0068] and wherein the lowermost (.lamda..sub.L) and uppermost
(.lamda..sub.U) said wavelengths in each said group of wavelengths
are separated by a first small optical frequency difference; [0069]
and wherein each of the said at least two groups comprises a
wavelength pair, said pair in each group defining a midpoint
wavelength therebetween, and being mutually spaced by a second
small optical-frequency difference, the second small
optical-frequency difference being equal to or less than the first
small optical-frequency difference, and defining a midpoint
wavelength therebetween, said second small optical-frequency
difference (.delta..nu.) being the same for corresponding
wavelength pairs in different groups, and wherein the I-SOP and
A-SOP are substantially constant for each said wavelength in each
said group, and wherein at least one of the midpoint wavelength,
I-SOP and A-SOP is different between the respective said groups,
the measurement instrumentation being operable to: i) compute at
least one difference between a pair of measured power parameters
each corresponding to either or an average of the measured optical
power parameters at wavelengths corresponding to respective ones of
a wavelength pair centered about said midpoint wavelength, said
wavelength pair comprised within each of the said at least two
groups, each said measured power parameter being proportional to
transmitted coherent optical power of the said analyzed and
subsequently detected light, thereby defining for said at least two
groups a set of at least two measured power parameter differences;
ii) compute a mean-square value of said set of at least two
measured power parameter differences; and iii) calculate the
polarization-related optical path characteristic as a predetermined
function of said mean-square value, said predetermined function
being dependent upon the said second small optical-frequency
difference between the wavelengths corresponding to the said each
of at least said two pairs of wavelengths.
[0070] According to a third aspect of the invention, there is
provided a method of measuring a polarization-related
characteristic of an optical path wherein light comprising
polarized light is propagated, the method comprising:
[0071] polarization analyzing light having propagated in the
optical path according to at least two different analyzer states of
polarization (A-SOP);
[0072] for each said at least two different analyzer states of
polarization: [0073] detecting transmitted coherent optical power
of the analyzed light at each wavelength of light in a group of
wavelengths, wherein said group comprises at least one wavelength
pair, said pair defining a midpoint wavelength therebetween and
being mutually spaced by a small optical-frequency difference, and
[0074] computing a difference between a pair of measured power
parameters each corresponding to a respective one of the
wavelengths in said wavelength pair, each said measured power
parameter being proportional to transmitted coherent optical power
of the said analyzed and subsequently detected light, thereby
defining a set of corresponding at least two measured power
parameter differences;
[0075] computing a mean-square value of said set of measured power
parameter differences; and
[0076] calculating the polarization-related optical path
characteristic as a predetermined function of said mean-square
value.
[0077] Preferred embodiments and implementations of the foregoing
aspects of the invention are set out in the dependent claims
appended hereto.
[0078] The foregoing and other objects, features, and advantages of
the present invention will become more apparent from the following
detailed description, in conjunction with the accompanying drawing,
of preferred implementations of embodiments of the invention which
are described by way of example only.
BRIEF DESCRIPTION OF THE DRAWINGS
[0079] Two-Ended "Test-Source-Based" PMD Measurement (FIGS. 1
through 1L)
[0080] FIG. 1 is a simplified generalized schematic illustration
measurement instrumentation having two portions connected to
opposite ends, respectively, of an optical path, specifically a
fiber-under-test (FUT), for performing two-ended measurements on
the optical path to determine DGD at one or more wavelengths and/or
mean DGD and/or rms DGD;
[0081] FIG. 1B is a simplified schematic diagram similar to FIG. 1
but of measurement instrumentation using a tunable laser light
source, one input-SOP controller (scrambler), one analyzer SOP
(A-SOP) controller (scrambler), a polarizer/analyzer and where only
the analyzed light is detected, by means of one detector, and where
normalization of the detected powers is carried out by means of an
averaging procedure over a plurality of acquisitions;
[0082] FIG. 1C is a simplified schematic diagram of measurement
instrumentation similar to that illustrated in FIG. 1B, for which
normalization of the detected analyzed powers is also carried out
by means of an averaging procedure over a plurality of
acquisitions, but where the analyzed light is split into two parts
and respectively detected by two detectors connected to the
coupler, in order to measure simultaneously two repeated powers,
thereby reducing uncorrelated noise contributions to the
measurement;
[0083] FIG. 1D is a simplified schematic diagram of measurement
instrumentation similar to that shown in FIG. 1 but of measurement
instrumentation using a tunable laser light source, one input-SOP
controller (scrambler), one analyzer SOP (A-SOP) controller
(scrambler), a coupler, a polarizer/analyzer and two detectors; one
detector for measuring analyzed light after the polarizer and the
other detector for measuring non-analyzed light, i.e. light that is
proportional to a total output light power from FUT, said measured
non-analyzed light being used to normalize the detected analyzed
powers;
[0084] FIG. 1E is a simplified schematic diagram of measurement
instrumentation similar to that shown in FIG. 1D but having a
single detector and an optical switch for connecting the detector
alternatively to measure analyzed light from the polarizer and
non-analyzed light from the coupler proportional to a total output
light power from the FUT, said measured non-analyzed light also
being used to normalize the detected analyzed powers;
[0085] FIG. 1F is a simplified schematic diagram of measurement
instrumentation using a tunable laser light source, one input-SOP
controller (scrambler), one analyzer SOP (A-SOP) controller
(scrambler), a polarization beam splitter (PBS), serving as a
polarization analyzer, and two detectors connected to the two
outputs thereof, each detector thereby detecting
orthogonally-analyzed optical powers, and these
orthogonally-analyzed powers being used to normalize the detected
analyzed powers;
[0086] FIG. 1G is a simplified schematic diagram of measurement
instrumentation similar to that shown in FIG. 1F but rather than
employing two detectors each in continuous optical continuity with
the respective outputs of the PBS, only one detector is used, and
the orthogonally-analyzed light exiting each of the two output of
the PBS is directed to the detector, successively, by means of an
optical switch. The orthogonally-analyzed powers also being used to
normalize the detected analyzed powers;
[0087] FIG. 1H is a simplified schematic diagram of measurement
instrumentation similar to that shown in FIG. 1 but which has a
polarimetric head for analyzing light from the FUT;
[0088] FIG. 1I is a simplified schematic diagram of broadband light
source based two-ended PMD measurement instrumentation which is
similar to that shown in FIG. 1B but uses a light source to provide
spectrally wide light encompassing the desired wavelength range and
a narrow-band tunable filter (between polarizer and a detector) to
enable detection of only that fraction of light corresponding to a
small spectral width centered about the passband wavelength of the
narrow-band tunable filter;
[0089] FIG. 1J is a simplified schematic diagram of broadband light
source based two-ended PMD measurement instrumentation similar to
that shown in FIG. 1I but employs a dispersion element
(multi-channel filter) and multi-channel detector array means that
measures analyzed light after the polarizer simultaneously or
within a short time period;
[0090] FIG. 1K is a simplified schematic diagram of broadband light
source-based two-ended PMD measurement instrumentation which is
similar to that shown in FIG. 1F but uses a light source to provide
the spectrally wide light encompassing the desired wavelength
range, a PBS in the polarization-controller-and-analyzer means, two
synchronously-controlled narrow-band tunable filters between the
PBS and the respective detectors, to enable polarization-diverse
detection of light corresponding to a small spectral width centered
about the passband wavelength of the narrow-band tunable
filter;
[0091] FIG. 1L illustrates schematically an alternative broadband
source for the measurement instrumentation of FIGS. 1I, 1J and 1K
that is particularly well-suited for in-channel measurement of DGD
and shows, in broken lines, an optional optical amplifier,
preferably a semiconductor optical amplifier (SOA), and, for use
where chromatic dispersion is to be measured, a source of RF
modulation and, if appropriate, a polarizer.
Two-Ended Partial-DGD Measurement and Determination of PMD
Therefrom (FIGS. 2H Through 2K)
[0092] (For ease of understanding, the letter suffixes of FIGS. 2H
to 2K have been chosen to indicate similarities in the basic
hardware between these Figures and their counterparts, FIGS. 1H to
1K, for the two-ended "test-source-based" implementations.)
[0093] FIG. 2H is a simplified schematic illustration of
measurement instrumentation suitable for measurement of
partial-DGD, employing narrow-band tunable filtering (i.e. having a
spectral passband less than the spacing of the closely-spaced
optical frequencies to be measured), and employing a polarimetric
head as a polarization analyzer.
[0094] FIG. 2I is a schematic diagram measurement instrumentation
suitable for measurement of partial-DGD, which employs narrow-band
tunable filtering, and a polarization controller and polarizer
(serving as an analyzer) combination to actively vary the A-SOP.
Note that only one detector is used, and hence normalization
requires averaging over many approximately uniformly-distributed
random A-SOP values; or the generation of a fixed grid of A-SOPs
uniformly distributed on the Poincare Sphere;
[0095] FIG. 2J is a simplified schematic illustration similar to
FIG. 2I but where a dispersion element (e.g. bulk-optic diffraction
grating) and detector array replace the tunable filter and
detector;
[0096] FIG. 2K is a simplified schematic illustration of elements
of partial-DGD measurement instrumentation comprising a
polarization beam splitter (PBS) and an A-SOP controller, two
tunable filters A and B, and two detectors A and B to measure
analyzed light in a polarization-diverse manner. In one embodiment,
the A-SOP controller generates random A-SOPs. In a variant, the
A-SOP controller generates at least two and preferably three known
A-SOPs, preferably mutually orthogonal (90 degrees) on the Poincare
Sphere;
[0097] FIG. 2M is a simplified schematic illustration of a
high-resolution optical spectrum analyzer based on
polarization-diverse heterodyne detection. A narrow-linewidth
tunable laser serves as a Local oscillator (LO) and is tuned so
that a portion of its light beats with orthogonally-polarized
portions of the SUT light at respective detectors, and the relative
optical power of the analyzed SUT light at two chosen filtered RF
frequencies can be determined. The A-SOP controller, shown disposed
along the optical path of the SUT before the PBS, could
equivalently be placed along the optical path of the LO light;
[0098] FIG. 2N is a simplified schematic illustration similar to
FIG. 2M but of measurement instrumentation comprising one detector.
The A-SOP controller, shown disposed along the optical path of the
SUT before the beamsplitter BS, could equivalently be placed along
the optical path of the LO light;
[0099] FIG. 11 shows how PMD determination may be carried out using
measurement instruments suitable for partial-DGD measurement of a
plurality of SUTs at any (non-filtered) monitoring point along a
link. For the case of a filtered monitoring port (e.g. an optical
DeMux port), DGD.sub.P of the respective SUT may be
measured/monitored;
[0100] FIG. 12A illustrates several measured DGD.sub.P for
different fiber-launched input SOPs corresponding to a SUT having a
fixed DGD value of 18.5 ps, obtained using prototype
instrumentation corresponding to the design shown in FIG. 2K;
[0101] FIG. 12B plots DGD.sub.P measurement uncertainty (.sigma.)
vs the number of A-SOPs associated with the particular measurement,
for a test setup having a fixed DGD value of 18.5 ps using a
prototype instrument based on the embodiment of FIG. 2K;
[0102] FIG. 13 shows an example of PMD values corresponding to
three different measurements (i.e. 5.32 ps, 4.91 ps, and 5.56 ps,
respectively) of a particular fiber link comprising a PMD emulator
derived from DGD.sub.P measurements of sixteen different
50-GHz-spaced live ITU channels, using a prototype instrument based
upon the design of FIG. 1. The "expected" PMD value of 5.44 ps was
determined by averaging two separate results as measured by a
Reference Test Method (RTM) between 1530 nm and 1610 nm.
Single-Ended Overall PMD Measurement (FIGS. 3-3G)
[0103] FIG. 3 corresponds to FIG. 1 but is a simplified schematic
diagram of measurement instrumentation for single-ended measurement
of overall PMD;
[0104] FIGS. 3B to 3G correspond to FIGS. 1B to 1G, respectively,
and illustrate corresponding single-ended measurement
instrumentation in which both portions of the measurement
instrumentation are at the same, proximal end of the FUT.
Single-Ended Cumulative PMD Measurement
[0105] FIG. 4 is a simplified schematic diagram of a
polarization-sensitive optical time domain reflectometer (POTDR)
embodying an aspect of the present invention;
[0106] FIG. 4A is a simplified schematic diagram of another
polarization-sensitive optical time domain reflectometer embodying
an aspect of the present invention;
[0107] FIG. 4B is a simplified schematic diagram of yet another
polarization-sensitive optical time domain reflectometer embodying
an aspect of the present invention;
[0108] FIG. 4C is a simplified schematic diagram of still another
polarization-sensitive optical time domain reflectometer embodying
an aspect of the present invention;
[0109] FIG. 5A is a flowchart illustrating operation of the light
source means and input I-SOP controller of the two-ended PMD
measurement instrument of FIGS. 1D and 1F;
[0110] FIG. 5B is a flowchart illustrating operation of
polarization controller-and-analyzer means of the two-ended PMD
measurement instrumentation of 1D and 1F;
[0111] FIG. 5C is a flowchart illustrating details of the
acquisition of a k.sup.th group of powers, as described in the
flowchart of FIG. 5B;
[0112] FIG. 5D is a flowchart illustrating a power (data)
acquisition step of the flowchart of FIG. 5C;
[0113] FIG. 6A illustrates sections of a flowchart illustrating
operation of the single-ended PMD measurement of FIGS. 3D and
3F;
[0114] FIG. 6B is a flowchart illustrating a group of power (data)
acquisition steps of the flowchart of FIG. 6A;
[0115] FIG. 6C is a flowchart illustrating a power (data)
acquisition step of the flowchart of FIG. 6B;
[0116] FIG. 7A is a flowchart illustrating operation of the POTDR
of FIG. 4;
[0117] FIG. 7B is a flowchart illustrating a trace acquisition step
of the flowchart of FIG. 7A;
[0118] FIG. 8A is a schematic diagram illustrating another
alternative tunable pulsed light source that can be used for
single-ended overall PMD measurement;
[0119] FIG. 8B illustrates schematically yet another alternative
tunable pulsed light source that can be used for both single-ended
overall PMD measurement and single-ended cumulative PMD
measurement;
[0120] FIG. 9 is a simplified schematic diagram of light source
means comprising a laser source that has been modified to ensure
that the emitted light has a high degree of polarization (DOP);
[0121] FIG. 10A is a schematic diagram illustrating another
alternative tunable pulsed light source-that can be used for
single-ended overall PMD measurement;
[0122] FIG. 10B illustrates schematically yet another alternative
tunable pulsed light source that can be used for both single-ended
overall PMD measurement and single-ended cumulative PMD
measurement;
[0123] FIG. 9 is a simplified schematic diagram of light source
means comprising a laser source that has been modified to ensure
that the emitted light has a high degree of polarization (DOP);
[0124] FIG. 10A illustrates several measured DGD for different
fiber-launched input SOPs corresponding to a SUT having a fixed DGD
value of 18.5 ps, obtained using prototype instrumentation
corresponding to the design shown in FIG. 2K;
[0125] FIG. 10B plots DGD.sub.P measurement uncertainty (.sigma.)
vs the number of A-SOPs associated with the particular measurement,
for a test setup having a fixed DGD value of 18.5 ps using a
prototype instrument based on the embodiment of FIG. 2K;
DESCRIPTION OF PREFERRED EMBODIMENTS
[0126] In the drawings, the same or similar components in the
different figures have the same reference numeral, where
appropriate with a prime or suffix letter indicating a
difference.
1.5 Preferred Embodiments
[0127] The various embodiments of the present invention are
predicated upon the same underlying theory. The following four
preferred embodiments, including their respective implementations,
will be described in more detail in this Section: [0128] 1)
Two-ended determination of PMD and/or DGD(.upsilon.) using test
light source; [0129] 2) "Two-ended" determination of PMD and/or
DGD.sub.P(.upsilon.) using one or more data-carrying signals (SUT)
as the test light source(s); [0130] 3) Single-ended determination,
using optical reflectometry, of the overall PMD of an optical link
(FUT); [0131] 4) Single-ended determination, using optical
reflectometry, of PMD(z), i.e. the cumulative value of the PMD at
any point along a FUT.
[0132] The invention should not be construed as being limited to
these preferred embodiments, nor to the afore-mentioned
applications, but may be otherwise embodied and/or find application
to the determination of other polarization-related characteristics
of an optical link or, more generally, any single-mode optical
fiber.
[0133] Each of the preferred embodiments of this invention
described hereinafter comprises three main parts, namely (i) light
source means (which, in the case of Embodiment (2), is not
comprised within the test instrumentation), (ii)
polarization-controller-and-analyzer means, (iii) detection means,
and (iv) [[analog and digital processing means, together with one
or more control units. In so-called two-ended cases, the light
source means will be located at a proximal end of the FUT while a
second portion of the polarization-controller-and-analyzer means,
the detection means, and, conveniently, the analog-and-digital
processing means will be located at the distal end of the FUT.
[0134] Although methods embodying this invention usually will
employ the above-described four parts or sections, each preferred
embodiment may comprise different possible implementations,
according to the nature of the application, e.g. as described in
Section 2 hereinabove.
[0135] It should be noted that the detection of analyzed power of
light corresponding to two closely-spaced wavelengths (i.e. optical
frequencies) is common to all embodiments of this invention. For
convenience, a "midpoint wavelength" is defined "notionally" as the
mean of these two closely-spaced wavelengths, .lamda..sub.U,
.lamda..sub.L, where the "U" and "L" subscripts designate
"uppermost" and "lowermost", respectively. As such, the midpoint
wavelength is not explicitly needed anywhere in the computations
(to be described hereinbelow), and neither detected wavelengths
constituting a pair is equal the midpoint wavelength. Only the
knowledge of the optical-frequency spacing (sometimes referred to
as wavelength "step" hereinbelow) is needed. (When more than one
wavelength pair is used per group, as will be further discussed
hereinbelow, it is useful to introduce the concept of "center
wavelength" as a wavelength "label" corresponding to the particular
group.)
[0136] Preferred implementations of the three main embodiments for
PMD measurement, including measurement methods and measurement
instrumentation configurations for two-ended PMD measurement,
single-ended overall PMD measurement and single-ended cumulative
PMD measurement according to the invention, and modifications,
alternatives and substitutions thereto, will now be described in
Sub-sections 5.2-5.5, with reference to FIGS. 1 to 3C.
1.6 Embodiment (1)
Two-Ended Test-Source-Based PMD and/or DGD Measurement
1.6.1 Description of Apparatus and Summary Description of Operating
Mode
[0137] For Embodiment (1), there is also normally a "first portion"
of polarization-controller-and-analyzer means disposed in the
optical path between the light source means and the proximal end of
the FUT. A first control unit at the proximal end of the FUT
controls the light source means and the first portion of the
polarization-controller-and-analyzer means and a second control
unit at the distal end of the FUT controls the second portion of
the polarization-controller- and analyzer means and the
analog-and-digital signal processing means.
[0138] For two-ended "test-source-based" measurement of PMD and/or
DGD in either unlit fiber or "dark channels" of an in-service
optical link (Embodiment (1)), the light source means usually
comprises an at least partially polarized light source, for example
a tunable laser or a broadband source, and supplies light to an
input SOP (I-SOP) controller for controlling the SOP of light from
the light source means before injection ("launch") into the FUT.
The polarization-controller and analyzer means may comprise, in
addition to an analyzer SOP (A-SOP) controller, a polarizer and a
detection means/system comprising one detector, or a PBS and two
detectors, or a coupler and a polarizer with two detectors, and so
on. Where the light source is broadband, the
polarization-controller-and-analyzer means may also comprise a
tunable filter for selecting the optical frequency. (Alternatively,
but less advantageously, the light source could comprise such a
tunable filter.) The analog-and-digital processing means may
comprise a data acquisition unit, a sampling-and-averaging unit,
wherein analog-to-digital conversion is carried out, and a data
processor unit.
[0139] For this embodiment, the
polarization-controller-and-analyzer means and the analog and
digital processing means must be configured to measure two or more
closely-spaced wavelengths. For example, where the light source
means at the proximal end emits broadband polarized light, this
could be effected using narrow-band optical filtering within the
second portion of the polarization-controller-and-analyzer means,
at the distal end. Alternatively, the source at the proximal end
may be a laser that is able to set or modulate its optical
frequency to produce two or more closely-spaced wavelengths at
different times, in which case the
polarization-controller-and-analyzer means does not necessarily
comprise optical filtering.
[0140] In the following description for the two-ended PMD
measurement, the term "modulated optical pulse" is used to refer to
propagating light, which, over a defined time interval, is
differentiated from at least some other pulses by one or more of a
characteristic wavelength, characteristic average power,
characteristic pulse duration, characteristic superposed amplitude
or phase modulation at a frequency much greater than the reciprocal
of the pulse duration, characteristic extinction ratio following
its duration, characteristic duration of sampling of the said light
in the acquisition process, or any other measurable distinguishing
property.
[0141] In a first preferred implementation of Embodiment (1)
illustrated in FIG. 1, measurement instrumentation for two-ended
measurement of DGD/PMD comprises light source means 42 situated at
or adjacent a proximal end of fiber-under-test (FUT) 18. A first
portion 44A of a polarization-controller-and-analyzer means 44 is
disposed between light source means 42 and the proximal end of FUT
18, and comprises an input SOP controller means 14A (conveniently
referred to as an I-SOP controller or scrambler means), which
controls the SOP of light from the light source 12 before injecting
it into the FUT 18 via connector 16A. A second portion 44B of
polarization-controller-and-analyzer means 44 is situated at or
adjacent a distal end of the FUT 18 and connected thereto by a
connector 16B.
[0142] A first (input) control unit 30A controls the wavelength of
the light source 12 and the setting of the input I-SOP controller
14A, specifically to scramble the SOP of the light from light
source 12 before it is injected into the FUT 18.
[0143] The second portion 44B of
polarization-controller-and-analyzer means 44 comprises an output
SOP controller (A-SOP) 14B (conveniently referred to as an A-SOP
controller or scrambler means), followed by a polarization
discriminator 20. The output of the polarization discriminator is
supplied to detection means, specifically detection means/system
22. If the detection means 22 is not able to correctly measure high
optical power levels, power controller means (not shown), for
example an optical attenuator, may be interposed to attenuate the
light extracted from the FUT 18 before it is applied to the
detection means 22. The purpose of the optical attenuator is to
ensure that the light level at the distal end is not so high as to
potentially "saturate" or render non-linear the detection means 22.
Such may be the case if, for instance, the measurement is carried
out over a short optical fiber link, wherein the overall
attenuation induced by the fiber is small. For long links, the
optical attenuator will normally be set to induce minimum
attenuation.
[0144] The analog-and-digital signal processing unit 40 comprises a
sampling-and-averaging unit 32 and a data processor means 34,
optionally with a display means 36 for displaying results.
Components of the polarization-controller-and-analyzer means 44B
and the analog-and-digital signal processing unit 40 are controlled
by a second, output control unit (A) 30B which also controls the
detection system 22.
[0145] Under the coordination of control unit 30B, the
sampling-and-averaging unit 32, in known manner, uses an internal
analog-to-digital converter to sample the corresponding electrical
signals from the detectors 22B and 22C as a function of time (as
shown, for example, in FIGS. 1C, 1D, 1F), and the sampled signal is
time-averaged over a portion of its duration to provide a
corresponding digital level. This portion is chosen so as to avoid
transient effects and/or bandwidth limiting effects in the detected
power, polarization, and/or wavelength arising from one or more of
the light source means 12,--the
polarization-controller-and-analyzer means (comprising the I-SOP
controller 14A, the A-SOP controller 14B and, where applicable,
polarization discriminator means 20), and/or any distortion in the
(pulsed) signal arising from bandwidth limitations of the analog
electronics.
[0146] The resulting averaged powers are used by data processor 34
to derive the DGD at a particular wavelength or PMD value over a
prescribed wavelength range of the FUT 18, as will be described in
more detail hereinafter according to the particular implementation
of the embodiment.
[0147] Various configurations of the two-ended measurement
instrumentation of FIG. 1 that employ an A-SOP controller 14B are
illustrated in FIGS. 1B to 1G and 1I to 1K, and a further
implementation in which the second portion of the
polarization-controller-and-analyzer means and detection
system/means are replaced by a polarimetric head 45 is illustrated
in FIG. 1H; these configurations will now be described briefly. The
measurement instrumentation configurations depicted in FIGS. 1 to
1H have in common that they use a tunable laser source 12A whereas
those depicted in FIGS. 1I to 1K use a broadband source 12B.
[0148] Thus, in each of the "two-ended" measurement instrumentation
configurations illustrated in FIGS. 1B to 1H, the light source 12A
comprises a tunable modulated laser source 12A whose output is
coupled to either a polarization maintaining fiber (PMF) or
singlemode fiber (SMF), as appropriate, for injecting modulated
optical pulses into the fiber-under-test (FUT) 18 via the (input)
state of polarization (I-SOP) controller means 14A and input
connector 16A. The output light extracted from the FUT 18 via
connector 16B and A-SOP controller 14B is analyzed by optical
components comprising or equivalent to the polarization
discriminator 20 of FIG. 1, and the analyzed light is measured
during a time period during which light from the light source means
12A is detected, successively, at each of two different
wavelengths, .lamda..sub.L.sup.(k) and .lamda..sub.U.sup.(k), that
are closely-spaced relative to each other.
[0149] The main differences between the different configurations
lie in the second portion 44B of the
polarization-controller-and-analyzer means 44, and consequently in
the manner in which normalization of the detected analyzed powers
may be done. (Details of the normalization procedures will be
provided hereinbelow.)
[0150] FIGS. 1B and 1C illustrate measurement instrumentation
configurations for which, at a given A-SOP setting, only light
power corresponding to one analysis condition is measured.
Consequently, for both of these configurations, normalization of
the analyzed light powers is carried out using an averaging
procedure (over changes in at least one, and preferably at least
two of A-SOP, I-SOP, and midpoint wavelength) described
hereinbelow.
[0151] In FIG. 1B, in the polarization-controller-and-analyzer
means 44 of the measurement instrumentation, the polarization
discriminator comprises a linear polarizer 20A and the detection
means comprises a single detector 22A. The measurement
instrumentation illustrated in FIG. 1C is similar to that
illustrated in FIG. 1B but differs in that a coupler 21 is disposed
after the polarizer 20A, and two detectors 22B and 22C are
connected to respective outputs of the coupler 21 to measure two
repeated powers. Such repeated power measurements enable the
contribution of uncorrelated noise to be suppressed in the
processing steps, as will be described hereinbelow.
[0152] FIGS. 1D and 1E illustrate measurement instrument
configurations for which, at a given A-SOP setting, both
non-analyzed light power and light power corresponding to one
analysis condition may be directly measured. Consequently, for both
of these configurations, normalization of each of the detected
analyzed powers may be carried out by normalization with respect to
the corresponding non-analyzed light power, as described in more
detail hereinbelow.
[0153] FIG. 1D shows measurement instrumentation similar to that
shown in FIG. 1B but which differs in that it has two detectors 22B
and 22C and a coupler 21 interposed between the A-SOP controller
14B and the polarization discriminator (polarizer) 20A. Detector
22B is connected to the coupler 21 via polarizer 20A and measures
analyzed light received therefrom and detector 22C is connected
directly to the coupler 21 and measures non-analyzed light that is
proportional to a total power of the light extracted from the FUT
18. Thus, the SOP of the extracted light is transformed by the
A-SOP controller or scrambler 14B, following which the light is
split into two parts by coupler 21. The first detector 22B
connected to one of the two outputs of the coupler 21 via the
polarizer 20A detects one of the (analyzed) polarization components
and the second detector 22C connected to the other output of the
coupler 21 measures a power that is proportional to a total output
light power from FUT. Preferably, the respective light portions are
detected approximately simultaneously by detectors 22B and 22C,
although they may be detected at slightly different times provided
that any variation (e.g. instabilities) of the total output light
power from the FUT occurs over a longer time scale than the
difference in detection times.
[0154] The measurement instrumentation shown in FIG. 1E differs
from that shown in FIG. 1D in that the former employs only one
detector 22A, and the optical switch 23, controlled by control unit
30B, connects the input of detector 22A in alternating fashion to
the output of the coupler 21 and the output of polarizer 20A to
measure, respectively, the analyzed light and non-analyzed output
light power from the FUT 18.
[0155] FIGS. 1F and 1G illustrate measurement instrument
configurations for which light power is analyzed in a
polarization-diverse manner, i.e. a PBS analyzes the light under
orthogonal analysis conditions. Since the sum of the detected
powers of these two orthogonally-analyzed parts is proportional to
the total non-analyzed optical power (i.e. the Stokes parameter
S.sub.0), normalization of each of the detected analyzed powers may
be readily carried out for both of these configurations, as
described in more detail hereinbelow.
[0156] The measurement instrumentation shown in FIG. 1F employs two
detectors 22B, 22C, each in optical continuity with a respective
one of the two outputs of PBS 20C. The SOP of the light from the
distal end of the FUT 18 is transformed by the A-SOP controller
14B, following which the light is decomposed by the PBS 20C into
two components having orthogonal SOPs, typically linear SOPs at 0-
and 90-degree relative orientations, and detected approximately
simultaneously by detectors 22B, 22C. Of course, these detectors
need to be suitably calibrated to take into account the relative
detector efficiencies, wavelength dependence, etc., as will be
described hereinafter. In FIG. 1G, an optical switch 23 and a
single detector 22A are used instead. For this configuration, the
control unit 30B causes the switch 23 to connect the detector 22A
alternately to the respective output ports of the PBS 20C to
measure the analyzed light from each port.
[0157] For both of the configurations of FIGS. 1E and 1G, an
optical switch 23 is employed to successively select for detection
by detector 22A light routed through one of two optical paths: in
the case of FIG. 1E, either directly from coupler 21 or via
polarizer 20A and in the case of FIG. 1G, from one or the other of
the two outputs of PBS 20C. For both of these configurations, the
light from the two different optical paths is detected at different
times, the time interval preferably being kept as small as
practicable. This enables use of only one detector (and associated
electronics) while maintaining many of the advantages associated
with the use of two detectors. Of course, the cost reduction
associated with the use of only one detector likely would be
largely counteracted by the increased cost of introducing the
optical switch, and there would also be a measurement time
penalty.
[0158] The measurement instrumentation illustrated in FIG. 1H is
similar to that shown in FIG. 1B but differs in that the second
portion 44B of the polarization-controller-and-analyzer means 44
comprises a polarimetric head 45 having its input connected to the
FUT 18 via connector 16B and its output connected to detection
system 22.
[0159] Preferred implementations of the two-ended
"test-source-based" embodiment will now be described with reference
to FIGS. 1I, 1J and 1K, which use, instead of a tunable laser
source 12A, a broadband source 12B that has a very wide spectrum,
or a tunable broadband source that has a moderately wide spectrum
whose center wavelength is tunable. The measurement instrumentation
illustrated in FIG. 1I is similar to that described with reference
to and as shown in FIG. 1B, but differs in that its light source
means 42 comprises a polarized broadband light source 12B instead
of a tunable laser source and its
polarization-controller-and-analyzer means 44 differs from that
shown in FIG. 1B because it comprises a narrow-band tunable filter
27 placed after the polarizer 20A in order to spectrally filter,
and hence render coherent, the analyzed light before it is applied
to the detector 22A. Tunable filter 27 is controlled by control
unit 30B.
[0160] It should be appreciated that the tunable filter 27 could
alternatively be placed anywhere in the optical path between the
output of the FUT at connector 16B and the detector 22A, while
remaining in close proximity to control unit 30B, and is not
limited to being placed between the polarizer 20A and the detector
22B as shown in FIG. 1I. Indeed, more generally the tunable filter
27 could be placed anywhere between the broadband source 12B and
the detector 22A. However, placing the tunable filter 27 in the
light source means 42 at the proximal end of the FUT 18 may lead to
control and synchronization difficulties, as communication between
the tunable filter 27 at the proximal end and the control unit 30B
at the distal end of the FUT may be difficult.
[0161] The measurement instrumentation illustrated in FIG. 1J is
similar to that shown in FIG. 1I but differs in that the tunable
filter 27 is replaced by a spectrometer means or multi-channel
filter means, specifically a dispersion element 27A, for example a
grating-based wavelength separator, to separate the different
wavelengths of light as a function of angle. The single detector
22A is replaced by detection means for detecting light powers at
these wavelengths approximately simultaneously, for example, a
multi-channel detector array 22B or similar means. Alternatively,
such a detector array 22B may be replaced by several fiber
pigtailed photodetectors that may be connected to a fiber array to
detect light at different spatial positions, or simply to launch
light at different spatial positions having different optical
wavelengths into different photodetectors. Although there would be
a higher cost associated with this design, it could measure DGD or
PMD rapidly.
[0162] In another implementation, shown in FIG. 1K, the measurement
instrumentation is similar to that shown in FIG. 1I, but differs in
that the tunable filter 27 of FIG. 1I is replaced by two
synchronously-controlled narrow-band tunable filters 27B, 27C,
conveniently as respective channels of a two-channel grating-based
scanning monochromator 27, and the polarizer 20A of FIG. 1I is
replaced by a PBS 20C. The two orthogonal analyzed outputs from the
PBS 20C are conveyed (via optical fiber) to respective ones of the
two channels of the scanning monochromator 27. Detectors 22B, 22C,
detect light, substantially simultaneously, from respective ones of
the two outputs of the two-channel scanning monochromator 27,
resulting in "polarization-diverse" detection as a function of
wavelength. (An example of an optical spectrum analyzer based on
such a polarization-diverse two-channel scanning monochromator
design is described in commonly-owned U.S. Pat. No. 6,636,306 (He
et al.) The analog-and-digital signal processing unit 40 then can
process this data to extract DGD and PMD information.
[0163] Once suitably calibrated to take into account the relative
detector efficiencies, wavelength dependence, etc., as will be
described hereinafter, the sum of the detected powers from
detectors 22B and 22C, respectively, is proportional to the total
incident (i.e. non-analyzed) power (often referred to as the Stokes
parameter S.sub.0) within the monochromator 27 optical
bandwidth.
[0164] For implementations where the tunable filter 27 is employed,
the tunable filter 27 is operated to allow the selection and
subsequent detection of each of the wavelengths corresponding to
the groups comprising the wavelength pair; the selected filtered
light corresponding to the two or more wavelengths being
subsequently detected by two or more detectors, respectively, e.g.
detectors 22B and 22C. It should be noted that the tunable filter
27 can be a single channel filter that is operated in a "continuous
sweep" mode, or may be operated under a "stepped wavelength"
selection mode where a particular step may correspond to an optical
frequency at which two detected analyzed powers are acquired (i.e.
repeated powers, as will discussed in more detail hereinbelow). It
should be also noted that the tunable filter 27 can be designed as
a spectrometer, for example as shown in FIG. 1J, enabling powers at
different wavelengths to be measured contemporaneously. Also note
that different polarization components may be detected by different
detectors, as shown in FIG. 1K, or the same detector but at
different times by using appropriate polarization controlling
means.
[0165] Preferably, in the "two-ended test-source-based"
implementations of the measurement instrument shown in FIGS. 1 to
1K, there is little or no "upstream" communication between the
control unit 30B at the distal end of the FUT 18 and the control
unit 30A at the proximal end. For the implementations shown in
FIGS. 1 to 1H, the control unit 30B comprises software or firmware
that allows it to determine, from information encoded onto the
optical signal by the optical light source means 42, conveniently
under the control of control unit 30A, whether a particular
detected modulated optical pulse extracted from the FUT 18
corresponds to an uppermost, lowermost, or, where applicable,
intermediate closely-spaced wavelength. If a "widely broadband"
source means is employed in the implementations shown in FIGS. 1I
to 1K, there is advantageously no need for the control unit 30B to
receive wavelength information from the light source means 42, as
all wavelength selection is performed at the same end of the FUT as
the control unit 30B. If a tunable "moderately broadband" light
source means 42 is employed in the implementations depicted in
FIGS. 1I to 1K, suitable for measuring the DGD of a particular DWDM
channel, there is a need to initially tune ("set") the light source
means 42 to encompass all or most of the passband of the desired
DWDM channel, an operation that may necessitate communication
between operators at the two corresponding sites.
[0166] The preferred implementations described hereinbefore are
common to principal aspects of this invention. Further details of
the preferred implementations, including details of their
operation, corresponding to each of these principal
aspects/implementations will be described in more detail in
.sctn.5.2.2-5.2.6 hereinbelow.
1.6.2 Measurement of DGD at a Particular Wavelength
[0167] In a narrow DWDM channel, it is frequently not practical to
measure the DGD at more than one wavelength (.lamda..sub.mid)
within the channel (or at least not more than a very limited number
of wavelengths), since the optical-frequency spacing of the
closely-spaced wavelengths may be a significant fraction of the
useable optical passband of the DWDM channel and, consequently,
measurement at another midpoint wavelength may cause one of the two
closely-spaced wavelengths to experience excessive attenuation,
polarization-dependent loss, and other deleterious effects that may
render the measurement unreliable or impractical. (As will be
described in more detail hereinafter, the choice of a very small
optical-frequency spacing may not be compatible with the
measurement of a small DGD value.)
[0168] It may be useful to perform this DGD measurement as a
function of optical frequency at at least two optical frequencies
("midpoint wavelengths"), within an "optical channel" bandwidth, as
such a measurement enables an estimation of at least one component
of the second-order PMD, i.e. the component proportional to
d(DGD(.upsilon.))/d.upsilon.. As known in the prior art (see, for
instance, Foschini et al, Journal of Lightwave Technology, vol.
17(9), pp 1560-1565 (1999), in particular Eq. 8) for a strongly
mode-coupled FUT, such as is the case with almost all long telecom
single-mode fibers, this measurement of this second-order PMD
component provides an independent (i.e. uncorrelated) additional
estimate of DGD. In other words, although the DGD so-obtained at
the particular wavelength is not the real ("first-order") DGD, if
this measurement is repeated for a plurality of DWDM channels, for
instance, these additional "second-order-PMD" DGD estimates can be
used to improve the overall uncertainty of the PMD value determined
via an rms (or arithmetic mean) of all the DGD estimates, whether
derived directly, or indirectly via the second-order PMD. It should
also be noted that the measurement of DGD at a particular
wavelength is not limited to "in-channel" applications such as
testing optical links through DWDM channels.
[0169] Note that, for DGD measurement in a "dedicated" DWDM
channel, i.e., a measurement that is always to be undertaken at
approximately the same particular wavelength, it is not necessary
that the light source means 12 or 12B be widely tunable or very
broadband, but only that it be either:
a "moderately" tunable coherent light source capable of emitting
coherent light at each of two different closely-spaced wavelengths
centered about the aforesaid "particular wavelength", for the case
where there is no narrowband optical filtering in the
analyzing-and-detection means; a "moderately" broadband source
capable of emitting at least partially polarized light having a
spectral width encompassing at least the "closely-spaced
wavelengths" separation, and preferably all or most of the bandpass
of the "dedicated" DWDM channel-under-test, for the case where the
analyzing and detection means comprises narrow-band optical
filtering.
[0170] Thus, depending upon the particular measurement
implementation, the light source means 42 may comprise one of a
tunable coherent source (e.g., a laser), a "widely" broadband
source (for instance, having a spectral width encompassing all
desired DWDM channels to be measured, for instance), or a "hybrid"
thereof, for instance, a tunable "moderately" broadband source. In
this latter case, the source should be at least sufficiently
broadband to encompass all or most of the DWDM channel passband,
thereby clarifying the meaning of "moderately", and this broadband
"spectral slice" may be tuned or "set" to be centered upon any one
of a number of other DWDM channel wavelengths, for instance in the
telecommunications C and/or L bands. More details concerning the
tunable light source, widely broadband light source, or tunable
moderately broadband source means are provided in a later
sub-section.
[0171] In field installations, DGD can vary with time and/or
environmental conditions, on time scales that may range from
minutes to weeks, or in some cases even years. For many measurement
applications, the speed ("update rate") of the measurement is not
critical. Consequently, it is advantageous for cost reasons to use
inexpensive polarization scramblers for the Input-SOP (I-SOP)
controller 14A and for the Analyzer-SOP (A-SOP) controller 14B of
the polarization-controller-and-analyzer means 44. An example of a
low-cost SOP scrambler that may be suitable for both of the I-SOP
and A-SOP controllers 14A and 14B is described in co-owned U.S.
Pat. No. 8,373,852 (Ruchet et al), the contents of which are
incorporated herein by reference.
[0172] The actual SOP of light exiting the input I-SOP controller
14A is, in general, unknown, but undergoes "continuous"
transformation, i.e. is varied slightly between groups of
closely-spaced wavelengths, such that over a sufficiently long
time, normally corresponding to the minimum time for a reliable DGD
measurement, the SOPs will cover the Poincare sphere approximately
uniformly.
[0173] The analyzer A-SOP controller 14B, located at the distal end
of the FUT 18, may also cause the SOP of the light exiting the FUT
18 to be varied slowly in a similar manner to the input I-SOP
controller 14A, although in general the respective rates of
variation would not be the same and the SOPs exiting either the
I-SOP controller 14A or the A-SOP controller 14B would be
uncorrelated. Alternatively, the analyzer A-SOP controller 14B may
vary the SOP in a discrete and random fashion, since there are
normally no synchronization difficulties with the co-located
control unit 30B.
[0174] More specifically, for a particular measurement sequence k,
the control unit 30B causes the light signal, analyzed by the
intervening polarization discriminator, such as a polarization beam
splitter (PBS) or polarizer, to be measured during a portion of
time during which light from the light source means 42 is detected,
successively, at each of two different wavelengths,
.lamda..sub.L.sup.(k) and .lamda..sub.U.sup.(k), that are
closely-spaced relative to each other, during which portion of time
the SOPs exiting the I-SOP controller 14A and A-SOP controller 14B,
respectively, are approximately constant and form a k-th SOP couple
(I-SOP.sub.k, A-SOP.sub.k). (Preferably, the aforementioned portion
is less than 50% of the "physical" pulse length, for reasons that
will be explained further below.) The midpoint wavelength of the
pair of modulated light pulses is defined as the average of the
actual optical frequencies of the modulated light pulses, which to
a very high degree of approximation can be expressed in terms of
wavelength as
.lamda..sub.mid.sup.(k)=(.lamda..sub.L.sup.(k)+.lamda..sub.U.sup.(k))/2.
(The labels L and U refer, for convenience and ease of
understanding, to "lowermost" and "uppermost" with respect to the
midpoint wavelength .lamda..sub.mid.sup.(k) and more accurately the
midpoint wavelength is expressed as
.lamda. mid ( k ) = 2 .lamda. L ( k ) .lamda. U ( k ) .lamda. L ( k
) + .lamda. U ( k ) . ) ##EQU00001##
[0175] The measured analyzed light signal is converted to an
electrical signal by the sampling and averaging means 32 and
subsequently digitized before application to the data processor 34
for subsequent processing thereby.
[0176] During the transition from one closely-spaced wavelength to
the other, the light from the light source means 12A is briefly
extinguished, say for about 40 .mu.s, a period that is much shorter
than the typical reaction period of DWDM channel equalizers found
in many optical networks. The precise period of this extinction
serves to encode, for use by the control unit 30B, information
indicating whether the subsequent pulse corresponds to an uppermost
or lowermost wavelength.
[0177] The measurement sequence described above is repeated for K
different groups, each group corresponding to a slightly different
I-SOP and A-SOP. In practice, if the SOP is "scanned" (i.e.
transformed) in a continuous fashion, the aforesaid "sufficiently
long time" typically would correspond to K values greater than 1000
to obtain fully satisfactory results.
[0178] The time period corresponding to light emission at each of
the closely-spaced wavelengths is not particularly critical, but
clearly a longer duration will lead to a longer overall measurement
time for this method. A good compromise between measurement time
and limitations on the light-source wavelength switching speeds has
been found to be a period of about 1 ms.
[0179] If the expected DGD to be measured is not roughly known, it
is possible that the optical-frequency difference of the
closely-spaced wavelength pairs will be too large to permit
accurate measurement of high DGD values, or, conversely, too small
to permit measurement of low DGD values. In such a case, it may be
desirable to perform a preliminary rough DGD estimation using this
method using only a limited number of K values. (It should be noted
that, with the continuous SOP scanning approach, K necessarily must
still be relatively large, e.g. >500, for a rough measurement,
whereas if the alternative "macroscopic-step SOP selection"
approach is used, as described hereinafter, K may be a much smaller
value, e.g. approximately 10.) Then, depending on the result, the
spacing of the closely-spaced wavelengths may be adjusted, while
maintaining the midpoint wavelength at the same value. However, as
mentioned above, in a narrow DWDM channel, which may, for instance,
only have a useable passband width of approximately 35 GHz, it is
not always possible to increase the wavelength spacing.
[0180] An alternative approach for "adapting" the optical frequency
difference between the closely-spaced wavelengths is to use more
than two closely-spaced wavelengths in each group, the wavelength
spacing between pairs of wavelengths being unequal. If, as
described above, the preliminary DGD estimation indicates that the
wavelength spacing should be different, one need only slightly
shift the midpoint wavelength corresponding to the "optimal"
closely-spaced wavelength pair to the midpoint wavelength
corresponding to the initial closely-spaced wavelength pair.
[0181] Advantageously, in order to estimate, and partially
compensate for, the contribution of noise in the measurements,
"repeated measurements" are taken for each group at the same two
closely-spaced wavelengths, these repeated measurements being in
principle substantially perfectly correlated to the "original"
measurements, in the absence of noise (i.e. identical if taken
under the same polarization analysis conditions, or perfectly
complementary if taken under orthogonal polarization conditions,
e.g. via the two outputs of a polarization beam splitter). In
practice, such noise may arise from any combination of ASE noise
(from intervening optical amplifiers in the fiber link),
polarization noise (caused by swaying aerial cables, for instance),
light source power fluctuations, uncorrelated electronic noise,
etc. The method by which this technique is used to improve the
measurement sensitivity will be described in more detail
hereinafter.
[0182] It should be noted, however, that it is actually convenient
not to transmit distinct "physical" repeated pulses in the
preferred implementation, but rather to perform the functional
equivalent in the acquisition process by sampling the "physical
pulse" (corresponding to the period during which the laser emits at
a particular wavelength) during a different portion of time than
the portion during which the "initial" measurement was taken.
Consequently, in a preferred implementation, each "physical pulse"
comprises two "optical modulated pulses".
[0183] The computational method by which the data thus acquired can
be converted into a reliable DGD measurement, including in the
presence of significant ASE noise, will be described in more detail
hereinafter.
1.6.3 RMS or Mean DGD Measurement Using Repeated DGD(.lamda.)
Measurements
[0184] By repeatedly applying the above-described method of
measuring DGD at a particular wavelength of the invention over a
prescribed wavelength range, it is possible to estimate the
polarization mode dispersion (PMD) of a fiber link (according to
either or both of the "rms" or "mean" PMD definitions) from the DGD
as a function of wavelength. Preferably, the wavelengths should be
approximately uniformly distributed across a prescribed wavelength
range.
[0185] For reasons of overall measurement time, it is advantageous
to replace the continuous SOP scanning described in the Summary of
Invention hereinbefore with "macroscopic-step SOP selection", i.e.
where I-SOP controller 14A and A-SOP controller 14B set the
different input and analyzer SOPs in a pseudo-random manner, such
that the points whereby such SOPs conventionally are represented on
the Poincare sphere are uniformly-distributed over the surface of
said sphere, whether the distribution is random or a uniform grid
of points. An example of a suitable commercially-available
controller for such an application is the General Photonics Model
PolaMight.TM. (multifunction polarization controller).
[0186] As mentioned in the context of the above-described
measurement of DGD at a particular wavelength, it is frequently the
case that the optical frequency difference of the closely-spaced
wavelength pairs is, for instance, too large to permit accurate
measurement of high DGD values, or too small to permit measurement
of low DGD values. In such a case, it may be desirable to perform a
preliminary rough DGD estimation using this method but with a
limited number of K values (e.g. 10), and then, depending on the
result, change the spacing of the closely-spaced wavelengths. Note
that, in this case, where the rms or mean DGD is calculated over a
prescribed wavelength range, it is usually not necessary to
maintain exactly the same midpoint wavelength for this measurement
with a different optical-frequency difference. The final DGD
averaging over the wavelengths can take into account this slightly
different wavelength.
[0187] A preferred method of carrying out this approach with
various implementations of the light source means 42 will now be
described, which is applicable to the measurement instrumentation
configurations already described with reference to FIGS. 1, 1B to
1K. (For simplicity of the foregoing description, we assume that
the "repeated pulse" method, described in the measurement of DGD at
a particular wavelength above, is not applied. The "intermediate
wavelength" method described here can be readily generalized to
include the "repeated pulse" method.)
[0188] First, the light source means 42 injects into the FUT 18,
for each group comprising a wavelength pair of optical pulses, a
third additional optical pulse having a wavelength (.lamda..sub.1L)
intermediate and unequally spaced with respect to the uppermost and
lowermost wavelengths (.lamda..sub.1U,.lamda..sub.1L) respectively,
of the group. The input SOP selected by I-SOP controller 14A and
the analyzer-SOP determined by A-SOP controller 14B, respectively,
are approximately constant for all three optical pulses. All three
analyzed pulses are detected by the detection system or means 22,
and are identified by their respective "extinction periods", as
described in the measurement of DGD at a particular wavelength
above. The three aforementioned optical pulses correspond to three
different combinations of optical-frequency differences (in
comparison with two different close-spaced wavelengths, which, of
course, correspond to only one possible optical frequency
difference), and hence only add about 50% to the overall
measurement time. Using the computation method described in more
detail hereinafter with reference to the flowchart shown in Fig. #
noise- and/or sensitivity-optimized DGD measurements can be made at
different approximately uniformly spaced (midpoint) wavelengths
over the prescribed wavelength range.
[0189] It should be noted that, if a significantly uneven
distribution of the same number of DGD(.lamda.) were used, a PMD
value could still be calculated by a straightforward modification
of the method that would be obvious to someone of average skill in
the art, but this PMD value would not be, in general, as reliable
as a PMD value obtained with approximately uniformly distributed
wavelengths.
[0190] For the case where the light source means 42 comprises a
tunable laser 12A as in FIGS. 1B to 1H and 10A), it is desirable
that the choice of midpoint wavelengths defined by the
closely-spaced wavelengths that are generated by the tunable laser
source 12A (FIG. 1(B-H)) or by tunable filter 27 (FIG. 1I) be
predetermined for the prescribed wavelength range (e.g. C band,
from 1530-1565 nm), in order to avoid having to use potentially
complicated communication between the light source means 42 and the
polarization-controller-and-analyzer means 44. In this way, there
is no need for the numerical values of the injected wavelengths to
be explicitly communicated, as these values can be inferred by the
control unit 30B from simple coding information in the extinction
times, as discussed earlier. It may, however, be desirable for an
initial "ready" signal to be sent from the light source means 42 to
begin the measurement sequence. Again, this signal could be encoded
in the light injected into the FUT, via the extinction period or
other simple pulse frequency modulation.
[0191] Once a set of DGD(.lamda.) values have been obtained as
described above, it is straightforward to compute, using standard
statistical definitions, either or both of the rms DGD and the mean
DGD from the different values of DGD obtained within the prescribed
wavelength range. Note that such a measurement is particularly
useful, since most current commercial approaches do not permit the
PMD to be directly measured using both rms and mean
definitions.
1.6.4 RMS DGD Measurement (without Individual DGD(.lamda.)
Measurements)
[0192] The underlying measurement approach can be applied for the
direct measurement of the rms DGD (i.e. PMD according to the rms
definition) across a prescribed wavelength range. If information
concerning the DGD as a function of wavelength is not required,
implementations of the "two-ended test-source-based" embodiment of
the invention may provide for a much more rapid PMD measurement
(for the same overall level of accuracy) than the method of RMS
measurement using repeated DGD(.lamda.) measurements described
above. In addition, since the polarization-controller- and analyzer
means 44 does not need to "know" the actual value of the wavelength
being transmitted (only whether the wavelength corresponds to the
"uppermost", "lowermost" or one or more "intermediate"
wavelengths), there is no need for the use of predetermined
wavelengths or an explicit "start" signal for the measurement,
thereby simplifying the measurement procedure.--
[0193] The computational method by which the data thus acquired can
be converted into a reliable DGD measurement, including in the
presence of significant ASE noise, is much the same as in the above
described measurement of DGD at a particular wavelength, except
that individual measurements taken with each group of
closely-spaced wavelengths are averaged over "center wavelengths"
(see later for a definition of center wavelength) approximately
uniformly distributed across the prescribed range, as well as over
different I-SOPs and A-SOPs. In certain implementations, the choice
of midpoint wavelengths may be quasi-random, or at least not
sequential in ascending or descending wavelength. In other
implementations, it may be preferable to perform the measurements
sequentially in ascending or descending wavelengths. Computational
details will be described hereinafter.
[0194] As with the above described rms or mean DGD measurement
using repeated DGD(.lamda.) measurements, it is advantageous to
inject more than two different closely-spaced wavelengths in each
group of wavelengths, in order that the optimal optical-frequency
spacing can be used in the computational process.
[0195] Before the measurement procedure for these implementations
is described in more detail, and with a view to facilitating an
understanding of such operation, the theoretical basis will be
explained, it being noted that such theory is not to be
limiting.
1.6.5 RMS DGD Measurement Using Rapid Wavelength Sweeping
[0196] An alternative approach to measure the rms and/or mean DGD
over a prescribed wavelength range is to use a rapidly swept
tunable laser (FIGS. 1B-1H) (or polarized broadband source/tunable
narrowpass filter combination (FIG. 1I), or a polarized broadband
source/polarization-diverse scanning monochromator combination
(FIG. 1K)), where either or both of I-SOP and A-SOP vary little or
not at all during the sweep. If the detection electronics are
sufficiently rapid, this "spectral acquisition step" will provide a
quasi-continuum of detected polarization-analyzed transmitted
coherent optical power data as a function of optical frequency. In
the subsequent data analysis, any desired closely-spaced wavelength
step could be selected, and the average DGD determined from
different wavelength pairs so selected in a similar fashion to that
described earlier. Of course, if I-SOP and A-SOP vary during the
sweep, this would further improve the accuracy of the measurement,
provided that neither I-SOP nor A-SOP varies significantly between
any two closely-spaced wavelengths in the sweep. Furthermore,
repeating this procedure with multiple sweeps will of course
further improve its accuracy.
[0197] This alternative approach also has the advantage that there
is no need for encoding in the source (12A, 30A; 12B, 30A) to
identify "upper, lower and intermediate" closely-spaced
wavelengths, as described earlier. (Of course, for the swept
tunable laser case, there may be a need to indicate the beginning
of the sweep, but such an indication would be straightforward to
implement).
1.6.6 Various Modifications to the Two-Ended PMD Measurement
Means
[0198] The invention encompasses various modifications to the
two-ended PMD measurement instrumentation configurations shown in
FIGS. 1-1K. Although these modifications may be applied separately,
certain implementations of the invention may include several such
modifications.
[0199] A person of ordinary skill in this art would be able,
without undue experimentation, to adapt the procedure for
calibrating the relative sensitivities of the two detectors 22B and
22C, as shown in FIG. 1G or 1K, including the losses induced by the
intervening coupler, etc., described hereinbefore with reference to
the two-ended PMD measurement of FIGS. 1G and 1K. That said, it
should be appreciated that, in the implementation of FIG. 1D,
calibration of the mean relative gain is not required; the measured
total power is independent of SOP, and there is no need for an
"absolute" calibration to directly measure absolute transmission
values; they can be obtained to within an unknown constant factor.
The subsequent normalization over the mean powers averaged over
SOPs, as described hereinbefore, eliminates the unknown factor.
[0200] Where the detection means 22 comprises a single detector 22A
(e.g., FIG. 1B) detecting only analyzed light, normalized powers
(or transmissions) can be obtained by computing an average of all
of the powers in first and second groups of powers, and dividing
each of the powers by the said average power to obtain first and
second groups of normalized powers, as described in detail
hereinbefore.
[0201] FIG. 1B illustrates PMD measurement instrumentation suitable
for determining DGD or PMD using normalized powers obtained in this
way. The PMD measurement illustrated in FIG. 1B is similar to that
illustrated in FIG. 1D but with coupler 21 and detector 22C
omitted. The data processor 34 will simply apply different
normalization equations.
[0202] Where a polarimetric head 45 is used (see FIG. 1H), several
(typically three) different polarization components of light
exiting from FUT 18 can be measured, either simultaneously or at
different times, dependent on the polarimetric-head design
[0203] It should be noted that the single-ended measurement
instrumentation of FIG. 3 could also be adapted to use a
polarimetric head 45 in its polarization-controller-and-analyzer
means 44, although this would likely be accompanied by a
significant reduction in dynamic range.
[0204] In the polarized broadband light source based two-ended PMD
measurement instrumentation shown in FIG. 1I, a tunable filter 27
is used to select light wavelength. This tunable filter can be
located after polarizer 20A (FIG. 1I) or before polarizer 20A. It
is normally preferable that the tunable filter be
polarization-insensitive. Normally, the tunable filter will be
operable to select different wavelengths at different times.
[0205] Although the tunable filter 27 in FIG. 1I need only exhibit
low or modest polarization-dependent loss (PDL), it should be noted
that, if the tunable filter 27 is highly polarization sensitive,
e.g. polarization-dependent loss (PDL) >20 dB, it may combine
the functions of polarizer 20A and (low or modest PDL) tunable
filter 27 in FIG. 1I.
[0206] In any of the above-described implementations, the input
I-SOP controller 14A and analyzer A-SOP controller 14B each operate
in such a manner that, for a given SOP of the light received at its
input (which can be any SOP on the Poincare Sphere), the SOP of the
light leaving its output (i.e. leaving either I-SOP 14A or A-SOP
14B) will be any other one of a number of substantially uniformly
distributed SOPs on the Poincare Sphere, whether the distribution
is of random or deterministic nature. Typically, the number of
input and output states of polarization is about 100-100,000, but
it could be any practical number allowing for a reasonable coverage
of the Poincare Sphere. However, it may also be possible to use
just one SOP for both the I-SOP and the A-SOP. It is noted that the
distribution of the SOPs need not, and generally will not, be truly
random; so "pseudo-random" might be a more appropriate term in the
case where a random distribution is indeed used for convenience
because it is easier and less expensive to implement than a uniform
grid of SOPs (the latter being in any case very susceptible to
movement of the FUT 18 during measurement).
[0207] The detection means 22, whether a single detector, a pair of
detectors, a filter plus detector, or a detector array, and the
sampling-and-averaging unit 32, may be as used in standard
commercial power meters that are known to a person skilled in this
art.
[0208] The control unit 30B may advantageously be a separate
computer. However, it is noted that a single computer could perform
the functions of the data processor 34 and the control unit
30B.
[0209] Various other modifications to the above-described
implementations may be made within the scope of the present
invention. For instance the tunable modulated light source 12 and
components of respective parts 44A and 44B of the
polarization-controller-and-analyzer means could be replaced by
some other means of providing the different polarization states of
the modulated light entering the FUT 18 and analyzing the resulting
light leaving the distal end of FUT 18.
[0210] The polarimetric head 45 used in the measurement
instrumentation shown in FIG. 1H, (typically comprising splitters
with three or four analyzers) analyzes more than one polarization
component of the signal or power approximately simultaneously, but
other similar configurations are feasible. Alternatively, an I-SOP
controller 14A may launch three or more pre-defined input SOPs of
light, for example corresponding to a Mueller set, which is well
known in the art. The polarimetric head 45 then may be used in
place of an A-SOP controller at the distal part 44B of the
polarization-controller-and-analyzer means and the detection
means.
[0211] It should be noted that each group is not limited to one
pair of modulated optical pulses or one pair of series of modulated
optical pulses. Indeed, it may use three or more different
closely-spaced wavelengths per group of powers, instead of the
minimally-required two closely-spaced wavelengths .lamda..sub.L and
.lamda..sub.U.
[0212] However, it should also be noted that more than one pair of
modulated optical pulses and more than one pair of light pulses
usually may not be required for two-ended overall PMD measurement
if one may know a rough PMD value of the FUT. Otherwise, such as
discussed previously for auto pre-scan, more than one pair of
modulated optical pulses or more than one pair of series of light
pulse may be used for the acquisition.
[0213] It should also be noted that a single DGD at one given
midpoint wavelength may be obtained by averaging over a large
number of random I-SOP and A-SOP settings for a given constant
midpoint wavelength having two closely-spaced wavelengths.
Therefore, the DGD as a function of wavelength in a given
wavelength range may also be obtained by measuring many individual
DGDs at different midpoint wavelengths within the given wavelength
range. The mean DGD and/or rms DGD may be then be computed
therefrom by averaging over all or most of these individual DGD
values at different wavelengths in the given wavelength range.
Alternatively, the rms DGD may also be computed from a mean-squared
difference that is obtained by averaging over wavelength and/or
SOP, without ever explicitly measuring the DGD at a particular
wavelength.
[0214] Although the above-described method of operation changes the
midpoint wavelength for each SOP, this is not an essential feature
of the present invention. While superior performance can be
obtained by covering a large wavelength range in order to obtain
the best possible average of DGD, as per the definition of PMD, a
PMD measurement embodying the present invention will work with no
bias and may provide acceptable measurements of PMD, with a
constant center-wavelength or even both constant input and output
SOPs and constant center-wavelength with one pre-defined wavelength
step (or frequency difference).
1.7 Embodiment (2)
Partial-DGD Measurement Employing Data-Carrying Signals and PMD
Estimation Derived Therefrom
1.7.1 Description of Hardware and Summary of Operating
Procedure
[0215] FIG. 2K shows a preferred implementation of an apparatus
suitable for measuring average partial DGD (DGD.sub.P). The SUT 60
carries modulated data of any modulation format (e.g. OOK, DPSK,
QPSK, etc.) for which the detected DOP is greater than zero, and,
preferably, exceeds 50%, and will usually encompass a spectral
extent roughly equivalent to its modulation symbol rate (i.e.
typically between 10-50 GHz), spaced by typically either 50 or 100
GHz from its nearest neighbor in an adjacent ITU channel. SUT 60 is
input into analyzer-and-detection means 101 (i.e. the PMD
monitor-and-analyzer) disposed at or adjacent e.g. a monitor port
tapped from an optical transmission line 24 or the distal end of an
optical path 24. As shown in FIG. 2K, the analyzer-and-detection
unit 101 normally comprises an A-SOP controller 12, a polarization
beam splitter (PBS) 14 serving as a polarization discriminating
means, tunable filter means comprising two tunable filters
(16A,16B), and two photodetectors (18A, 18B). In the preferred
implementation, the tunable filter means is usually disposed such
that the tunable filters (16A,16B) have approximately the same
passband width (which normally determine instrumental resolution
bandwidth--RBW), central passband wavelength and passband shape.
The A-SOP controller 12, tunable fibers A and B (16A,16B), and two
photo-detectors A and B (18A,18B), are controlled by control unit
30.
For most DWDM optical networks, a monitor port along the optical
link may extract portions of all signals (SUTs) corresponding to
the different spectrally-multiplexed ITU channels, but at the
distal end of the optical link, after the optical demultiplexer
(just before the Rx), there is usually only one extracted SUT
corresponding to a single ITU channel.
[0216] Under the coordination of control unit 30, the
sampling-and-averaging circuitry 34, in known manner, uses an
internal analog-to-digital converter to sample the corresponding
electrical signals from the detectors 18A and 18B as a function of
time, and the sampled signal is time-averaged over a portion of its
duration to provide a corresponding digital level. This portion is
chosen so as to avoid transient effects that might arise during the
measurement process, e.g. as the A-SOP is rapidly changed by the
A-SOP controller 12.
[0217] Variants of the instrument configuration of FIG. 2K are
illustrated in FIGS. 2I, 2M and 2H and will now be described
briefly.
[0218] The instrument illustrated in FIG. 2I is similar to that
illustrated in FIG. 2K but differs in that the polarizer 15 is used
instead of PBS 14 as a polarization-discrimination means (i.e.
analyzer), and only one tunable filter 16 and one photodetector 18
are employed.
[0219] FIG. 2M illustrates an alternative apparatus, a heterodyne
Optical Spectrum analyzer, which may be employed with methods of
this invention. An optical local oscillator 52, conveniently a
tunable laser, is disposed, via splitting and combining optics (56,
54A, 54B) so that portions of its polarized output are combined
with two orthogonal A-SOPs of the SUT at respective detectors 18A,
18B. Each detector (and associated pre-amplification stage--not
shown) then provides an electrical signal of the rf baseband, whose
spectrum effectively provides high-resolution spectral information.
As described in J. Jiang et al (op.cit), it is convenient to
electrical filter, via bandpass filters 38A,38B and rf power meters
36A, 36B), the polarization-diverse beat signal at pre-determined
rf spacing .DELTA..nu.. It should be appreciated that this spacing
is equivalent to the spacing of the "closely-spaced optical
frequencies" described in preferred embodiments of methods of this
invention.
[0220] In an alternate implementation shown in FIG. 2H a
spectrally-resolved polarimeter, e.g. tunable filter (TF) 16,
polarimetric head 20 and detection system 18E comprising detectors,
may be used, where the polarimetric head 20 may be disposed either
before or after TF 16. The polarimetric head 20 may be designed to
constitute a space-division polarimeter (i.e. normally employing a
separate detector for each portion of analyzed light) or a
time-division polarimeter (i.e. normally employing an analyzer
whose polarization axis varies very rapidly over orthogonal SOPs on
the Poincare sphere). Advantageously, the embodiment of FIG. 2H, in
conjunction with the method of this embodiment, may provide fast
and accurate DGD.sub.P measurement that could be rendered operable
to provide updated DGD.sub.P values on a time scale of a few ms or
less.
[0221] If the rapidity of DGD.sub.P determination is most critical
and cost of somewhat less importance, the polarization-diverse
configuration of FIG. 2K or the single-detector configuration of
FIG. 2I, may be operable to select the A-SOPs in a deterministic
manner. For instance, A-SOP controller 12 may be a polarization
state generator (e.g. PolaPal.TM. polarization state generator from
General Photonics Corp.), which can rapidly and successively
transform the SOP of the SUT signal 60 between a set of predefined
analyzer SOPs, preferably but not limitatively corresponding to
three orthogonal A-SOPs on the Poincare sphere) whilst the tunable
filters 16A, 16B are scanned in wavelength. For such
"deterministic" embodiments, it is preferable that the time
interval corresponding to acquisition of a set of these rapidly
switched analyzer states (A-SOP) be shorter than the time interval
required for the tunable filters 16A and 16B to scan over an
optical-frequency range equal to the passband of the filter (i.e.
RBW).
[0222] In another variant of the configuration of FIG. 2K or FIG.
2I, the A-SOP controller 12 may be a two-state polarization switch,
which for instance may rapidly transform the A-SOP between two
A-SOPs which are orthogonal on the Poincare sphere (e.g. A-SOPs
corresponding respectively to linear polarization at 0 and 45
degrees--not to be confused with "orthogonal" with respect to a
linear polarizer, for instance). The use of only these two A-SOPs
suffices if SUT depolarization, e.g. due to amplified spontaneous
emission (ASE) and signal depolarization, etc., is known or
negligible. Again, the time interval corresponding to the
acquisition of the two rapidly switched analyzer states (A-SOP) is
preferably shorter than the time interval required for the tunable
filters (16A,16B; 16) to scan over an optical-frequency range
approximately equal to the passband of the filter (i.e. RBW).
Although the aforedescribed two A-SOPs may have any known mutual
non-zero angle, it is preferable that they be orthogonal on the
Poincare Sphere, as this permits the third Stokes component to be
extracted based on the first two measured Stokes components
corresponding to orthogonal analyzer A-SOPs.
[0223] FIG. 11 shows an example of a practical application of such
instrument for measuring DGD.sub.P of live signals (SUTs). However,
this type of field measurement may also be employed to measure link
PMD, provided that: a) a plurality of spectrally multiplexed
signals (e.g. corresponding to a many DWDM channels) may be
detected; b) the respective transmitters are co-located (e.g. in
the same rack or within the same central office); c) the relative
SOPs among this multiplicity of signals launched (input) into the
fiber link are random (i.e. uncorrelated); and d) following
propagation through the fiber link, the DOP of these signals (i.e.
the corresponding SUTs) is greater than 0, and, preferably greater
than 50%. As indicated in FIG. 11, such a PMD determination
measurement can be carried out non-intrusively by simply extracting
("tapping") a small fraction of the power of the DWDM channels via
a monitor port. Note that such a monitor port may be located at any
location along the optical fiber link where there may be an
available monitor port, e.g. 26 or 27, or, alternatively, after the
optical DeMux filter the Rx side 28 (if additional optical
switching means--not shown--is provided to enable a portion of each
de-multiplexed DWDM channel to be detected). The DGD.sub.P-based
PMD instrument 101 may be located in any convenient location,
provided that there is an optical-fiber connection between the
monitor port (26; 27) and the input 10 to the instrument 101.
Advantageously, the method presented in this invention not only can
measure overall PMD of a fiber link but, if acquisitions are taken
at such monitor ports along the link, it also can be used to
identify and quantify potential high-PMD sections within the
link.
[0224] For a large number of randomly chosen SOP conditions of the
(transmitter) signal as it is launched into the fiber, the
"worst-case" DGD.sub.P of the SUT at a given wavelength is equal to
the DGD of the optical link at that same wavelength (neglecting any
second- or higher-order PMD effects). This behavior was
experimentally confirmed, as illustrated in FIG. 12A 201A. Sixteen
measured (average) DGD values were computed using
hereinbelow-described equation (24a) for corresponding sixteen
different launched input-SOPs, are shown in FIG. 12A 201A. The
maximum DGD.sub.P value is very close to the 18.5-ps DGD value of a
single high-birefringence fiber emulator (i.e. displaying "weak"
mode coupling) at that same wavelength as independently measured
with a "reference test method" (RTM--implemented in a model
FPMD-5600, EXFO Inc.). Each DGD.sub.P value presented in FIG. 12A
201A is computed from acquisitions employing 1000 random A-SOPs.
FIG. 12A 201B presents a histogram plot of the distribution of the
DGD.sub.P values corresponding to FIG. 12A 201A.
[0225] FIG. 12B 202 provides an indication of the dependence of the
DGD.sub.P measurement uncertainty on the number of different A-SOP
analyzer states used for each computed DGD.sub.P value. For
example, the measurement uncertainty (.sigma.) obtained from
sixteen different DGD.sub.P measurements, each having an A-SOP
number of 20, is indicated in FIG. 12B 36. Note that the
measurement uncertainty (.sigma.) is defined here as a measured
DGD.sub.P (always for sixteen measurements), each measurement
corresponding to a particular number of A-SOPs divided by the
"expected" DGDP value, where the "expected" value is assumed to be
that obtained using an A-SOP number of 1000. These measurements
were undertaken on a testbed employing the aforedescribed PMD
emulator having a fixed DGD value of 18.5 ps, and with a
commercially available polarization-diverse OSA instrument (i.e.
FTB-5240BP, EXFO Inc., which incorporates a polarization
controller/scrambler after its input), having the design
configuration depicted in FIG. 2K.
[0226] FIG. 13 203 is an example of three separate PMD
measurements, each corresponding to different launched-light SOPs
into sixteen different 50-GHz-spaced ITU-channel lightpaths, on a
test bed comprising an in-line (strong-mode-coupled) PMD emulator,
the average DGD value of which had been previously measured by a
reference test method (implemented in a model FPMD-5600, EXFO Inc.)
to be 5.44 ps between 1530 nm and 1610 nm. For each of the three
sets of launched SOPs, sixteen corresponding spectrally-averaged
DGD.sub.P values are determined. For all three sets of
measurements, the launched SOPs are the same for the six
spectrally-averaged DGDP measurements between 1545 and 1550 nm,
whereas the other ten spectrally-averaged DGD.sub.P measurements
have different (randomly oriented) launched SOPs, and for each of
the three sets, a respective PMD value was calculated (i.e. 5.32
ps, 4.91 ps and 5.56 ps, respectively). The average of these three
PMD measurements yields a PMD estimate of 5.26 ps, which differs by
only 3.2% in comparison with the RTM PMD value. (Although for each
channel, "average" DGD.sub.P rather than DGD.sub.P(.nu.) was used,
it should be appreciated that DGD.sub.P(.nu.) alternatively could
have also employed, leading to little change in the statistical
uncertainty of the PMD estimation.)
[0227] The preferred embodiments described hereinbefore are common
to principal aspects of this invention. However, the details of the
preferred embodiments, including details of their operation,
corresponding to each of these principal aspects will be described
in more detail in the next sub-sections.
1.7.2 Measurement of DGD.sub.P at a Particular Optical
Frequency
[0228] For monitoring and measuring DGD.sub.P as a function of
optical frequency (wavelength) in a narrow high bit-rate working
data-carrying signal (SUT) bandwidth, i.e., a measurement that is
always to be undertaken at approximately the same small particular
wavelength range of a signal bandwidth, however, such acquisition
can be for many SUTs in many channels, for example if a monitor
port 26 or 27 is used. As described in the "Background Art" section
hereinbefore, the DGD.sub.P is very sensitive to launch SOP and
time-varying environmental conditions, and consequently the
PMD-induced system penalty for the traffic signal also varies.
[0229] The A-SOP controller 12 may be operable to vary the SOP of
the SUT 60 continuously and slowly, or alternatively and
preferably, the A-SOP controller 12 may vary A-SOP in a discrete
and random fashion, where the resulting A-SOPs are approximately
uniformly distributed in the Poincare sphere. or alternatively, in
order to achieve fast DGD.sub.P monitoring or measurement of a
limited number (e.g. 3-6) of predetermined set of analysis states
may be used, e.g. four A-SOPs corresponding to four
equidistantly-spaced points on the Poincare sphere.
[0230] More specifically, for a particular measurement sequence k,
the light signal analyzed by the intervening polarization
discriminator, such as a polarization beam splitter (PBS) 14 or
polarizer 15, to be measured during a portion of time during which
light from the SUT 60 is detected, successively, at each of two
closely-spaced optical wavelengths, .lamda..sub.L.sup.(k) and
.lamda..sub.U.sup.(k), that are closely-spaced relative to each
other, during which portion of time the SOPs exiting the A-SOP
controller 12 is approximately constant. The midpoint wavelength of
this closely-spaced pair is defined as the average of the actual
optical frequencies of the SUT 60 lights, which to a very high
degree of approximation can be expressed in terms of wavelength as
.lamda..sub.mid.sup.(k)=(.lamda..sub.L.sup.(k)+.lamda..sub.U.sup.(k))/2.
(The labels L and U refer, for convenience and ease of
understanding, to "lowermost" and "uppermost" with respect to the
midpoint wavelength .lamda..sub.mid.sup.(k) and more accurately the
midpoint wavelength is expressed as
.lamda. mid ( k ) = 2 .lamda. L ( k ) .lamda. U ( k ) .lamda. L ( k
) + .lamda. U ( k ) . ) ##EQU00002##
[0231] The measured analyzed light signal is converted to an
electrical signal by the sampling-and-averaging means and
subsequently digitized before application to the data processor for
subsequent processing thereby.
[0232] The measurement sequence described above is repeated for K
different groups, each group corresponding to a different A-SOP
with the same or approximately the same SOP in the group. In
practice, K should be greater than 20 to 1000 to obtain
satisfactory results for random scrambling of the A-SOPs, or
preferably a limited number of predetermined set of analysis states
may be used.
[0233] If the expected DGD.sub.P to be measured is not roughly
known, it is possible that the selected optical-frequency
difference of the closely-spaced wavelength pairs for the
computation is, for instance, corresponding to an optimized
optical-frequency difference to permit accurate measurement of
DGD.sub.P value from the SUT 60. However, as mentioned above, in a
narrow DWDM channel, which may, for instance, only have a useable
optical passband width of approximately 35 GHz, it is not always
practical to select very different optical-frequency
differences.
[0234] Advantageously, in order to estimate, and partially
compensate for, the contribution of noise in the measurements,
"repeated measurements" are acquired for each group at the same two
closely-spaced wavelengths, these repeated measurements being in
principle substantially perfectly correlated to the "original"
measurements, in the absence of noise (i.e. identical if taken
under the same polarization analysis conditions, or complementary
if taken under orthogonal polarization conditions, e.g. via the two
outputs of a polarization beam splitter). In practice, such noise
may arise from any combination of ASE noise (from intervening
optical amplifiers in the fiber link 24), cross-phase-modulation
(XPM) induced signal depolarization, polarization noise (caused by
swaying aerial cables, for instance), optical-source power
fluctuations, uncorrelated electronic noise, etc. The procedure by
which this technique is used to improve the measurement sensitivity
and accuracy will be described in more detail hereinafter. It
should be appreciated however that this "repeated-measurement"
procedure is predicated upon the use of a "mean-square" average
(rather than, e.g. a simple arithmetic mean) of the acquired
.DELTA.T values corresponding to the detected power difference
between the closely-spaced wavelengths.
[0235] The computational method by which the data thus acquired can
be converted into a reliable DGD.sub.P monitoring and measurement,
including in the presence of significant ASE noise, nonlinear
polarization scattering, etc, will be described in more detail
hereinafter.
1.7.3 Measurement of Spectrally- and Non-Spectrally-Averaged
DGD.sub.P Using DGD.sub.P(.nu.)
[0236] By repeatedly applying the above-described method of
measuring DGD.sub.P at a particular wavelength over a prescribed
wavelength range in a SUT 60 bandwidth, it is possible to
accurately estimate the PMD-induced PMD power penalty of a SUT 60
related to the system performance of a network according to a
either "mean" or "rms" DGD.sub.P value or signal
spectrally-weighted "mean" or "rms" DGD.sub.P value over a SUT
bandwidth from the said obtained DGD.sub.P as a function of
wavelength.
[0237] Once a set of DGD.sub.P(.lamda.) values have been obtained
as described above and a light power spectrum S(.lamda.) of a SUT
60 has been extracted, it is straightforward to compute either
means or rms DGD.sub.P or a spectrally-weighted average DGD.sub.P
from the different values of DGD.sub.P(.lamda.) obtained within the
prescribed SUT 60 bandwidth wavelength range.
[0238] Moreover, it is also possible to estimate the PMD of the
optical path (i.e. lightpath) in the DWDM network by either or both
of the "rms" or the "mean" DGD.sub.P (without any weighting) from
the said obtained DGD.sub.P as a function of wavelength, and
preferably, the wavelengths should be approximately uniformly
distributed across a wavelength range, which most preferably
consists of many `discontinuous` small wavelength regions from a
number of different SUTs bandwidths located along the ITU channel
grid (e.g. having spacings of either 50 or 100 GHz).
1.7.4 Measurement of DGD.sub.P Using Rapid Wavelength Sweeping
[0239] A preferred approach (see FIG. 2K) for measuring DGD.sub.P
at each wavelength, especially an average (mean or rms) DGD.sub.P
value or a signal spectral weighted average DGD.sub.P value over a
prescribed wavelength range in a SUT bandwidth is to use a rapidly
wavelength sweeping by a tunable narrow bandpass filter, e.g. from
an OSA with a polarization controller 12 for the A-SOP setting, or
other similar technique, e.g. a polarization-diverse scanning
monochromator, where A-SOP from an output polarization controller
12 varies little or not at all during the sweep. If the detection
electronics are sufficiently rapid, this "spectral acquisition
step" will provide a quasi-continuum of detected
polarization-analyzed transmitted coherent optical power data as a
function of optical frequency. In the subsequent data analysis, any
desired closely-spaced wavelength step could be selected. Of
course, if A-SOP or the state of polarization of a SUT varies
slightly during the sweep, provided that the A-SOP or signal light
polarization does not vary significantly between any two
closely-spaced wavelengths in the sweep, this would further affect
the accuracy of the DGD.sub.P monitoring and measurement. However,
such impacting can be reduced by an averaging over many A-SOPs.
Furthermore, repeating this procedure with multiple sweeps with a
approximately uniform A-SOP distribution will further improve its
accuracy and also enable relatively rapid DGD.sub.P monitoring. For
example, it may be envisaged that a DGD.sub.P value having an
acceptable level of uncertainty be obtained with only 4-6
A-SOPs/scans of tunable filters 16A and 16B (e.g. by an OSA).
[0240] By applying the above-described method of measured DGD.sub.P
at each wavelength of the invention over a SUT bandwidth with
measured signal light power spectrum, it is possible to estimate
the polarization mode dispersion (PMD) induced power penalty of a
SUT 60 related to the system performance of a network according to
either the "mean" or "rms" or signal spectral weighted "mean" or
"rms" DGD.sub.P value from the obtained DGD.sub.P as a function of
wavelength. It is also possible to estimate the PMD of the
lightpath in the DWDM network by either or both of the "mean" or
the "rms" DGD.sub.P (without any weighting) from the said obtained
DGD.sub.P as a function of wavelength for a SUT (bandwidth) and
preferably over a number of different SUT bandwidths.
1.7.5 Various Modifications to the DGD.sub.P Monitoring and
Measurement Means
[0241] In any of the above-described implementations, the output
SOP controller 12 operates in such a manner for A-SOP to have
substantially uniformly distributed SOPs on the Poincare Sphere,
whether the nature of the distribution is random or
deterministic.
If the distribution is random, the number of analyzed states
(A-SOP) should be sufficiently large to ensure reasonable coverage
on the Poincare sphere. It should be appreciated that the
distribution of the SOPs need not be, and generally will not be,
truly random; so "pseudo-random" might be a more appropriate term
in the case where a random distribution is indeed used for
convenience because it is easier and less expensive to implement
than a uniform grid of SOPs.
[0242] If the distribution is deterministic, a smaller number of
predetermined set of A-SOPs may be employed, which should be
uniformly distributed on the Poincare sphere. The minimum number of
A-SOPs which can be uniformly distributed, i.e. equidistantly
spaced, on the Poincare Sphere, is four. It should be appreciated
that a (well-calibrated) polarimetric head, for which the A-SOPs
normally are mutually-orthogonal (e.g. 0-degree linear, 45-degree
linear, and left-circular), provides a deterministic distribution
of six equidistantly spaced points on the Poincare sphere, since,
for each of the aforementioned mutually-orthogonal A-SOPs, the
respective antipodal states are automatically determined.
[0243] The detection-system means, whether comprising a single
detector, a pair of detectors, a filter plus detector, or a
detector array, and the sampling-and-averaging circuitry unit, may
be as used in standard commercial power meters that are known to a
person skilled in this art.
[0244] The control unit may advantageously be a separate computer.
However, it is noted that a single computer could perform the
functions of the data processor and the control unit.
[0245] Where a polarimetric head 20 is used, several (typically
three) different polarization components of light comprising SUT 60
can be measured, either simultaneously or at different times,
dependent on the design of the polarimetric head 20.
[0246] The polarimetric head 20 used in the instrument shown in
FIG. 2H, (typically splitters with three or four analyzers and
photodetectors in parallel), measures more than one polarization
component of the signal or power approximately simultaneously, but
other similar configurations are feasible, e.g. to use a
polarization modulation for in a variant of the implementation of
FIG. 2K where polarization modulation period is much shorter than
that of a required scanning time of tunable filters cross a SUT
bandwidth and polarization modulation may switch between several
predefined analysis states, e.g. three orthogonal A-SOPs.
[0247] It should also be noted that a single DGD.sub.P at one given
midpoint wavelength may be obtained by averaging over a large
number of randomly output SOPs for a given constant midpoint
wavelength having two closely-spaced wavelengths. Therefore, the
DGD.sub.P as a function of wavelength in a given wavelength range
may also be obtained by measuring many individual
[0248] DGD.sub.Ps at different midpoint wavelengths within the
given wavelength range of a signal bandwidth. The
(non-spectral-weighted) mean DGD.sub.P and/or rms DGD.sub.P may be
then be computed therefrom by averaging over all or most of these
individual DGD.sub.P values at different wavelengths for several or
many different live channels SUT 60. Alternatively, the rms or mean
average value may also be computed from a mean-squared difference
or mean difference that is obtained by averaging over SUT
wavelengths and/or SOP, without ever explicitly measuring the
DGD.sub.P at a particular wavelength.
1.8 Embodiment (3)
Single-Ended Overall PMD Measurement
1.8.1 Description of Hardware and Summary of Operating Mode
[0249] For the "single-ended" embodiments (3) and (4), all of the
active components of the measurement instrumentation are at the
proximal end of the FUT, and hence the two control units may be
combined into a single control unit. (In single-ended embodiments
where the "overall PMD" is being measured, a highly-reflective
element may be connected to the distal end of the FUT to improve
the dynamic range of the measurement.)
[0250] As mentioned hereinbefore, if DGD/PMD is to be measured from
one end of the FUT 18, both parts of the
polarization-controller-and-analyzer means 44 and the processing
means 40 can be co-located with the light source means 42 at the
proximal end of the FUT 18, together with a single control unit 30
performing the control functions of the control units 30A and 30B
in the two-ended embodiments. This co-location enables certain
parts to be combined, their components being modified as
appropriate. Single-end measurement-instrumentation configurations
will now be described with reference to FIGS. 3 to 3G, which
correspond to FIGS. 1 to 1G for the two-ended
measurement-instrumentation configurations.
[0251] Thus, FIG. 3 shows a tunable OTDR-based single-ended overall
PMD measurement instrumentation similar to the two-ended
measurement instrumentation of FIG. 1 but in which the light source
means 42 and the polarization-controller-and-analyzer means 44 are
co-located at the proximal end of the FUT 18 and share a
backreflection extractor 52 which connects the input I-SOP
controller 14A and the analyzer A-SOP controller 14B to the FUT 18
via connector 16. The backreflection extractor 52 is bidirectional
in that it conveys the light from the I-SOP controller 14A to the
FUT 18 and conveys the backreflected light from the FUT 18 to the
A-SOP controller 14B. As was the case in FIG. 1, the tunable pulsed
light source 12 is connected to I-SOP controller 14A by PMF
29A--
[0252] A fiber patchcord with either a PC (FC/PC or FC/UPC)
connector or a fiber pigtailed mirror 50 is connected to the distal
end of FUT 18 to provide a localized reflector at the distal end of
the FUT 18. In fact, any type of reflector may be used if it can
reflect the light from the end of FUT 18 back into the measuring
instrumentation.
[0253] The other change, as compared with FIG. 1, is that the
measurement instrumentation shown in FIG. 3 has a single control
unit 30 which controls the tunable pulsed light source 12, the
I-SOP controller 14A and A-SOP controller 14B, the
sampling-and-averaging unit 32 and the data processor 34.
Otherwise, the components of the measurement instrumentation shown
in FIG. 3 are similar or identical to those of the measurement
instrumentation shown in FIG. 1 and operate in a similar manner.
The signal processing, however, must be adapted so as to allow for
the fact that the extracted light comprises light from the light
source 12 that travelled the FUT 18 for at least part of its length
and then was backreflected and travelled the same path back to the
backreflection extractor 52.
[0254] It should be noted that the term "tunable OTDR" mentioned
hereinbefore in the context of this single-ended overall PMD
measurement instrumentation is not limited to a fully functional,
commercial-type OTDR, but rather refers to an apparatus that can
provide optical pulses for injection into a fiber, and subsequently
detect and perform time-gate averaging only on those pulses
corresponding to reflections corresponding to a particular time
delay (i.e. distance corresponding to the end of the fiber).
Nonetheless, the use of an OTDR permits the FUT end to be
identified and the FUT length measured, thereby enabling the
time-gate window to be correctly selected.
[0255] It should be noted that the various modifications and
alternatives described with reference to the two-ended measurement
instrumentation of FIGS. 1 to 1H could, for the most part, be
applied to the single-ended measurement instrument shown in FIG. 3.
Such modified configurations of the single-ended measuring
instrument will now be described briefly with reference to FIGS. 3B
to 3G.
[0256] In the measurement instrumentation shown in FIG. 3B, the
light source means 42 and the polarization-controller-and-analyzer
means 44 share a polarization discriminator (polarizer) 20A and a
backreflection extractor comprising either a circulator or coupler
52A Like the polarizer 20A and circulator/coupler 52A, the I/A-SOP
controller 14 is used bidirectionally in the sense that it conveys
input light towards the FUT 18 via the connector 16 and
backreflected light returning from the FUT 18 in the opposite
direction. The I/A-SOP controller 14 hence combines the functions
of the separate I-SOP controller 14A and A-SOP controller 14B
depicted in FIG. 3, but where the scrambling is now necessarily
highly correlated for light traversing it in either direction. The
circulator/coupler 52A is connected to the light source means 42,
specifically tunable pulsed light source 12, by PMF 29A and to the
input of the polarization discriminator (polarizer) 20A by a second
PMF 29B. The circulator/coupler 52A conveys the backreflected light
to a detection system/means which, in FIG. 3B, is shown as a single
detector 22A. The output of the polarization discriminator
(polarizer) 20A is connected to the input of the bidirectional
I/A-SOP controller 14 by regular fiber. Other components are the
same as in FIG. 3.
[0257] The measurement instrumentation shown in FIG. 3D is similar
to that shown in FIG. 3B in that the light source means 42
comprises tunable pulsed light source 12, and shares a
backreflection extractor 52A and polarizer 20A with bidirectional
I/A-SOP controller 14 of the polarization-controller-and-analyzer
means 44. The backreflection extractor is shown as a
circulator/coupler 52A. However, the measurement instrumentation of
FIG. 3D differs from that of FIG. 3B because the
polarization-and-analyzer means 44 comprises a coupler 21 connected
between the backreflector extractor polarizer 20A and the I/A-SOP
controller 14, this coupler extracting a portion of non-analyzed
light. In addition, the detection means comprises two detectors 22B
and 22C, the former connected to the output of the
circulator/coupler 52A and the latter connected to an output of the
coupler 21. Respective outputs of the detectors 22A and 22B are
connected to the sampling-and-averaging unit 32.
[0258] As before, the input light from the light source means 42 is
injected into FUT 18 via a fiber connector 16 and backreflected
light reflected from any localized reflection (such as Fresnel
reflection) from the distal end 50 of FUT 18 returns back to the
polarization-controller-and-analyzer means 44 and enters the
I/A-SOP controller 14 in the reverse direction, following which the
light returns back to the coupler 21 which passes one portion via
the polarizer 20A to detector 22B via the circulator/coupler 52A
and a second portion directly to detector 22C.
[0259] In use, in the measurement instrumentation shown in FIG. 3F,
the input light from light source means 42 is launched into FUT 18
via fiber connector 16 and backreflected light caused by any
localized reflection (such as Fresnel reflection from the distal
end 50 of FUT 18) returns back to
polarization-controller-and-analyzer means 44 via fiber connector
16, entering the I/A-SOP controller 14 in the reverse direction.
Its I/A-SOP is transformed by the I/A-SOP controller (or scrambler)
14, following which the light is decomposed by the polarization
discriminator, specifically a PBS 20C, into two components having
orthogonal SOPs, typically linear SOPs at 0- and 90-degree relative
orientations. Detector 22C is connected to one of the two outputs
of the PBS 20C to receive one of these orthogonal components and
the backreflection extractor 52 (e.g. circulator/coupler) is
connected to the other output (with respect to backreflected light
from the FUT 18). Detector 22B is in turn connected to that output
port of the backreflection extractor 52 that transmits light from
the PBS 20C, so as to receive the other orthogonal component. Once
suitably calibrated to take into account the relative detector
efficiencies, wavelength dependence, circulator loss, etc., as will
be described hereinafter, the sum of the detected powers from
detectors 22B and 22C is proportional to the total backreflected
power (S.sub.0). The backreflected light may be detected
approximately simultaneously by detectors 22B and 22C.
[0260] In the measurement instrumentation shown in FIG. 3C, the
backreflected light reflected from any localized reflection from
the distal end 50 of FUT 18 returns back to the I/A-SOP controller
14 in the reverse direction, following which the light returns back
through the polarizer 20A and then is divided two parts by coupler
21. The detectors 22B and 22C are connected to two outputs of
coupler 21 to produce two repeated measured powers; detector 22B
being connected by way of circulator/coupler 52A.
[0261] It should be noted that simultaneously detecting the
backreflected light with two detectors 22B and 22C may not be
always necessary. It may also be detected at slightly different
time.
[0262] Also note that one detector with one optical switch 23 may
also be used. In this case, two detectors 22B and 22C may be
replaced by one detector 22A plus one optical switch 23 (FIGS. 3E
and 3G). The optical switch 23 is used to route the backreflected
light from different optical paths, either from circulator (or
coupler) 52A or the PBS 20C (FIG. 3G) or the coupler 21 (FIG. 3E),
into the same detector and thereby the backreflected light from
different optical paths may be detected at different times.
[0263] The control unit 30 not only controls the tunable laser
light source 12, but also controls the sampling and averaging
unit/circuitry 32, in known manner, specifically to use an internal
analog-to-digital converter to sample the corresponding electrical
signals from the detector 22 as a function of time to obtain the
corresponding electrical response signals. The electrical response
signals then may be sampled and averaged to provide the mean
response pulse for a particular series of light pulses, and the
backreflected light power for that series obtained by averaging
said mean response pulse over a substantial portion of its duration
to provide a backreflected light power. This procedure is repeated
resulting in a plurality of backreflected light powers. The said
duration represents a time window for averaging (or time gate) and
may depend upon the pre-filtering of the sampling-and-averaging
electronics. The resulting averaged powers are used by data
processor 34 to derive the DGD or PMD value, i.e., the differential
group delay (DGD) or polarization mode dispersion (PMD) of the FUT
18 from its distal end or any other connectors. It will be
appreciated that the usual conversions will be applied to convert
time delay to distance according to refractive index to obtain the
length of fiber.
[0264] In addition to controlling the sampling-and-averaging
circuit 32, the control unit 30 controls the wavelength of the
tunable pulsed laser source 12 and the I/A-SOP selected by I/A-SOP
controller 14. More specifically, for each setting k of the I/A-SOP
controller 14, the control unit 30 causes the light backreflected
power to be measured for at least one pair of wavelengths
.lamda..sub.L.sup.(k) and .lamda..sub.U.sup.(k), respectively, that
are closely-spaced relative to each other. The midpoint wavelength
of the pair of series of light pulses is defined as the average of
the actual wavelengths of the series of light pulses, i.e.,
.lamda..sub.k=(.lamda..sub.L.sup.(k)+.lamda..sub.U.sup.(k))/2. (The
labels L and U refer, for convenience and ease of understanding, to
"lower" and "upper" with respect to the midpoint wavelength
.lamda..sub.k).
[0265] It should be appreciated that, where the group comprises one
or more than one pair of series of light pulses, the midpoint
wavelength as defined above in fact differs for each pair in the
group.
[0266] The one, or more than one, pair of wavelengths in one group
may also be used to measure the powers of the backreflections from
the localized reflection at the distal end of FUT and then to
extract PMD values for the FUT 18. However, it may not be necessary
to use more than one pair of wavelengths for the single-ended PMD
measurement unless for auto pre-scan acquisition (see more detailed
discussion about auto pre-scan below). An optimal pair of
wavelengths may satisfy the relationship
PMD.sub.FUT.about..alpha..sub.L(.pi..delta..nu.).sup.-1, where
.nu..sub.L.sup.(k)-.nu..sub.U.sup.(k)=.delta..nu., and
.nu..sub.L.sup.(k) and .nu..sub.U.sup.(k) correspond to the pair of
wavelengths .lamda..sub.L.sup.(k) and .lamda..sub.U.sup.(k) under
.nu.=c/.lamda. where c is light speed in vacuum.
[0267] It must also be appreciated that the center wavelength is
only a conceptual definition, defined only for the purpose of
facilitating description when a group comprises more than two
wavelengths. In the limit where a group comprises only two
wavelengths, it is of course equivalent to the "midpoint
wavelength" defined hereinbefore. Center wavelength is not needed
anywhere in the computations, and there is no need for accurately
"centering" the group on some target center wavelength since the
latter is defined as the midpoint wavelength, and there is no need
to set the laser wavelength at the center wavelength. Only the
knowledge of the step(s) is needed, i.e., the difference between
any pair that is used in the computations of cumulative PMD,
irrespective of the center wavelength.
[0268] The I/A-SOP controller 14 sets the different I-SOPs and
A-SOPs in a pseudo-random manner, such that the points
conventionally representing SOPs on the Poincare sphere are
uniformly-distributed over the surface of said sphere, whether the
distribution is random or a uniform grid of points.
[0269] Before the tunable-OTDR-based single-ended overall PMD
measurement procedure is described in more detail, and with a view
to facilitating an understanding of such operation, the theoretical
basis will be explained, it being noted that such theory is not to
be limiting.
1.9 Various Modifications to the Single-Ended PMD Measurement
Means
[0270] Implementations of the "single-ended overall-PMD"
measurement embodiment encompass various modifications to the
measurement instrument shown in FIG. 3. For example, as illustrated
in FIG. 12A, in the light source means 42, the PMF 29A may be
replaced by a non-polarization-maintaining fiber connecting the
tunable pulsed laser source 12 directly to the input of
backreflection extractor 52, (the I-SOP controller 14A shown in
FIG. 3 being omitted).--
[0271] If the optical path between the output of tunable pulsed
light source means 12 and the input of the polarization
discriminator 20 (e.g. PBS in FIG. 3F) is polarization-maintaining,
the backreflection extractor of FIG. 3F would conveniently comprise
either a polarization-maintaining circulator or a
polarization-maintaining coupler (e.g., a 50/50 coupler). The
circulator is preferred, however, because it gives about 3 dB more
dynamic range than a 50/50 coupler.
[0272] It is also envisaged that the polarization discriminator 20
could be a polarizer or polarizer and coupler, as shown in FIGS. 3B
and 3C. In that case, the detector 22C would be connected to the
coupler 21 to receive backreflected light that is not
polarization-dependent.
[0273] If the optical path between the output of the tunable pulsed
laser source 12 and the input of the polarization discriminator,
e.g. polarizer 20A and polarization beam splitter (PBS) 20C, is not
polarization maintaining, the backreflection extractor, i.e.,
coupler or circulator 52A, need not be
polarization-maintaining.
[0274] A patchcord with either a FC/PC (or FC/UPC) connector or a
fiber-pigtailed mirror may be connected at the distal end of FUT to
create a localized reflection for measuring an overall PMD from the
FUT.
[0275] The light pulse length (or, equivalently duration) from the
tunable OTDR is usually preferably chosen to be long, for example
from 1 to over 20 .mu.s, but a short pulse length may also be
applied.
[0276] Instead of PBS 20C in FIG. 3F, the polarization
discriminator 20 may comprise a polarizer 20A and coupler 21
combination (FIG. 3D), at the expense of approximately 3-dB dynamic
range for the case of a 50/50 coupler. The second detector 22C
(FIG. 3D) is connected to one of the arms of the coupler 21 so as
to detect a fraction of the (non-analyzed) backreflected light for
processing to deduce the total backreflected power of the
pulses.
[0277] A person of ordinary skill in this art would be able,
without undue experimentation, to adapt the procedure described
hereinbefore for calibrating the relative sensitivities of the two
detectors A and B (22B and 22C), including the losses induced by
the intervening circulator or coupler, etc., for use with the
single-ended overall PMD measurement instrument of FIG. 3F. It
should be appreciated that, in the embodiment of FIG. 3D,
calibration of the mean relative gain is not required; the measured
total power is independent of SOP, and there is no need for an
"absolute" calibration to directly measure absolute transmission
values; they can be obtained to within an unknown constant factor.
The subsequent normalization over the mean traces averaged over
SOPs, as described hereinbefore, eliminates the unknown factor.
[0278] It is envisaged that, where the detection means 22 comprises
a single detector 22A (FIG. 3B), normalized powers can be obtained
by computing an average of all of the powers in first and second
groups of powers, and dividing each of the powers by the said
average power to obtain first and second groups of normalized
powers, as described in detail hereinbefore.
[0279] FIG. 3B illustrates a single-ended PMD measurement suitable
for obtaining the PMD using normalized powers obtained in this way,
which is similar to that illustrated in FIG. 3D but with coupler 21
and detector B 22C omitted. The data processor 34 will simply use
the different set of normalization equations.
[0280] In any of the above-described embodiments, the operation of
the I/A-SOP controller 14 is such that, for a given SOP of the
light (which can be any SOP on the Poincare Sphere) received at its
input, the SOP of the light leaving its output will be any one of a
number of substantially uniformly distributed SOPs on the Poincare
Sphere, whether the distribution is of random or deterministic
nature. Typically, the number of output states of polarization is
about 100-500, but it could be any practical number. However, it is
possible to use one I/A-SOP controller (rather than two SOP
controllers for the two-ended PMD measurement as shown in FIG. 1).
It is noted that the distribution of the SOPs need not, and
generally will not, be truly random; so "pseudo-random" might be a
more appropriate term in the case where a random distribution is
indeed used for convenience because it is easier and less expensive
to implement than a uniform grid of SOPs.
[0281] The detector means 22, whether a single detector or a pair
of detectors, and the sampling-and-averaging unit 32, may be the
same or similar to those employed in standard commercial OTDRs that
are known to a person skilled in this art.
[0282] Where the polarization discriminator 20 comprises a
polarizer 20A and coupler 21 combination rather than a PBS 20C,
there will be a penalty of approximately 3-dB dynamic range (for
the case of a 50/50 coupler). Hence, a circulator is generally
preferred, although in many cases such reduced power may not be
critical for the measurement.
[0283] The control unit 30 may advantageously be a separate
computer. However, it is noted that a single computer could perform
the functions of the data processor 34 and the control unit 30.
1.10 Embodiment (4)
Single-Ended Cumulative PMD Measurement
[0284] The polarization-sensitive optical time domain reflectometer
(POTDR) illustrated in FIG. 4 comprises tunable pulsed light source
means 12, bidirectional polarization controller means 14
(conveniently referred to as an I/A-SOP controller means),
sampling-and-averaging unit 32 and data processor means 34, all
controlled by a control unit 30, and detection means 22 comprising
first and second detectors A and B, 22B and 22C, respectively. The
tunable pulsed light source means 12 is coupled to a polarization
maintaining fiber (PMF) 29A for producing light pulses for
launching into a fiber-under-test (FUT) 18 from connector 16 via
the I/A-SOP controller means 14, which, as explained later, also
receives corresponding backreflected light from the FUT 18 via
connector 16.
[0285] The light source means 42 and
polarization-controller-and-analyzer means 44 comprise a
backreflected light extractor, specifically a
polarization-maintaining circulator 52 in FIG. 4, a polarization
discriminator (PD) means 20, specifically a polarization beam
splitter (PBS) in FIG. 4, and an input and analyzer-SOP controller
(or scrambler) I/A-SOP 14. The circulator 52 is coupled to the
input of PBS 20 by a second PMF 29B so that the optical path from
the tunable laser source 12 to the PBS 20 is
polarization-maintaining. Preferably, single-mode fiber is used to
optically couple the PBS 20 to the I/A-SOP controller (or
scrambler) 14.
[0286] Backreflected light caused by Rayleigh scattering and, in
some cases, discrete (Fresnel) reflections, from the FUT 18 enters
the I/A-SOP controller 14 in the reverse direction. Its SOP is
transformed by the I/A-SOP controller 14, following which the light
is decomposed by the PBS 20 into two components having orthogonal
SOPs, typically linear SOPs at 0- and 90-degree relative
orientations. The first detector 22C is connected to one of the two
outputs of the PBS 20 to receive one of these orthogonal components
and the circulator 52 is connected to the other output (with
respect to backreflected light from the FUT 18). The second
detector 22B is in turn connected to that output port of the
circulator 52 that transmits light from the PBS 20, so as to
receive the other orthogonal component. Once suitably calibrated to
take into account the relative detector efficiencies, wavelength
dependence, circulator loss, etc., as will be described
hereinafter, the sum of the detected powers from detectors 22B and
22C is proportional to the total backreflected power (S.sub.0).
[0287] Under the control of control unit 30, which also controls
the tunable laser source 12, the sampling-and-averaging unit 32, in
known manner, uses an internal analog-to-digital converter to
sample the corresponding electrical signals from the detectors 22B
and 22C as a function of time to obtain the corresponding
electrical impulse response signals, then averages the
impulse-response signals corresponding to a particular series of
light pulses to produce an OTDR trace for that series. The
resulting OTDR traces are used by a data processor 34 to derive the
cumulative PMD curve PMD(z), i.e., the polarization mode dispersion
(PMD) as a function of the distance z along the FUT 18 from its
proximal end, that is the end which is coupled to the
polarization-controller-and-analyzer means 44. It will be
appreciated that the usual conversions will be applied to convert
time delay to distance according to refractive index.
[0288] In addition to controlling the sampling and averaging
circuit 32, the control unit 30 controls the wavelength of the
tunable pulsed laser source 12 and the I-SOP and A-SOP couple
selected by I/A-SOP controller 14. More specifically, for each
setting k of the I/A-SOP controller 14, the control unit 30 causes
the backreflected power to be measured at at least one pair of
wavelengths .lamda..sub.L.sup.(k) and .lamda..sub.U.sup.(k),
respectively, that are closely-spaced relative to each other. The
midpoint wavelength of the pair of series of light pulses is
defined as the average of the actual wavelengths of the series of
light pulses, i.e.,
.lamda..sub.k=(.lamda..sub.L.sup.(k)+.lamda..sub.U.sup.(k))/2. (The
labels L and U refer, for convenience and ease of understanding, to
"lower" and "upper" with respect to the midpoint wavelength
.lamda..sub.k).
[0289] It should be appreciated that, where the group comprises
more than one pair of series of light pulses, the center wavelength
as defined above in fact differs for each pair in the group. It
must also be appreciated that the center wavelength is only a
conceptual definition, and was defined only for the purpose of
facilitating description of the basic one pair implementation. It
is not needed anywhere in the computations, and there is no need
for accurately "centering" the pair on some target center
wavelength since the latter is defined as the mean of the actual
pair. Nor is the laser wavelength set at the center wavelength.
Only the knowledge of the step is needed, i.e., the difference
between any pair that is used in the computations of cumulative
PMD, irrespective of the center wavelength, even if it were to be
random and unknown.
[0290] The I/A-SOP controller 14 sets the different (I-SOP, A-SOP)
couples in a pseudo-random manner, such that the points
conventionally representing SOPs corresponding to each member of
the couple are uniformly distributed over the surface of the
Poincare sphere, whether the distribution is random or a uniform
grid of points. Before the operation of the POTDR is described in
more detail, and with a view to facilitating an understanding of
such operation, the theoretical basis will be explained, it being
noted that such theory is not to be limiting.
Various Modifications to the Single-Ended Cumulative PMD
Measurement Means
[0291] The invention encompasses various modifications to the
embodiment shown in FIG. 4.
[0292] If the optical path between the output of tunable pulsed
light source means 12 and the input of the polarization
discriminator 20 is polarization-maintaining, the
polarization-maintaining circulator 18 in FIG. 4 could be replaced
by a polarization-maintaining coupler (e.g., a 50/50 coupler). The
circulator is preferred, however, because it gives about 3 dB more
dynamic range than a 50/50 coupler.
[0293] If the optical path between the output of the tunable pulsed
laser source 12 and the input of the polarization discriminator 20
is not polarization maintaining, the backreflection extractor,
i.e., coupler or circulator 52 need not be
polarization-maintaining.
[0294] Instead of a PBS for the polarization discriminator 20, the
polarization discriminator 20 may comprise a polarizer 20A and
coupler 21 combination, as shown in FIG. 4B, at the expense of
approximately 3-dB of dynamic range for the case of a 50/50
coupler. The detector 22C is connected to one of the arms of the
coupler 21 so as to detect a fraction of the backreflected light
for processing to deduce the total backreflected power of the
pulses.
[0295] In the POTDR of FIG. 4, an analogous procedure to that
described above with respect to the embodiment of FIG. 4 could then
be carried out, although not required as stated above, to calibrate
the relative sensitivities of the two detectors 22B and 22C,
including the losses induced by the intervening circulator or
coupler, etc.
[0296] A person of ordinary skill in this art would be able,
without undue experimentation, to adapt the calibration procedure
described hereinbefore with reference to the POTDR of FIG. 4 for
use with the embodiment of FIG. 4. It should be appreciated that,
in the embodiment of FIG. 4B, calibration of the mean relative gain
is not required; the measured total power is independent of SOP,
and there is no need for an "absolute" calibration to directly
measure absolute transmission values; they can be obtained to
within an unknown constant factor. The subsequent normalization
over the mean traces averaged over SOPs, as described hereinbefore,
eliminates the unknown factor.
[0297] It is envisaged that the detection means 22 might comprise a
single detector and normalized OTDR traces be obtained by computing
an average of all of the OTDR traces in first and second groups of
OTDR traces, and dividing each of the OTDR traces by the said
average OTDR trace, point by point, to obtain first and second
groups of normalized OTDR traces, as described in detail
hereinbefore.
[0298] FIG. 4A illustrates a POTDR suitable for obtaining the PMD
using normalized OTDR traces obtained in this way. The POTDR
illustrated in FIG. 4A is similar to that illustrated in FIG. 4B
but with coupler 21 and detector B 22C omitted. The data processor
34 will simply use the different normalization equations given in
the Method of Operation provided hereinbefore.
[0299] In any of the above-described embodiments, the operation of
the I/A-SOP controller 14 is such that, for a given SOP of the
light (which can be any SOP on the Poincare Sphere) received at one
end, the SOP of the light leaving the other end will be any one of
a number of substantially uniformly distributed SOPs on the
Poincare Sphere, whether the distribution is of random or
deterministic nature. The number of I-SOPs and A-SOPs is preferably
greater than 10, in each case, and typically is about 100-200 for
high quality results; but it could be any practical number. It is
noted that the distribution of each of the I-SOPs and A-SOPs need
not, and generally will not, be truly random; so "pseudo-random"
might be a more appropriate term in the case where a random
distribution is indeed used for convenience because it is easier
and less expensive to implement than a uniform grid of I-SOPs and
A-SOPs.
[0300] Although it is preferred to simultaneously measure the two
orthogonal polarization components simultaneously with respective
two detectors, it is envisaged that the two detectors in the
embodiments of FIGS. 4 and 4B could be replaced by one detector
plus one optical switch. The optical switch is used to route the
two orthogonal polarization components (FIG. 4) or to route the one
output from polarizer and another output directly from coupler
(FIG. 4B) of the backreflected light to the same detector, for
example alternately, so that two orthogonal polarization components
or one output from polarizer and another output directly from
coupler of the backreflected light can be detected sequentially by
the same detector.
[0301] A normalized OTDR trace for that series of light pulses
would be obtained by dividing at least one of the OTDR traces
corresponding to the two detected different polarization components
for that series by the sum of the OTDR traces corresponding to the
two detected different polarization components for that series.
This alternative may be used regardless of whether the
polarization-controller-and-analyzer means comprises a PBS or a
coupler. Any modification to the normalization and processing is
expected to be mirror and within the common general knowledge of a
person skilled in this art.
[0302] Alternatively, such an arrangement of one detector plus one
optical switch could be used to detect one polarization component
and the total optical power sequentially by the same detector. As
before, the optical switch would route one polarization component
and the total reference optical power to the same detector, and the
normalized OTDR trace corresponding to that particular series of
light pulses would be obtained by dividing the OTDR trace for that
series by the OTDR trace for that series corresponding to total
power. It should be noted that the use of one detector with one
optical switch instead of two detectors disadvantageously at least
doubles the total acquisition time in comparison with embodiments
using two detectors,
[0303] It is also envisaged that a rotating polarization
discriminator (PD), whether it is a polarizer or a PBS, may be used
to sequentially acquire two orthogonal components for example via
rotating the polarization discriminator by 90.degree. to switch
from detecting Px to detecting Py, or from detecting Py to
detecting Px. The detector means 22, whether a single detector or a
pair of detectors, and the sampling and averaging circuitry unit
232, may be the same or similar to those employed in standard
commercial OTDRs that are known to a person skilled in this
art.
[0304] The control unit 30 may advantageously be a separate
computer. However, it is noted that a single computer could perform
the functions of the data processor 34 and the control unit 30.
[0305] It may also be envisaged that certain parts of the signal
processing may be performed remotely, either approximately in "real
time" or during post-processing, for instance using "cloud
computing".
[0306] Various other modifications to the above-described
implementations of the embodiment may be made within the scope of
the present invention.
[0307] For instance, the tunable pulsed laser source 12 and I/A-SOP
controller 14 could be replaced by some other means of providing
the different polarization states of the pulses entering the FUT 18
and analyzing the resulting backreflected signal caused by Rayleigh
scattering and/or discrete reflections leaving the FUT 18.
[0308] Thus, a polarimetric head may be used (splitters with three
or more analyzers and photodetectors in parallel), which measures
more than one polarization component of the backreflected signal
simultaneously, or some other configuration, so that the power that
reaches the photodetectors is dependent on the SOP of the
backreflected light.
[0309] It should be noted that each group is not limited to one
pair of series of light pulses.
[0310] Indeed, it may be advantageous to use three or more
different closely-spaced wavelengths per group of traces obtained
with a common SOP, instead of the minimally-required two
closely-spaced wavelengths .lamda..sub.L and .lamda..sub.U (each
group then comprises 2N.sub..lamda. OTDR traces instead of four,
two sets of 2N.sub..lamda. traces in the case of the
two-photodetector embodiments, where N.sub..lamda. is the number of
wavelengths in a group of series of light pulses). For example, in
the case where three closely-spaced wavelengths are used, one can
choose the series of light pulses at the lowermost and intermediate
wavelengths as one pair, and the series of light pulses at the
intermediate and uppermost wavelengths as a second pair, such that
the wavelength step between the light pulses in one pair is greater
than the wavelength step between the light pulses in the other
pair, perhaps a few times larger.
[0311] Since there are three combinations of wavelength steps
corresponding to three wavelengths (i.e.,
N.sub..lamda.(N.sub..lamda.-1)/2), one can simultaneously obtain
the data corresponding to two significantly different wavelength
steps within a measurement time that is only 1.5 times greater than
the time required to perform a one-step measurement. Thus,
proceeding with three wavelengths (or more) per group proves highly
advantageous because the cumulative PMD value can increase
significantly along the length of the FUT 16 (from zero to the
overall PMD of the FUT), and hence the use of two, three, or more
different steps allows one to maintain a satisfactory relative
precision (e.g. in %) at all positions along the fiber. It will be
appreciated that one could also select the light series at the
lowermost and uppermost wavelengths as a third pair, with a
wavelength step greater than both of the others. The use of only
one step gives a particular absolute uncertainty, as for example
.+-.0.1 ps, which represents a small percentage uncertainty at a
distance where the PMD has grown to a value of 10 ps, but is not
good in percentage at short distances where the PMD is, for
example, only 0.2 ps. To obtain a smaller uncertainty for smaller
PMD values, a larger step must be selected. Hence the obvious
advantage of implementing such an alternate embodiment where more
than two wavelengths per group are used. It changes nothing to the
setup, nor to the principle of the invention as described above,
but saves time in the overall measurement process.
[0312] Although the above-described embodiment changes the center
wavelength for each SOP, this is not an essential feature of the
present invention. While superior performance can be obtained by
covering a large wavelength range in order to obtain the best
possible average of DGD, as per the definition of PMD, a POTDR
embodying the present invention will work with no bias and may
provide acceptable measurements of PMD(z), with a constant
center-wavelength.
1.11 Various Modifications Common to Preferred Embodiments
[0313] For the three preferred embodiments comprising a test light
source (i.e. Embodiments (1), (3), and (4)), if the degree of
polarization (DOP) of the light source 12;12A;12B is not high, the
DOP may be increased by inserting a polarizing element 19 (e.g.
polarizer, polarization beam splitter, etc.) into the optical path
downstream from the light source 12 (not shown in FIG. 1 but see
FIG. 11). However, if standard single-mode fiber (e.g. SMF-28 fiber
marketed by Corning Inc.) rather than polarization maintaining
fiber (PMF) is used to optically connect the light source 12 and
the polarizing element 19 (which for the OTDR-based "single-ended"
embodiments may be functionally replaced by polarizer/polarizing
splitter 20, 20A, 20C), it may be necessary to add an additional
polarization adjuster 13 (generally a "factory-set" polarization
controller), as shown in FIG. 11, in order to approximately
maximize the power transmitted through the polarizing element 19;
20, 20A, 20C.
[0314] Preferred implementations of the OTDR-based "single-ended"
embodiments couple the output of the light source into PMF. The
alignment of PMF 29A and 29B is fixed in the factory in such a
manner that substantially all of the optical power from the tunable
pulsed laser source 12 is maintained in one of the two axes of the
fiber 29A and 29B (conventionally, the "slow" axis). Since the
backreflection extractor 52 (e.g. circulator) is
polarization-maintaining, this alignment is maintained until the
distal end of PMF 29B, at its point of attachment to PBS 20. During
attachment of each end of the PMFs 29A and 29B to the component
concerned, the azimuthal orientation of the PMF 29A/B is adjusted
to ensure maximum transmission of the optical pulses towards the
FUT 18.
Underlying Theory
1.12 SOP Scrambling Analysis (SOP) for PMD Measurement
[0315] Although the applicant does not wish to be constrained by
theory, the following discussion of the underlying theory is
provided so as to facilitate understanding of the various
embodiments of the invention.
[0316] The computation of the DGD or rms DGD (i.e. PMD) is based on
a method designated "State of polarization Scrambling Analysis"
(SSA), which forms the basis of the present invention. The specific
theory applied to the various aspects of this invention is closely
related to the theory described in international patent application
No. PCT/CA2006/001610 and the above-identified United States
Continuation-in-Part application Ser. No. 11/727,759, the entire
contents of each of which are incorporated herein by reference.
[0317] PMD is usually quantified as the statistical RMS value of
differential group delay DGD(.lamda.), estimated by averaging over
a wide wavelength range, or over a period of time, ideally both, so
that the largest possible number of random occurrences of DGD are
observed to obtain its RMS value. (As mentioned hereinbefore, the
definition of PMD as the arithmetic mean of DGD(.lamda.) over a
wide wavelength range is an alternative, though it is less widely
employed. A skilled practitioner would readily be able to adapt the
equations for PMD given hereinbelow from "RMS" to "mean".)
[0318] In this section, we describe the theory underlying the SSA
method upon which the invention is predicated. As mentioned
hereinabove, the SSA method is applicable to the characterization
of PMD-related polarization characteristics of and arising from an
optical link (FUT).
[0319] It should be appreciated that measurement or monitoring of
partial-DGD employs a special case of SSA where the input SOP is
necessarily not actively scrambled as part of the measurement
process.
[0320] It should further be appreciated that, in all embodiments,
the term "scrambling" in the designation does not preclude the use
of predetermined SOP analysis conditions (e.g. via a polarimetric
head), nor, where applicable, the launching of a set of
predetermined "input" SOPs into the optical link. Such variants and
implementations are discussed within this application.
[0321] The methods of operation, data processing and computational
methods for preferred embodiments of applications will be described
in detail in Sections 7 and 8 hereinbelow.
[0322] To facilitate the description of SSA theory, it will first
be described with reference to the schematic measurement set-up
depicted in FIG. 1, associated with the two-ended
"test-source-based" approach of preferred Embodiment (1) described
in Section 5. It will become clear in context how the theory
applied to Embodiment (1) can be readily modified for the other
preferred embodiments.
[0323] In this specification, "analyzing" of the light refers to
apportioning the optical power that can be decomposed to align with
the transmission axis of a polarization analyzer for which the
maximum optical power may subsequently be detected. An example of
polarization-analyzer means is a combination of a polarization
controller and linear polarizer. The SOP of the light incident upon
the polarization-analyzer means that is maximally transmitted
therethrough is defined as the "analyzer-SOP", or simply "A-SOP".
As the polarization controller is adjusted (usually in a random
fashion), this A-SOP value varies accordingly, and this transmitted
power is detected.
[0324] All the embodiments described herein are predicated upon
polarized light, emitted by a light source, having a spectral width
greater than a small optical-frequency difference .DELTA..upsilon.
between two closely-spaced optical frequencies, .nu..sub.U and
.nu..sub.L, being launched into the FUT with a particular, usually
unknown, SOP (denoted "input-SOP", or "I-SOP"). It is convenient to
define a "notional" midpoint optical frequency, .nu..sub.mid
(=(.nu..sub.U+.nu..sub.L)/2). According to the particular preferred
embodiment, this light may be emitted by [0325] (i) (Embodiment 1)
a test light source, emitting either polarized coherent light (e.g.
from a laser) or polarized broadband light, the light source and
the "receiving instrumentation" being located at opposing ends of
the FUT; [0326] (ii) (Embodiment 2) one or more
permanently-installed network transmitters (Tx), which each are
modulated to normally carry network traffic, this modulation
necessarily imparting a spectral width to the light that is
approximately equal to the symbol rate. The "receiving"
instrumentation is located at the other end of the optical link.
For convenience, the light from each such Tx of interest that has
traversed the optical link is termed signal-under-test (SUT);
[0327] (iii) (Embodiments 3 and 4) a test light source, emitting
polarized coherent pulsed light, the light source ("OTDR source")
and the "receiving" portions of the instrumentation being
co-located.
[0328] Embodiments (1), (3) and (4) all preferably determine the
respective polarization-related polarization characteristics from
data corresponding to different I-SOP conditions, these different
I-SOP normally being generated by, for example, a polarization
controller. On the other hand, by virtue of the Tx sources being
part of an active network, there is normally no actively-induced
variation of I-SOP associated with Embodiment (2). (Any variations
of I-SOP associated with this latter embodiment tend to be slow
effects due to environmental changes, etc.).
[0329] All the preferred embodiments described hereinabove involve
analyzing and detecting the analyzed power of each member of the
pair of the closely-spaced optical frequencies, centered about
midpoint frequency, .nu..sub.mid, that has traversed the FUT, where
the analyzing conditions are the same for each member of the pair.
In implementations of the preferred embodiments (1), (3), and (4)
that do not comprise a polarimetric head, this analyzing and
detecting process is repeated for a large number K of I-SOP and
A-SOP conditions, i.e., comprising a large number of "SOP couples"
(I-SOP.sub.k, A-SOP.sub.k) each referring to both the input-SOP and
the analyzer-SOP of the received light. For Embodiment (2), there
is no variation of I-SOP induced by the measurement procedure
itself, and hence the analyzing and detection process is repeated
for a large number K of A-SOP conditions.
[0330] In implementations of the preferred embodiments employing a
polarimetric head, which typically analyzes for subsequent
detection optical power corresponding to three mutually-orthogonal
A-SOP conditions of the light, the number of A-SOP conditions,
K.sub.ASOP=3 suffices. (Of course, additional measurements may be
acquired for better averaging, etc., but theoretically only
K.sub.ASOP=3 is required.)
[0331] The A-SOP, and if applicable I-SOP, values may be chosen in
a random manner, such that the points conventionally representing
SOPs on the Poincare Sphere are approximately uniformly-distributed
over it, whether the distribution is random or a substantially
uniform grid of points.
1.13 Theory Specific to Embodiments (1), (3), and (4) Involving
Actively-Induced I-SOP Variation
1.13.1 Determination of DGD and PMD
[0332] A key element of SSA theory is that, on average over a
sufficiently large, uniformly distributed number K of said "SOP
couples", the mean-square difference between normalized powers
observed at .nu..sub.U and .nu..sub.L is related to the DGD at its
midpoint optical frequency .nu..sub.mid
(=(.nu..sub.U+.nu..sub.L)/2) by a simple relationship. This
relationship is valid in all cases for any type of practical FUT
regardless of its degree of randomness or its polarization-coupling
ratio, including even the extreme case of a PMF fiber, i.e.,
DGD ( v ) = 1 .pi. .delta. v arcsin ( .alpha. ds .DELTA. T 2 ( v )
SOP ) ( 6.1 ) ##EQU00003##
where .sub.SOP represents the average over the K SOP couples,
.delta..nu. (=|.nu..sub.U-.nu..sub.L|) is the "step", and
.alpha..sub.ds is a theoretical constant that is dependent on the
implementation of the embodiment, as will be described further
below. .DELTA.T(.nu.) is a difference between the analyzed
normalized powers (i.e. transmission values) observed at
closely-spaced optical frequencies .nu..sub.U and .nu..sub.L,
respectively, and its mean-square difference is,
.DELTA. T ( v ) 2 SOP = ( T U - T L ) 2 SOP = 1 K k ( T U ( k ) - T
L ( k ) ) 2 ( 6.2 ) ##EQU00004##
where the index k corresponds to a particular SOP couple.
[0333] For implementations for which there is no direct detection
of the non-analyzed power, e.g. for the polarizer-based
one-detector implementations illustrated in FIGS. 1B, 3B and 3A,
the normalized powers are
T L ( k ) = u o P L ( k ) P L SOP T U ( k ) = u o P U ( k ) P U SOP
( 6.3 a ) ##EQU00005##
where the reference mean-value u.sub.o is a theoretical constant
that is dependent on measurement set-up configuration, i.e. either
two-ended (FIG. 1B) or single-ended (FIGS. 3B and 4A) measurement
configuration, and the average power is defined,
P L SOP = 1 K k P L ( k ) . P U SOP = 1 K k P U ( k ) ( 6.3 b )
##EQU00006##
[0334] Furthermore, for a prescribed wavelength range, if one
carries out the averages indicated in equations (6.2) and (6.3)
over both many randomly-selected SOP couples and midpoint optical
frequencies, both of which are changed from one group comprising
two closely-spaced wavelengths to the next, the rms DGD (i.e. PMD)
over the prescribed wavelength range is obtained:
PMD = 1 .pi..delta. v arcsin ( .alpha. ds .DELTA. T 2 ( v ) SOP ; v
) ( 6.4 ) ##EQU00007##
where .sub.SOP;.nu. is averaged over both SOP and optical frequency
across a prescribed wavelength range.
[0335] In the limit of a sufficiently small optical-frequency
difference ("step") between the closely-spaced optical frequencies,
equations (6.1) and (6.4) tend to the following simpler
differential formulae:
DGD ( v ) = .alpha. ds .pi..delta. v .DELTA. T 2 ( v ) SOP ( 6.1 a
) PMD = .alpha. ds .pi..delta. v .DELTA. T 2 ( v ) SOP ; v ( 6.4 a
) ##EQU00008##
[0336] (Of course, any other alternative mathematical function that
provides a numerical result that falls within an acceptable
difference from the said following differential formula for
realistic values of DGD and PMD could be used instead, but such a
formula would not be based on firm theoretical underpinnings. This
would be true for any of the other analogous formulas presented
elsewhere in this specification.)
[0337] The relationship in equation (6.1) holds for
DGD.delta..nu.<1/2 for two-ended measurement configurations and
DGD.delta..nu.<0.3 for single-ended measurement configurations,
these relationships thus defining the meaning of "closely-spaced
wavelengths".
[0338] The normalized power will in fact be obtained differently in
each embodiment, i.e., by suitable programming of the data
processor 34. This explanation of the theory is provided for the
basic single-photodetector embodiment of FIGS. 1B, 3B and 3A, where
normalization over the average power is necessary, assuming total
power is stable when the (I-SOP, A-SOP) couple is changed, or as a
function of time. Note that the normalization procedure for the
two-ended measurement configuration (FIG. 1B) and single-ended
(FIGS. 3B and 4A) are very similar, but reference mean-values
(u.sub.0) (see equations (6.6) and (6.12)) are different. Also
note, for the single-ended cumulative PMD measurement, a normalized
power trace (T(z)) as function of distance z is computed. A
detailed description of this normalization procedure is provided
hereinafter.
1.13.2 Two-Ended PMD Measurement
[0339] The basic theory of the SSA method described above can be
applied to two-ended PMD measurement, where the test link may or
may not include an intervening optical amplifier. When optical
amplifiers are used in the test link, the amplified spontaneous
emission (ASE) from the amplifier will be mixed with the launched
polarized coherent light from the light source means and,
consequently, both ASE and launched light are measured by
photodetector 22A (FIG. 1B).
[0340] Below we describe how to apply the basic SSA theory to
two-ended PMD measurement for both the cases where ASE is absent
and where ASE is present, without or with optical amplifiers, for
the test link, by accessing two ends of FUT.
1.13.2.1 Two-Ended Measurement: DGD Measurement without Amplifiers
in the Test Link
[0341] If a tunable laser serves as a light source means, one can
select its optical frequency by either tuning in a stepwise
fashion, or frequency sweeping, or frequency modulation, or similar
means. Alternatively, if a polarized broadband light source is
used, then a tunable filter may be used to select the optical
frequency. In both cases, an input polarization controller is
placed at a proximal end of FUT and a
polarization-controller-and-analyzer means, for example an output
polarization controller, polarizer (or PBS) and a photodetector or
power meter (combined with tunable filter if polarized broadband
light source is used instead of tunable laser source) is located at
the opposing end of FUT for measuring the power from fibers at two
closely spaced optical frequencies, .nu..sub.U and .nu..sub.L,
around a given midpoint frequency, .nu..sub.mid, for a large number
K of input/output state of polarizations, i.e., comprising a large
number of "SOP couples" (I-SOP.sub.k, A-SOP.sub.k) each referring
to both the input-SOP and the analyzer-SOP of the analyzed light.
Both the I-SOP and the A-SOP values are preferably chosen in a
pseudo-random manner, such that the points conventionally
representing SOPs on the Poincare sphere are substantially
uniformly-distributed over the surface of said sphere, whether the
distribution is random or approximately a uniform grid of points.
By averaging over a sufficiently large, uniformly distributed
number K of said SOP couples, the DGD at its midpoint frequency
.nu..sub.mid is given by equation (6.1). Equation (6.1) is valid
for DGD.delta..nu.<1/2 for two-ended measurement configurations,
thus clarifying the meaning of "closely-spaced optical
frequencies".
[0342] This DGD value may be alternatively designated as the
"forward" DGD, a superfluous adjective if only two-ended
measurements are of concern, but a useful distinction in the
context of the "single-ended" embodiments to be described
hereinbelow.
[0343] If the scrambling is carried out in such a way that either
or both of the I-SOP and A-SOP is/are significantly different than
its/their respective predecessor(s) or successor(s), i.e. when they
are randomly or quasi-randomly selected on the Poincare sphere, K
should be greater than 10, typically about 100 to 200 for good
quality results.
[0344] On the other hand, if the scrambling is carried out in a
slow, continuous fashion, as described in more detail hereinafter,
such that at least one of I-SOP and A-SOP is only slightly
different than its respective predecessor or successor, then K
should be greater than 500, typically about 10,000, to ensure that
the measurement involves an average over a substantially uniform
Poincare Sphere distribution, thereby reducing the measurement
uncertainty.
[0345] As already mentioned, the PMD is defined in the context of
this description as the root-mean-square (rms) value of DGD
averaged over wavelength. The rms DGD (i.e. PMD) over the
prescribed wavelength range may now be computed by equation (6.4).
(It should be noted that a long time-averaged DGD measurement at a
given wavelength, for which the FUT is subject to generally slow
environmental perturbation, usually yields rms DGD rather than mean
DGD).
[0346] For Embodiment (1) ("two-ended test-source-based DGD and/or
PMD measurement") employing SOP scrambling at both ends, the
theoretical constant .alpha..sub.ds used in equations (6.1),
(6.1a), (6.4) and (6.4a) is:
.alpha. ds = 9 2 ( 6.5 ) ##EQU00009##
This value presupposes that changes in the I-SOP polarization
controller and A-SOP polarization controller are not correlated, as
would normally be the case. The relationship in Equations (6.1) and
(6.4) holds for DGD.delta..nu.<0.5, thus clarifying the meaning
of "closely-spaced optical frequencies".
[0347] For this two-ended configuration, the reference mean-value
u.sub.o used for normalization in equations (6.3a) is
u.sub.0=1/2 (6.6)
1.13.2.2 Two-Ended Measurement: DGD Measurement with Amplifiers in
the Test Link
[0348] In many field applications, optical amplifiers (typically
erbium-doped optical amplifiers) constitute part of the link.
Hence, the FUT 18 may comprise at least one, and possibly several,
optical amplifiers at various spacings (e.g. 60 km) within the FUT
18. When an optical amplifier is present, a power meter located at
distal end of FUT 18 will likely also detect (substantially
unpolarized) amplified spontaneous emission (ASE) light in addition
to the signal emitted by the optical generator means. The presence
of ASE in the detected signal can be taken into account by "scaling
down" the mean-square differences .DELTA.T(.nu.).sup.2.sub.SOP by a
factor that can be computed independently from the same raw data.
This factor, .sigma..sub.r.sup.2(.nu.), is a relative variance of
the normalized powers defined as,
.sigma. r 2 ( v ) = ( 1 .sigma. 20 ) 2 [ T ( v ) T '' ( v ) SOP - T
( v ) SOP 2 ] ( 6.7 ) ##EQU00010##
where the reference variance is .sigma..sub.20.sup.2= 1/12. The
notation T(.nu.)T''(.nu.).sub.SOP and T(.nu.).sub.SOP.sup.2 refer
to averages over both normalized powers at .nu..sub.U and
.nu..sub.L and T(.nu.) and T''(.nu.) are the normalized powers from
repeated measurements in one group at one given optical
frequency.
[0349] It should be noted that, if the noise power contribution may
be neglected, then T(.nu.) and T''(.nu.) may be the same normalized
power, i.e. corresponding to only one measurement in one group at
one given optical frequency, and hence
T(.nu.)T''(.nu.)=T.sup.2(.nu.).
[0350] Then the (forward) DGD at a given midpoint wavelength is
obtained by dividing the mean-square differences by the relative
variance in equation (6.7) as,
DGD ( v ) = 1 .pi. .delta. v arcsin ( .alpha. ds .DELTA. T 2 ( v )
SOP .sigma. r 2 ( v ) ) ( 6.8 ) ##EQU00011##
[0351] And, moreover, the (forward) rms PMD for a prescribed
wavelength range can be expressed by,
PMD = 1 .pi. .delta. v arcsin ( .alpha. ds .DELTA. T 2 ( v ) SOP ;
v .sigma. r 2 ) ( 6.9 ) ##EQU00012##
where the average over SOP in equation (6.8) is now replaced by the
average over both SOP and optical frequency (wavelength), and
.alpha..sub.ds is given by equation (6.5). The relative variance of
the normalized powers now is expressed as,
.sigma. r 2 = ( 1 .sigma. 0 ) 2 [ T ( v ) T '' ( v ) SOP ; v - T (
v ) SOP ; v 2 ] ( 6.7 a ) ##EQU00013##
[0352] It should be noted that, if the normalized powers T(.nu.)
are averaged over a sufficient large number of randomly scrambled
SOPs, then T(.nu.).sub.SOP.sup.2=1/4.
[0353] In the limit of a sufficiently small optical-frequency step,
equations (6.8) and (6.9) respectively tend to the following
differential formulae:
DGD ( v ) = .alpha. ds .pi..delta. v .DELTA. T 2 ( v ) SOP .sigma.
r 2 ( v ) ( 6.8 a ) ##EQU00014##
PMD = .alpha. ds .pi..delta. v .DELTA. T 2 ( v ) SOP ; v .sigma. r
2 ( 6.9 a ) ) ##EQU00015##
[0354] If launched power corresponding to each of the two
closely-spaced optical frequencies constituting a wavelength pair
are equal and if the FUT (including possible intervening filters)
introduces negligible differential spectral attenuation to members
of the pair, then these measured "closely-spaced" powers can
directly be applied to equations (6.8) and (6.9), i.e. there is no
need to normalize the measured powers (although, in that case
T(.nu.).sub.SOP.sup.2 may not equal 1/4). This obtains since the
normalization procedure described above (see Eq. 6.3) yields a
"constant factor" that is multiplied on measured powers in order to
obtain normalized power (between 0 and 1), this factor being
multiplied with both the mean-square difference and relative
variance. The mean-square difference and relative variance appear
in the numerator and denominator of equations (6.8) and (6.9),
respectively, and hence mutually cancel when calculating DGD or PMD
therefrom. In other words, equations (6.8) and (6.9) only require
the use of relative powers that are proportional to normalized
powers.
[0355] It should be appreciated that equations (6.8) and (6.9) are
applicable with or without the presence of amplifier noise on the
link under test.
[0356] Alternatively, an estimate of the PMD (i.e. rms or mean DGD
value over an optical frequency range) can be obtained by first
determining DGD(.nu.) (using either equation (6.1) or (10a)) at
each of a plurality of midpoint wavelengths, and then performing an
rms (or mean) average of these value. It is preferable that these
midpoints wavelengths be approximately uniformly spread across this
optical-frequency range, and that the range be significantly
greater than the optical-frequency spacing at which the DGD values
are correlated.
1.13.3 Single-Ended PMD Measurement
[0357] Single-ended PMD measurement is a very important measurement
technique for field applications. The above-described basic SSA
theory can also be applied to single-ended PMD measurement.
Single-ended measurement of PMD-related characteristics described
herein comprises two embodiments: Embodiment (3) measures the
overall PMD of a FUT by analyzing backreflected light from the
distal end of FUT, and Embodiment (4) enables determination of
cumulative PMD as a function of distance along the FUT. As implied
by the adjective "single-ended", both embodiments involve
measurement instrumentation located at only one end of the FUT.
1.13.3.1 Single-Ended Measurement: Overall PMD
[0358] Single-ended PMD measurement using backreflected light from
the distal end of the FUT may be used when there are no optical
amplifiers along the fibers. Below we describe the basic SSA theory
as applied to single-ended overall PMD determination via
measurement instrumentation adjacent only one end of FUT.
[0359] If a mirror (such as a fiber-pigtailed mirror) is connected
at the distal end of the FUT, and if one could neglect Rayleigh
backscattering and any spurious discrete reflections (e.g. from any
connectors or splices) along the FUT, the tunable OTDR could be
replaced by a tunable CW laser (no pulses) and a power meter for
measuring the power reflected from the mirror at the distal end of
the FUT at two closely spaced optical frequencies, .nu..sub.U and
.nu..sub.L, around a given midpoint frequency, .nu..sub.mid, for a
large number K of (I-SOP, A-SOP) couples, i.e., one such setting
referring to both the input-SOP and the analyzer-SOP of the
backreflected light. The SSA theory provides a relationship for the
roundtrip-DGD(.nu.) expressed in terms of the mean-square
differences of normalized powers (i.e. transmission) observed at
closely-spaced optical-frequencies .nu..sub.U and .nu..sub.L, each
pair corresponding to one of a multiplicity of (I-SOP, A-SOP)
couples. This relationship, analogous to Equation (6.1), is valid
in all cases for any type of practical FUT regardless of its degree
of randomness or its polarization coupling ratio, including the
extreme case of a PMF fiber, as,
DGD RoundTrip ( v ) = 1 .pi. .delta. v arcsin ( .alpha. ds .DELTA.
T 2 ( v ) SOP ) ( 6.10 ) ##EQU00016##
.sub.SOP represents the average over the K (I-SOP, A-SOP) couples,
.delta..nu.=(.nu..sub.U-.nu..sub.L) is the "step", .DELTA.T is the
difference between the normalized powers observed at .nu..sub.U and
.nu..sub.L, respectively. The relationship holds for
DGD.sub.RoundTrip.delta..nu.<1/2, thus clarifying the meaning of
"closely-spaced optical frequencies".
[0360] If changes in the I-SOP polarization controller and A-SOP
polarization controller are correlated (as would be the case in
preferred implementations for which a common "I/A-SOP" polarization
controller is employed), then
.alpha. ds = 15 4 ( 6.11 a ) ##EQU00017##
If, however, the I-SOP and A-SOP polarization controllers are not
correlated (e.g. see FIG. 3, then
.alpha. ds = 9 2 ( 6.11 b ) ##EQU00018##
[0361] The relationship in equation (6.10) holds for
DGD.delta..nu.<0.3 for single-ended measurement configurations,
thereby defining the meaning of "closely-spaced optical
frequencies".
[0362] The reference mean-value u.sub.o used in Equation (6.3a) for
single-ended measurement configurations, the reference mean-value
u.sub.o is
u.sub.0=2/3 (6.12)
The roundtrip DGD(.nu.) derived by equation (6.10) is not simply
twice the forward DGD(.nu.). The roundtrip DGD.sub.RMS (i.e. PMD)
extracted from an rms average of DGD(.nu.) values over a wavelength
range is also not simply twice double the forward DGD.sub.RMS. For
the latter case, however, when averaged over wavelength, or time,
the PMD value (i.e. rms DGD) is related to the roundtrip-PMD (i.e.
rms DGD.sub.RoundTrip) through a simple factor, the roundtrip
factor .alpha..sub.rt= {square root over (3/8)}, i.e.,
DGD.sub.RMS=.alpha..sub.rtDGD.sub.RoundTripRMS or
PMD=.alpha..sub.rtPMD.sub.RoundTrip, where PMD is defined as the
root-mean-square (RMS) value of DGD.
[0363] For the alternative definition of PMD, i.e., the mean value
of DGD, then .alpha..sub.rt=2/.pi..
[0364] Typically, in order to reliably measure overall PMD, a
tunable OTDR is used. The tunable OTDR launches relatively long
pulses into the FUT, the at least one photodetector in the OTDR
then detecting the backreflected power of the localized reflection
at the distal end of FUT.
[0365] The roundtrip DGD of the FUT section comprised between the
output of the instrument and the selected reflection is obtained as
previously from equation (12), where the power observed for a given
(I-SOP, A-SOP) couple is now obtained as, for example, the power of
the pulse backreflected from the selected reflection averaged over
a predetermined portion of the pulse duration.
[0366] It should be noted that the above defined backreflected
power may be obtained by averaging each response pulse over a
substantial portion of its duration, therefore it is preferable to
apply a long OTDR pulse (e.g. 1 to 20 .mu.s) for this single-ended
PMD measurement technique.
[0367] Furthermore, in preferred embodiments of the invention for
which overall total PMD is to be measured, the averages indicated
in equation (6.10) are preferably carried out over both I-SOP,
A-SOP and midpoint-wavelengths, all three of which are changed from
one group comprising two closely-spaced wavelengths to the next,
thus obtaining the roundtrip PMD instead of only one particular DGD
at one particular wavelength. A roundtrip rms DGD (i.e. roundtrip
PMD) over the prescribed wavelength range is expressed as:
PMD RoundTrip = 1 .pi..delta. v arcsin ( .alpha. ds .DELTA. T 2 ( v
) SOP ; v ) ( 6.13 ) ##EQU00019##
[0368] Moreover, the forward PMD value (simply denoted as "PMD",
and unless otherwise stated, assumed to be defined based on the RMS
definition) is related to the round-trip PMD by the same "round
trip factor", i.e. .alpha..sub.rt= {square root over (3/8)},
yielding:
PMD=.alpha..sub.rtPMD.sub.RoundTrip (6.14)
[0369] In the limit of a sufficiently small optical-frequency
difference ("step") between the closely-spaced wavelengths,
equations (6.10) and (6.13) tend to the following simpler
differential formulae:
DGD RoundTrip ( v ) = .alpha. ds .pi..delta. v .DELTA. T 2 ( v )
SOP ( 6.10 a ) PMD RoundTrip = .alpha. ds .pi..delta. v .DELTA. T 2
( v ) SOP ; v ( 6.13 a ) ##EQU00020##
[0370] A measurement of PMD based on equation (6.13) or (6.13a)
offers the advantage of a relatively short acquisition time, since
there is no need to perform intermediate determination of the
DGD.sub.RoundTrip(.nu.) according to equations (6.10) or (6.10a).
Nevertheless, rms DGD.sub.RoundTrip or mean DGD.sub.RoundTrip may
be obtained from individually measured DGD.sub.RoundTrip(.nu.) for
many different midpoint optical frequencies .upsilon. by
root-mean-square or mean DGD.sub.RoundTrip(.nu.) from equation
(6.10) or (6.10a) over a prescribed optical frequency range,
e.g.
rms DGD RoundTrip = DGD RoundTrip 2 ( v ) v ##EQU00021##
and mean DGD.sub.RoundTrip=DGD.sub.RoundTrip(.nu.).sub..nu..
Forward rms DGD and mean DGD are then obtained by simply
multiplying a roundtrip factor of {square root over (3/8)} and
2/.pi. on rms DGD.sub.RoundTrip and mean DGD.sub.RoundTrip,
respectively.
[0371] It should be noted that the pulse length used for the
single-ended overall PMD measurement should be less than fiber
(FUT) length, preferably significantly less (to avoid excessive
Rayleigh scattering noise, for instance), e.g. 1 .mu.s corresponds
to a fiber length of approximately 100 meters. It is also preferred
to average the detected backreflected light power over several or
many optical pulses, e.g. from 10 to 1000 pulses.
[0372] Also, it should be emphasized preferred PMD measurement from
the single-ended overall PMD measurement should use several or many
different midpoint wavelengths, e.g. 20 to 2000, in order to
improve the fundamental PMD measurement accuracy.
1.13.3.2 Single-Ended Measurement: Cumulative PMD
[0373] Equations (6.10) and (6.13) applicable for overall PMD
determination also apply to single-ended cumulative PMD
measurement, for which the cumulative PMD is determined as a
function of distance z by analyzing the Rayleigh backscattering
light for each location (z) along FUT length. In order to resolve
fiber beat length it is necessary to employ a short light pulse,
for example from a tunable OTDR. However, the use of an unduly
short light pulse would limit the measurable FUT length and an
excessivly long pulse might not be able to resolve the beat length
of fiber.
[0374] Indeed, if a very short light pulse is used, OTDR "traces",
or backreflected power as a function of distance z, are the same as
if the above single-ended overall PMD measurement were repeated an
infinite number of times, with the end reflector shifted by a
distance increment dz between measurements. Providing that the
pulses are very short, and also ignoring the fact that the
"coherence noise" always adds to an OTDR trace, the same result as
in equation (6.10) is obtained, except that it is obtained as a
function of distance z in one step. The different .DELTA.T(.nu.,z)
values obtained with different (I-SOP, A-SOP) couples are now
differences between whole OTDR traces as a function of z, instead
of just one number, and give DGD.sub.RoundTrip(.nu.,z). Note
T(.nu.,z) is a normalized trace as a function of fiber length
z.
[0375] It is generally impractical to employ very short pulses in
the field, however, since attaining a useful dynamic range would
require an exceedingly long measurement time. Also, reduction of
the high level of coherence noise resulting from the use of short
pulses may require an unacceptably large equivalent laser
linewidth, which results in a small maximum measurable PMD. The
present invention takes account of the finding that, with
spectrally-broad pulses, the mean-square differences
.DELTA.T(.nu.,z).sup.2.sub.SOP are simply "scaled down" by a factor
that can be computed independently from the same raw data. This
factor, .sigma..sub.r.sup.2(z,.nu.), is the relative variance of
the traces, a function of z depending on local characteristics of
the fiber, defined as,
.sigma. r 2 ( z , v ) = ( 1 .sigma. 10 ) 2 [ T ( z , v ) T '' ( z ,
v ) SOP - T ( z , v ) SOP 2 ] ( 6.15 ) ##EQU00022##
where the reference variance is .sigma..sub.10.sup.2= 4/45, and T''
represents a repeated measurement. The roundtrip DGD at a given
midpoint wavelength then is obtained by dividing the mean-square
differences in equation (12) by the relative variance in equation
(14), i.e.
DGD RoundTrip ( z , v ) = 1 .pi..delta. v arcsin ( .alpha. ds
.DELTA. T 2 ( z , v ) SOP .sigma. r 2 ( z , v ) ) ( 6.16 )
##EQU00023##
[0376] Furthermore, in preferred implementations of the invention,
the averages indicated in equations (6.15) and (6.16) are
preferably carried out over both (I-SOP, A-SOP) couples and center
wavelengths, both of which are changed from one group comprising
two closely-spaced wavelengths to the next, thus obtaining the
roundtrip PMD instead of only one particular DGD at one particular
wavelength.
PMD RoundTrip ( z ) = 1 .pi..delta. v arcsin ( .alpha. ds .DELTA. T
2 ( z , v ) SOP ; v .sigma. r 2 ( z ) ) ( 6.17 ) ##EQU00024##
[0377] Since the typical user would prefer that the more
practically useful "forward" PMD value be displayed rather than the
roundtrip value, the round-trip result is multiplied by the
above-specified roundtrip factor, .alpha..sub.rt= {square root over
(3/8)}. Thus, the forward PMD is
PMD(z)=.alpha..sub.rtPMD.sub.RoundTrip(Z) (6.18)
where the average over (I-SOP, A-SOP) couples in equation (14) is
also replaced by the average over both (I-SOP, A-SOP) couples and
wavelength, i.e.
.sigma. r 2 ( z ) = ( 1 .sigma. 10 ) 2 [ T ( z , v ) T '' ( z , v )
SOP ; v - T ( z , v ) SOP ; v 2 ] ( 6.15 a ) ##EQU00025##
[0378] Alternatively, the roundtrip rms DGD (i.e. roundtrip PMD
according to the rms definition) can also be obtained by performing
a root-mean-square average on the plurality of calculated roundtrip
DGD correspond to a respective plurality of midpoint wavelength,
as
rms DGD RoundTrip ( z ) = DGD RoundTrip 2 ( z , v ) v , ( 6.19 )
##EQU00026##
where T'' represents a repeated measurement. Of course, by
performing this "intermediate" calculation of DGD at each optical
frequency, the overall time required to determine the PMD would be
longer than directly applying Equation (6.17).
[0379] Forward rms DGD(z) is then obtained by simply multiplying
rms DGD.sub.RoundTrip by the roundtrip factor .alpha..sub.rt=
{square root over (3/8)}.
[0380] Analogous calculations may be carried out to determine the
forward mean DGD(z), employing the roundtrip factor
.alpha..sub.rt=2/.pi.. However, for such calculations the
additional noise reduction achieved using repeated measurements T''
may not be rigorously correct, since relative variances (rather
than arithmetic means) are used in equations (6.15) and
(6.15a).
[0381] In the limit of a sufficiently small optical-frequency
difference ("step") between the closely-spaced wavelengths,
equations (6.16) and (6.17) tend to the following simpler
differential formulae:
DGD RoundTrip ( z , v ) = .alpha. ds .pi..delta. v .DELTA. T 2 ( z
, v ) SOP .sigma. r 2 ( z , v ) ( 6.16 a ) PMD RoundTrip ( z ) =
.alpha. ds .pi..delta. v .DELTA. T 2 ( z , v ) SOP ; v .sigma. r 2
( z ) ( 6.17 a ) ##EQU00027##
[0382] As yet another possible, although less desirable
alternative, it is envisaged that, the averages over (I-SOP, A-SOP)
couples and wavelengths in the above equations (8), (11), (13) and
(16) could be replaced by averages over a large range of optical
frequencies only, for which the (I-SOP, A-SOP) couple is kept
constant. However, in this "constant-SOP" case, the method loses
its applicability to all FUT types, i.e., if only the midpoint
wavelength is scanned without scrambling of the (I-SOP, A-SOP)
couples being applied, these relationships are no longer
universally valid, and may be significantly less reliable and/or
accurate--even if still roughly valid. Generally, if no scrambling
is performed, the methods are only valid if the FUT is "ideal" or
"nearly ideal", i.e., it exhibits excellent random coupling and has
an infinite or "near-infinite" polarization coupling ratio, and if
one chooses a large value of the PMD.DELTA..nu. product (typically
>10), where .DELTA..nu. is the width of the optical frequency
range. As a consequence, in practice, small PMD values cannot be
measured within a reasonable degree of uncertainty. In addition,
one frequently wishes to perform measurement on older installed
fibers, which are generally much less "ideal" than fibers produced
since about 2001.
[0383] It should also be noted that any of the equations for
computed DGD or PMD described herein, including those including a
factor for relative variance, may be applied to both normalized
power (including normalized OTDR trace) and relative power
(including relative OTDR trace). It should also be appreciated that
relative power or relative OTDR trace is proportional to normalized
power or normalized OTDR trace, respectively.
[0384] It should be noted that a pulse length used for the
single-ended cumulative PMD measurement should be not very
significantly greater than the fiber beat length, e.g. preferably
less than ten times the beat length.
[0385] As well, each measured OTDR trace should comprise an average
over several or many optical pulses, e.g. from 10 to 10,000
pulses.
[0386] Also note that preferred PMD measurement from the
single-ended cumulative PMD measurement should use several or many
different midpoint wavelengths, e.g. 10 to 1000, as a greater
number of such midpoint wavelengths will lead to a better
fundamental PMD measurement accuracy.
1.14 Details of Theory Specific to Embodiment (2)
Partial-DGD Measurement and Determination of DGD Therefrom
1.14.1 Pulse Spreading of Traffic Signal as a Manifestation of
Optical-Link PMD
[0387] The effect of PMD in an optical link is to induce temporal
pulse spreading on a data-carrying signal (SUT) propagating
therethrough. As discussed in Section 2.1 hereinabove, the extent
of this pulse spreading is given by the partial-DGD'' (denoted
herein equivalently as DGD.sub.P, or, for convenience in equations,
.tau..sub.PB) is strongly dependent upon both the wavelength of the
SUT and the SOP of the SUT as it enters the optical link. The input
SOP may vary in an unpredictable manner over relatively short times
(typically seconds to minutes) if patchcords or cabling at or near
the network transmitter are moved or otherwise perturbed.
Measurement of PMD-induced partial DGD is particularly important
for optical communication systems because it is associated with
PMD-induced system penalty, generally termed "PMD penalty" [1].
[0388] The partial-DGD, .tau..sub.PB(.nu.,.phi.), of a
signal-under-test (SUT) at an optical frequency, .nu., may be
expressed as:
.tau..sub.PB(.nu.,.phi.)=.tau.(.nu.)sin .phi. (6.20)
where .tau.(.nu.) is the differential group delay (DGD) of a
lightpath at an optical frequency, .nu.. .phi. is the angle between
two Stokes vectors defining, respectively, a PSP axis (e.g. slow
axis) of the lightpath and the SOP of the SUT at either the input
(as launched into the optical fiber link) or at the output of the
fiber link (just before the analyzer), this angle being
optical-frequency dependent and between 0 to 180 degrees.
[0389] The partial-DGD, .tau..sub.PB(.nu.,.phi.), of the SUT 60,
defined in equation (6.20), corresponds to the magnitude of a
perpendicular component of the polarization dispersion vector (PDV)
with respect to the SOP of the SUT, the magnitude of the PDV being
equal to the DGD (.tau.(.nu.)), of the optical fiber. Thus, the
partial-DGD, .tau..sub.PB(.nu.,.phi.), of SUT 60 may vary from zero
(no broadening) to the DGD(.nu.) value (maximum broadening),
dependent upon the launched input-SOP with respect to the "slow"
Input-PSP axis of the optical path and also vary in time as the DGD
or PSP axis of the optical fiber may vary in time.
[0390] Performing rms averaging of equation (6.20) over all
possible .phi. yields:
.tau. PB 2 ( v , .PHI. ) .PHI. = 2 3 .tau. ( v ) ( 6.21 )
##EQU00028##
Equation (6.21) relates the rms DGD and DGD of the lightpath at the
optical frequency of the SUT.
[0391] Moreover, if DGD.sub.P values of a large of number of
data-carrying signals (SUTs) are measured, where all the SUTs are
generated by transmitters at or adjacent the proximal end of the
optical link under test and where the respective wavelengths of the
SUTs are spread across a substantial wavelength region (e.g. more
than half of the telecom C-band extending from 1530-1565 nm), it is
possible to estimate the PMD of all or part of the optical link
(e.g. see equations (7a), (10a), (17a) and (28a)).
[0392] The method described herein to monitor and/or measure
DGD.sub.P of a SUT and, in a further aspect of the invention, to
estimate the PMD of the optical link, is not predicated upon
knowledge of the DGD of the lightpath (i.e. the DGD of the optical
link at the particular wavelength of the optical channel
corresponding to the lightpath, e.g. particular DWDM channel) nor
upon the angle .phi. between the two Stokes vectors corresponding
to the aforementioned lightpath PSP axis and the SOP of the input
light.
[0393] We also point out here that it may be difficult or
impractical to measure DGD.sub.P according to the definition of
equation (6.20), since both DGD and .phi. need to be known.
[0394] Note that, in order to simplify the notation in the
subsequent description, .tau..sub.PB(.nu.,.phi.) will be expressed
as .tau..sub.PB(.nu.) since .phi. does not need to be known or
determined for measuring the DGD.sub.P in implementations of this
embodiment, even though .tau..sub.PB is, in general, dependent on
the angle .phi..
1.14.2 Random Output SOP Scrambling Analysis for DGD Monitoring of
Traffic Signals
[0395] The conceptual measurement process underlying determination
of partial-DGD is very similar to that presented in Sec. 6.2.1
hereinabove, except that there is no "test-induced" variation of
I-SOP, the state of polarization of the SUT as it enters the
optical link (FUT). In other words, only A-SOP are varied--no
explicit averaging is performed over I-SOP as part of the basic
method to determine DGD at any particular moment. The A-SOP values
should be chosen in a random or predefined manner, such that the
points conventionally representing SOPs on the Poincare sphere are
approximately uniformly-distributed over its surface, whether the
distribution is random or comprises a uniform grid of points.
Hence, SSA theory provides that, on average over a sufficiently
large number, K, of such A-SOP values, a statistical moment,
specifically the variance (second moment) of the differences
between normalized powers observed at each of two closely-spaced
optical frequencies, .nu..sub.U and .nu..sub.L, is related to the
DGD at its midpoint optical frequency .nu..sub.mid
(=(.nu..sub.U+.nu..sub.L)/2) by a simple relationship. This
relationship is valid for all practical lightpaths regardless of
their degree of randomness or polarization coupling ratio,
including the extreme case of weakly-coupled optical fiber, e.g.
PMF fiber, in the optical path, i.e.,
DGD P ( v ) = 1 .pi..delta. v arcsin ( .alpha. ds .DELTA. T 2 ( v )
SOP ) ( 6.22 ) ##EQU00029##
where the theoretical constant .alpha..sub.ds= {square root over
(3)}, .sub.SOP represents averaging over K A-SOP values (I-SOP is
not varied as part of the measurement procedure), and
.delta..nu.(=|.nu..sub.U-.nu..sub.L|) is the small
optical-frequency difference ("step").
[0396] .DELTA.T(.nu.) is a difference between the analyzed
normalized powers (i.e. transmissions) observed at optical
frequencies .nu..sub.U and .nu..sub.L, respectively, and its second
moment or mean-square difference is,
.DELTA. T 2 ( v ) SOP = ( T U - T L ) 2 SOP = 1 K k ( T U ( k ) - T
L ( k ) ) 2 ( 6.23 ) ##EQU00030##
where the index k corresponds to a particular A-SOP, and where, for
polarization-sensitive one-detector implementations shown in FIGS.
2I and 2N, the normalized powers are,
T L ( k ) = u o P L ( k ) P L SOP T U ( k ) = u o P U ( k ) P U SOP
( 6.24 a ) ##EQU00031##
Here, the reference mean-value u.sub.o=1/2 is a theoretical
constant, and the average power is defined as,
P L SOP = 1 K k P L ( k ) . P U SOP = 1 K k P U ( k ) ( 6.24 b )
##EQU00032##
[0397] As depicted schematically in FIG. 11 measurements may be
undertaken at or adjacent the corresponding network receiver 28
(e.g. via a monitor port), or at monitor port 26 or 27 (tapped from
the link) at an intermediate location along between the Tx 22 and
Rx 28. For convenience, the following description assumes that an
OSA having polarization-diverse detection means is employed.
[0398] Furthermore, in preferred implementations of the embodiment,
for a prescribed optical-frequency range within the SUT bandwidth,
e.g. defined as that lying between optical frequencies for which
the (filtered) signal is 1 to 20 dB below its peak value, the
computed DGD.sub.P in equation (6.22) may be convoluted with the
SUT spectral profile to yield the PMD-induced
[0399] DGD.sub.P parameter, expressed as:
.tau. _ PB SUT = .intg. v S ( v ) .tau. PB ( v ) v .intg. v S ( v )
v ( 6.25 ) ##EQU00033##
where S(.nu.) is the optical-frequency-dependent signal power
determined from an average over at least one but preferably a large
of number of measured optical powers at each optical frequency
under conditions of negligible ASE, e.g. OSNR>20 dB as:
S(.nu.)=P(.nu.).sub.SOP (6.26)
[0400] The convolution procedure of equation (6.25) is necessary in
order to obtain reliable DGD.sub.P(.nu.) values across a
substantial portion of the SUT spectral profile.
[0401] However, if S(.nu.) is sufficiently "flat" over the
optical-frequency range encompassed by any pair of two
closely-spaced frequencies across some specified restricted portion
of the signal spectrum, then S(.nu.) may be considered constant in
equation (6.25), and consequently the mean DGD.sub.P value over a
specified optical-frequency range of the SUT bandwidth simplifies
to:
.tau..sub.PB.sub.SUT=.tau..sub.PB(.nu.).sub..nu. (6.25a)
or alternatively a rms DGD.sub.P value:
.tau. _ PB SUT = .tau. PB 2 ( v ) v ( 6.25 b ) ##EQU00034##
where .sub..nu. indicates an average over a specified
optical-frequency range, e.g. of a SUT bandwidth between .about.3
dB to .about.20 dB.
[0402] The signal power of a SUT 60 about each (midpoint) optical
frequency is extracted from average of the power difference
.DELTA.P(.nu.) for a large number of A-SOPs, so as to remove ASE
power arising from, e.g., in-line optical amplifiers:
S ( v ) = .DELTA. P ( v ) SOP or ( 6.26 a ) S ( v ) = .DELTA. P 2 (
v ) SOP ( 6.26 b ) ##EQU00035##
[0403] It should be appreciated that the calculated spectral power,
S(.nu.), in equations (6.26) and (6.26a) may be multiplied by any
factor that must be kept constant for any optical frequency within
a frequency range of interest and preferably power value P(.nu.)
used in equations (6.26) is an averaged value of
P(.nu.+1/2.delta..nu.) and P(.nu.-1/2.delta..nu.), i.e. P(.nu.)
being measured power at each midpoint optical frequency.
[0404] Based on above computed average DGD.sub.P value over a
specified wavelength range, e.g. of a SUT bandwidth, in equations
(6.25), (6.25a), or (6.25b), the degree to which the PMD of the
lightpath may impair the may be expressed as the PMD penalty, .eta.
(usually expressed in dB), where:
.eta. = A ( .tau. _ PB SUT 2 B ) 2 ( 6.27 ) ##EQU00036##
where B is the bit period (or symbol period, if the SUT comprises a
multibit/symbol modulation format), and A is a dimensionless
parameter dependent on modulation format, pulse shape, network
characteristics (e.g. optical noise, optical filter, etc.), and
receiver characteristics (e.g. electric filter, noise, etc.),
etc.
[0405] It should be appreciated that the above equation (6.27) is
not the only possible one and it may be expressed as any other
formula, for example, a PMD penalty, .eta.(.phi.), may be expanded
to higher order:
.eta. = A 1 ( .tau. _ PB SUT 2 B ) 2 + A 2 ( .tau. _ PB SUT 2 B ) 4
( 6.27 a ) ##EQU00037##
B is the bit (symbol) period, and A.sub.1 and A.sub.2 represent
predetermined parameters, for example, that may be extracted from
prior knowledge, or gleaned from experiments or simulations.
[0406] For measurement of link PMD for an in-service network, one
may perform an rms average over computed DGD.sub.P for each of a
plurality of SUTs, each corresponding to a network transmitter (Tx)
having respective central wavelengths that are distributed across a
significant spectral region (e.g. the telecom C, or C+L bands):
PMD = 3 2 .tau. PB 2 ( v ) v ( 6.28 a ) ##EQU00038##
where .sub..nu. indicates an average over each of the SUTs.
Improved accuracy may be obtained by evaluating DGD.sub.P across
each of the SUT bandwidths as a function of optical frequency, for
instance employing the convolution procedure of equation (6.25). It
should be appreciated that such link PMD estimation is predicated
upon all of the SUTs used in the measurement corresponding to
co-located Tx at the opposite end of the FUT. In addition, it is
preferable that the number of SUTs used in equation (6.28) be as
large as practical, in order that there be an increased statistical
probability that a wide variety of different input SOPs may be
launched into the FUT, thereby improving the PMD estimate.
[0407] Alternatively, equation (6.28a) can be expressed as:
PMD = 1 .pi. .delta. v arc sin ( 9 2 .DELTA. T 2 ( v ) SOP ; v ) (
6.28 b ) ##EQU00039##
where the subscripted bracket .sub.SOP;.nu. indicates an average
over both the A-SOP and midpoint optical frequencies.
[0408] In the limit of a sufficiently small optical-frequency
difference ("step"), equations (6.22) and (6.28b) tend to the
following simpler differential formula:
.tau. PB ( v ) = 1 .pi..delta. v 3 .DELTA. T 2 ( v ) SOP ( 6.22 a )
PMD = 1 .pi. .delta. v 9 2 .DELTA. T 2 ( v ) SOP ; v ( 6.28 c )
##EQU00040##
[0409] Of course, any other alternative mathematical function that
provides a numerical result that falls within an acceptable
difference from the said following differential formula for
realistic values of DGD.sub.P and PMD could be used instead. This
would be true for any of the other analogous formulas presented
elsewhere in this specification.
[0410] It should be noted that the relationships in equation (6.22)
or (6.28b) hold for .tau..sub.PB.delta..nu.<0.20 or
PMD.delta..nu.<0.15.
[0411] The normalized power will in fact be obtained differently in
each implementation (FIGS. 2H, 2I, 2K), i.e., by suitable
programming of the data processor. This explanation of the theory
is provided for the basic single-photodetector implementation of
FIGS. 2I and 2J, where normalization over the average power (i.e.
equation (6.24b)) is necessary, assuming total power is stable when
the A-SOP is changed, or as a function of time. Note that the
normalization procedure for the measurement configuration of FIGS.
2H and 2K is different. A detailed description of this
normalization procedure is provided hereinafter.
[0412] It should be noted that equation (6.22) yields a DGD value
for a SUT at a given midpoint wavelength, defined as the average
wavelength of the particular closely-spaced optical frequencies.
Equation (6.25) provides a signal spectral-weighted average of DGD
value for a prescribed SUT bandwidth used for estimating a
PMD-induced power penalty. Equation (6.28b) yields an estimated PMD
value for a prescribed wavelength range from a large number of SUTs
(e.g. >10-40). The PMD definition employed here is based on the
root-mean-square (rms) value of DGD averaged over optical
frequency.
1.14.3 DGD.sub.P Monitoring of Traffic Signal Including ASE and
Nonlinear Depolarization
[0413] The foregoing method for DGD.sub.P monitoring and
optical-link PMD measurement presuppose negligible depolarization,
that might arise from e.g. ASE of optical amplifiers, nonlinear
depolarization, etc. However, in many field applications, optical
amplifiers (typically erbium-doped optical amplifiers (EDFAs),
Raman amplifiers) have been inserted into the optical fiber link.
That is, the optical link 24 may comprise at least one, and
possibly several, optical amplifiers at various spacings (e.g.
.about.50 km), and several or many data-carrying signals (e.g.
20-60 in C-band) and long optical fiber segments. When an optical
amplifier and a multiplicity of traffic signals are present with a
long optical path, a power meter located at tap monitor port 26 or
27 or at distal end of a lightpath (e.g. at a receiver (Rx) side
28) will likely also detect (substantially unpolarized)
amplificatied spontaneous emission (ASE) light. As well, there may
be partial depolarization introduced by nonlinear effects, e.g.
inter-channel cross-phase modulation (XPM), in addition to any
residual depolarization on the light arising directly from the Tx
22. The presence of these depolarization effects in the detected
signal can be taken into account by "scaling down" the mean-square
differences .DELTA.T(.nu.,.phi.).sup.2.sub.SOP by a factor that can
be computed independently from the same raw data. This factor,
.sigma..sub.r.sup.2(.nu.), is a relative variance of the normalized
powers defined as,
.sigma..sub.r.sup.2(.nu.)=12.left
brkt-bot.(T(.nu.)T''(.nu.).sub.SOP-T(.nu.).sub.SOP.sup.2.right
brkt-bot. (6.29)
The notation T(.nu.)T''(.nu.).sub.SOP and T(.nu.).sub.SOP.sup.2
refer to averages over both normalized powers at .nu..sub.U and
.nu..sub.L, and T(.nu.) and T''(.nu.) are the normalized powers
from repeated measurements in one group at one given optical
frequency. Then an (optical-frequency-dependent) DGD.sub.P at a
given midpoint wavelength is obtained by dividing the mean-square
differences by the relative variance in equation (6.28b) as,
.tau. PB ( v ) = 1 .pi..delta. v arc sin ( 3 .DELTA. T 2 ( v ) SOP
.sigma. r 2 ( v ) ) ( 6.30 ) ##EQU00041##
[0414] It should be noted that, if the noise power contribution may
be neglected, then T(.nu.) and T''(.nu.) may be the same normalized
power, i.e. corresponding to only one measurement in one group at
one given optical frequency, and hence
T(.nu.)T''(.nu.)=T.sup.2(.nu.).
[0415] It further should be noted that, if the normalized powers
T(.nu.) are averaged over a sufficient large number of randomly
scrambled SOPs, then T(.nu.).sub.SOP.sup.2=1/4.
[0416] It should be appreciated that Eq. (6.30) may be replaced by
Eq. (6.22) if depolarization effects are negligible or small. Use
of Eq. (6.22) for calculating DGD.sub.P of a significantly
depolarized SUT (e.g. DOP.about.30%, due to a large fraction of
co-propagating ASE and/or signal depolarization from XPM) would
likely lead to a significant error, but may suffice for a very
rough DGD.sub.P estimation.
[0417] Therefore, in order to obtain the PMD-induced DGD.sub.P
parameter to estimate a PMD penalty, the spectral-power-weighted
average over computed DGD.sub.P in equation (6.30) may be
calculated using equations (6.25) and (6.26).
[0418] Preferably such signal power at each wavelength is extracted
from an average over at least one power difference, .DELTA.P(.nu.),
from at least two analyzed optical powers at each wavelength of
light for a large number of A-SOPs to remove the ASE contribution,
and thereby the signal light power at each wavelength of a SUT 60
can be expressed as:
S ( v ) = .DELTA. P ( v ) SOP or ( 6.26 a ) S ( v ) = .DELTA. P 2 (
v ) SOP ( 6.26 b ) ##EQU00042##
where .sub.SOP represents an average over the A-SOPs and
.DELTA.P(.nu.) is a power difference value between two measured
powers from either [0419] (i) two power measurements corresponding
to two A-SOPs for the implementations of FIG. 2K using two
photodetectors PD.sub.x 18A and PD.sub.y 18B with a PBS 14 or FIG.
2I using single tunable filter (TF) 16 and single photodetector
(PD) 18 with linear polarizer 15 where the only available powers
are obtained here from the photodetector 18; or [0420] (ii) from
two simultaneously measured powers using photodetectors PD.sub.x
18A and PD.sub.y 18B for same A-SOP for the implementation of FIG.
2K employing a PBS 14 and two tunable filters TF.sub.x 16A and
TF.sub.y 16B,
[0421] Alternatively, if S(.nu.) is set to equal to any constant
value for above equations (6.25), a mean DGD.sub.P value over a
specified wavelength range of a SUT bandwidth is obtained as:
.tau..sub.PB.sub.SUT=.tau..sub.PB(.nu.).sub..nu. (6.25a)
or alternatively an rms DGD.sub.P value as:
.tau. _ PB SUT = .tau. PB 2 ( v ) v ( 6.25 b ) ##EQU00043##
where .sub..nu. is to average over a specified wavelength range,
e.g. of a SUT bandwidth.
[0422] Based on above computed average DGD.sub.P value over all or
at least a portion of the SUT bandwidth, in equation (6.25),
(6.25a) or (6.25b), the corresponding PMD-induced impairment on the
SUT propagating through a lightpath (e.g. of a DWDM network) may be
related to the PMD penalty, .eta., via equations (6.27) or (6.27a)
presented above.
[0423] In a further implementation of Embodiment (2), measurement
of DGD.sub.P values at for a plurality of different SUTs,
preferably roughly uniformly spaced across a wide spectral region
(e.g. telecom C band) may be used to estimate the link PMD:
PMD = 3 2 .tau. PB 2 ( v ) v or ( 6.31 ) PMD = 1 .pi. .delta. v arc
sin ( 9 2 .DELTA. T 2 ( v ) .sigma. r 2 ( v ) SOP ; v ) ( 6.32 )
##EQU00044##
where the average over A-SOP in equation (6.30) is now replaced by
the average over both SOP (i.e. A-SOP) and optical frequency. Note
that a relative variance of the normalized powers may also be
further calculated via a simple average over optical frequency, but
such an average is usually not reliable because the power density
of the SUTs usually is usually not flat.
[0424] In the limit of a small step, equations (6.30) and (6.32)
tend to respective simpler differential formulae:
.tau. PB ( v ) = 1 .pi. .delta. v 3 .DELTA. T 2 ( v ) SOP .sigma. r
2 ( v ) ( 6.30 a ) PMD = 1 .pi. .delta. v 9 2 .DELTA. T 2 ( v )
.sigma. r 2 ( v ) SOP ; v ( 6.32 a ) ##EQU00045##
[0425] It should be noted that, if two powers of "closely-spaced
optical frequencies" are equal and there is negligible differential
spectral attenuation from SUT 60 for these "closely-spaced
wavelengths", the measured powers for "closely-spaced wavelengths"
can directly be applied to equations (6.30) and (6.32), i.e.
without need for normalization of the measured powers (note in this
case, T(.nu.).sub.SOP.sup.2 may not be equal 1/4). This arises
since, under this condition, the normalization procedure described
above may only produce a `constant factor` that is multiplied on
measured powers in order to obtain normalized power (between 0 and
1), but by using equations (6.30) and (6.32) to compute DGD or PMD,
this constant `factor` is eventually cancelled because the same
`factor` is applied to both the mean-square difference and relative
variance if they are both directly computed from measured powers.
In other words, if equations (6.30) and (6.32) are used, only
relative powers that are proportional to normalized powers are
required to be obtained to calculate the DGD.sub.P or PMD.
[0426] It should be appreciated that equations (6.30) and (6.32)
are applicable whether or not amplifier noise is present on the
link under test.
[0427] However, it should be noted that the equations (6.28a) and
(6.31) no longer represent simple rms or mean averaging of all
DGD.sub.P(.nu.) values but include a statistical theoretical
constant
( i . e . 3 2 ) . ##EQU00046##
Also note a similar equation may be applied for mean averaging over
all single DGD.sub.P(.nu.) values with a different a statistical
theoretical constant. (However, it is not the same as a standard
PMD definition, i.e. PMD is calculated/defined by rms or mean DGD
values at different frequencies.)
[0428] We point out here that the calculation of a PMD estimate for
an optical link 24 via equations (6.28a) and (6.31) is based on the
statistical relationship between the measured DGD.sub.P values and
the PMD. Moreover, equation (6.28a) or (6.31), or similar
algorithms, may also be applied to other PMD measurement methods
known by those skilled in this art, for example, measured maximum
(polarization) differential time delays at different optical
frequencies by a phase shift method, measured SOP or arc lengths at
different optical frequencies e.g. by a spectrally-resolving
polarimetric head, etc.
Data Processing and Computation
[0429] Measurement of a polarization-related characteristic of an
optical path (FUT) according to aspects of the present invention,
including two-ended PMD measurement, single-ended overall PMD
measurement and single-ended cumulative PMD measurement, are all
based upon the random input and output state-of-polarization
scrambling analysis (SSA) approach described herein, but their
detailed implementations are not the same. For example, the
two-ended measurement requires that the light source means be
placed at one end of FUT and analyzer-and-detection means at the
other end of FUT. The nature of the light source may also be
different, for example, two-ended PMD measurement may employ either
a continuous wave (CW) or pulsed light source if it can select or
modulate optical frequency of light to produce two or three closely
spaced wavelengths for the measurement, but for the single-ended
PMD measurement, it is necessary to use a pulsed light source
(usually a tunable OTDR) to resolve the reflections from the distal
end of FUT. There are also differences in operation between
single-ended "overall PMD" measurements and single-ended cumulative
PMD measurements, for instance with respect to pulse length, number
of closely spaced wavelengths, acquired data and data
processing.
[0430] Therefore, below we will describe the method of operation,
data processing and computation in three different sections for
Two-Ended PMD Measurement, "Two-ended" Partial-DGD Measurement,
Single-ended Overall PMD Measurement and Single-ended Cumulative
PMD Measurement.
1.15 Method of Operation
1.15.1 Method of Operation
Embodiment (1)--Two-Ended "Test-Source-Based" DGD and/or PMD
Measurement
[0431] The method of operation for a measurement instrument of
Embodiment (1) ("two-ended PMD measurement) for measurement of DGD
and/or PMD, as shown generically in FIG. 1, will now be described
in more detail with reference to the flowcharts shown in FIGS. 5A,
5B, 5C and 5D.
[0432] In steps 4.1 and 4.2, the user first installs the
application and, if applicable, inserts the test modules in the
platforms. Then the user starts testing software to cause the
system to initialize the test modules, specifically initializing
the wavelength of the polarized light source 12 (either tunable
laser source 12A or broadband light source 12B), the Input SOP
controller (I-SOP) 14A, the analyzing means 14B and 20 and the
detection 22 and processing section 34. Then the one end of fiber
under test (FUT) 18 is connected to source module before I-SOP 14A
and the distal end of FUT 18 are connected to
analyzer-and-detection module, and patch cords with either a PC or
an APC connector (such as FC/PC or FC/APC), or direct bulkhead
connectors, are used to connect the modules with the FUT. Most
instrument parameters will usually be factory set according to
customer requirements, but the user may manually select parameters
for both the light source and analyzer by steps 4.1c and 4.3,
respectively. Assuming that the user selects manual parameter
setting, the program proceeds to the manual parameter setting steps
4.1c and 4.4 and prompts the user as follows:
(a) Set a center wavelength for the tunable laser source 12A or
tunable filter 27. (b) Set a wavelength range [.lamda.min,
.lamda.max] for the group center wavelengths that will be
encompassed by the light source 12 providing that is correspond to
an accessible wavelength range of the FUT 18. (c) If available
(i.e. not fixed at factory), set the step or difference .delta..nu.
(or .delta..lamda.) between the pairs closely-spaced optical
frequencies .nu..sub.U and .nu..sub.L (or wavelengths).
Alternately, the user may enter the anticipated PMD value for the
FUT and leave the processor to compute and then select the
optical-frequency step. As an example, the step can be conveniently
set to .delta..nu.=.alpha..sub..delta..nu.PMD.sup.-1 where
.alpha..sub..delta..nu..about.0.15 to 0.2 and, thus, .delta..lamda.
can be extracted from
.delta..lamda..apprxeq.(c/.nu..sub.c.sup.2).delta..nu. where
.nu..sub.c=(.nu..sub.U+.nu..sub.L)/2. (Note: there is an optimal
step for a given PMD value, as large as possible so as to maximize
signal-to-noise ratio, but small enough to satisfy the above
condition, i.e., PMD.delta..nu.<0.15 to 0.2. It is also noted
that closely-spaced optical frequencies may also be more than two
and this may be especially interesting for testing and monitoring
where DGD or PMD from FUT may be varied versus time.) (d) Set the
number K of center-wavelengths and/or states of polarization
selected by the I-SOP scrambler 14A and A-SOP scrambler 14B, i.e.,
the number (K) of groups of data to be acquired. For example, K may
be set to 1000 to 100,000. Or, optionally, for the continuously
scanning input and output SOP mode, only the number K of
center-wavelengths and then set a scanning time for both input SOP
controller 14A and analyzer SOP controller 14B and 20. Or,
optionally, if only one center-wavelengths is selected, set the
number K of states of polarization selected by the I-SOP scrambler
14A and A-SOP scrambler 14B or a scanning time for the continuously
scanning both I-SOP scrambler 14A and A-SOP scrambler 14B. (e)
Optionally, set the number of pulses to be averaged to obtain each
individual power (for example 2 or >100) for a series of
modulated optical pulses to be launched into the FUT. No setting is
required if only one modulated optical pulse is to be launched into
the FUT. (f) Set an overall total acquisition time for each
individual PMD measurement and number of PMD measurement, as well
as the waiting time between two successive measurements. (g) Select
the modulated optical pulse duration Tp. Typically, a long pulse
length is selected for the measurement because it leads to a high
dynamic range, and a high signal-to-noise ratio although a short
pulse may still be used. (Typically, the modulated optical pulse
length is chosen to be between 100 .mu.s and 1 s, although pulse
lengths outside of this range are also feasible. (h) Optionally,
set an input power of the tunable light source means. (i)
Optionally, adjust the power entering the analyzer module from the
FUT by means of an optical attenuator in the optical path, for
example, at a location just after the input of the analyzer module.
Normally, however, this would be automatically set by the
instrument. [(j) Optionally, enter the cable or fiber name and/or
other relevant information. (k) Save all measurement parameters to
a data file that will be retrieved for data processing by the data
processor 34.
[0433] If, in decision step 4.3, the user selects automatic
parameter setting, the program starts the auto parameter setting
procedure in step 4.5 and carries out the following steps:
(a) Select pre-defined certain default measurement parameters,
namely [0434] (1) The center wavelength range [.lamda.min,
.lamda.max] that will be covered by the light source 12; [0435] (2)
Number K of SOPs and/or center wavelengths by the I-SOP scrambler
14A and A-SOP scrambler 14B (for example, 1000-10,000) for one PMD
data acquisition, or, alternatively, a scanning time of both or
either of I-SOP scrambler 14A and A-SOP scrambler 14B; [0436] (3)
Time for each individual acquisition (measurement), waiting time
between any two individual acquisitions, and number of repeated
acquisitions; [0437] (4) Frequency pulse duration Tp (or length)
for tunable coherent source; and [0438] (5) Launched light power
and received power. (b) The test module may also be designed to
have a pre-scan acquisition using a reduced number of groups, such
as K=50-100, to obtain estimations of optimal wavelength step
frequency difference .delta..nu. (or .delta..lamda.) between the
two closely-spaced optical frequencies .nu..sub.U and .nu..sub.L
(or wavelengths .lamda..sub.U and .lamda..sub.L). Pre-scan data
acquisition is performed to find the appropriate step or difference
.delta..nu. (frequency) or .delta..lamda. (wavelength) between the
two closely-spaced optical frequencies .nu..sub.U and .nu..sub.L,
(or .lamda..sub.U and .lamda..sub.L). For example, such data
acquisition may be carried out by using, for each group, four
different laser wavelengths to obtain a total combination of six
different frequency or wavelength steps. In this case, good
communications between the two ends of the FUT may be required. (c)
Auto mode may also be designed to automatically produce cable or
fiber name and/or other relevant information;
[0439] Once the measurement parameters have been entered, whether
manually or automatically, the program proceeds to step 4.6 and
computes wavelength step .delta..lamda. (or frequency difference
.delta..nu.) if the anticipated total PMD of the FUT has been
specified or estimated via the aforementioned auto-setting
procedure, and the appropriate sequence of wavelengths based on the
parameter settings. It is preferred to use three or four (or even
more) different laser wavelengths to produce three or six (or even
more) different wavelength steps to cover a wide measurable PMD
range.
[0440] Finally, all the measurement parameters, whether directly
specified or computed as described above, are stored in the header
of the data file or instrument (Step 4.7).
[0441] It should be noted that a linewidth of the tunable coherent
source will usually be set, in the factory or by design, at a
relatively small level (e.g. of <1 to 2 GHz) in order to ensure
the ability to measure a high PMD (e.g. >50 ps) from the
FUT.
[0442] It should be noted that, conveniently, at each SOP and/or
center wavelength, the frequency difference .delta..nu. (or
wavelength step .delta..lamda.) between the two closely-spaced
optical frequencies .nu..sub.U and .nu..sub.L (wavelengths
.lamda..sub.U and .lamda..sub.L) may remain the same or similar.
Each SOP and/or wavelength may only be set in a short time
period.
[0443] It should be re-emphasized, that in order to obtain a
reliable PMD measurement of the FUT, it is preferable that the
acquisition should be undertaken for several or many (I-SOP, A-SOP)
couples and/or different center wavelengths.
[0444] FIG. 4C shows in more detail the data acquisition step 4.10
to acquire a kth group of powers. The pre-defined wavelength step
of .delta..lamda. can be used to compute a sequence of wavelengths
.lamda.s as already discussed in step 4.6. The frequencies
.nu..sub.L.sup.(k) and .nu..sub.U.sup.(k are calculated to satisfy
the relation .nu..sub.L.sup.(k)-.nu..sub.U.sup.(k)=.delta..nu.
where .delta..nu. is the frequency difference (or when the
wavelength difference .delta..lamda. is used, it satisfies
.lamda..sub.U.sup.(k)-.lamda..sub.L.sup.(k)=.delta..lamda.). The
maximum measurable PMD, PMD.sub.maX corresponding to a given step
.delta..nu., can be estimated as
PMD.sub.max.about..alpha..sub.rt(.pi..delta..nu.).sup.-1 and
.delta..lamda. can be extracted from
.delta..lamda.=(.lamda..sub.0.sup.2/c).delta..nu. where
.lamda..sub.0=(.lamda..sub.min+.lamda..sub.max)/2. The control unit
30 control (b) of the test module to obtain the kth group of powers
as follows: [0445] (1) Set SOP.sub.k by the I-SOP scrambler 14A and
A-SOP scrambler 14B (step 4.3.1 of FIG. 4C) if macroscopic SOP step
selection is used for either or both of the scramblers (14A,14B),
or, if continuous SOP scanning is used for either or both of the
scramblers (14A,14B), set a scan time for both or either of input
and output SOP scramblers (14A,14B) where the I-SOP and A-SOP may
be slowly continuously and randomly scanned to uniformly cover the
Poincare Sphere. It should be noted I-SOP and A-SOP (14A,14B) may
be set via either stepwise SOP adjustment or continuous SOP
scanning according to the control mode that is selected. [0446] (2)
Control the light source 12 or tunable filter 27 to set the lower
wavelength to .lamda..sub.L.sup.(k) (Step of 4.3.2 of FIG. 4C).
Detection and processing unit 34 will acquire data of powers as
P.sub.xL and P.sub.yL (step 4.3.3 of FIG. 4C). More details of this
data acquisition are shown in FIG. 4D and be described below. The
same data acquisition process is repeated to obtain duplicate or
repeated powers of P.sub.xL'' and P.sub.yL'' (step 4.3.4 of FIG.
4C). [0447] (3) Repeat the same data acquisition for the upper
wavelength .lamda..sub.U.sup.(k) (where the .lamda..sub.U.sup.(k)
is also set by the light source 12 or tunable filter 27 while
keeping the approximately same input and output SOPs conditions for
both I-SOP scrambler 14A and A-SOP scrambler 14B. The detection and
processing unit 36 then acquires, in addition to the just
previously-acquired data of powers P.sub.xU and P.sub.yU,
corresponding duplicates P.sub.xU'' and P.sub.yU'' (steps 4.3.5,
4.3.6 and 4.3.7 of FIG. 4C). Alternatively, the repeated data may
be acquired over a short time period, and then split it as two data
that present at different time.
[0448] FIG. 4D gives more detail of the data acquisition of step
4.3.3 shown in FIG. 4C for acquisition of P.sub.yL and P.sub.xL in
the kth group of powers. The launched modulated optical pulses from
the light source 12 are sent into FUT 18 and the output modulated
optical pulses then exit the distal end of FUT 18. The exited
modulated optical pulses are then sent into the test analyzer
module of instrument to be split into two routes--y and x--by
either a PBS 20 or 20C or a coupler 21, for example a 3-dB coupler,
with one of two output arms being connected with a linear polarizer
20A. The split light optical pulses entering into routes y and x
are detected by two photodetectors, for example, two APDs such as
22B and 22C (or 20) (Steps of 4.4.1 and 4.4.2 of FIG. 5D).
Alternatively, the exited modulated optical pulses incident into
the test analyzer module are directly sent to a linear polarizer.
The light pulses are either directly detected by one photodetector,
for example, one APD such as 22A (FIG. 1B) or split into two
routes--y and x--by a coupler 21, for example a 3-dB coupler,
entering into routes y and x are detected by two photodetectors,
for example, two APDs such as 22B and 22C (FIG. 1C). The
"durations" of the response signals of modulated optical pulses
from the distal end of FUT are sampled or sampled and averaged to
obtain "response" pulse signals, such as P.sub.y(t) and P.sub.x(t)
(Steps of 4.4.3 and 4.4.4 of FIG. 5D). The final sampled or
sampled-and-averaged power of P.sub.yL or P.sub.xL are then
obtained by averaging said previously acquired response pulse
signals over a substantial portion of its duration about the center
of the pulse of impulse response signals, Py(t) or Px(t), (Steps
4.4.5 and 4.4.6 of FIG. 5D). The portion of the pulse duration to
be averaged usually depends on the electronic pre-filtering.
[0449] Once the kth group of powers has been acquired as described
above, in Step 4.10 (see FIG. 4B), the data of group k is saved
into the data file in Step 4.11. Step 4.12 then increments the
group number register.
[0450] The data acquisition step 4.10 and group storing step 4.11
will be repeated for different center-wavelengths and/or I-SOPs and
A-SOPs selected by the I-SOP scrambler 14A and A-SOP scrambler 14B
in accordance with the manual parameter setting step of 4.4 or from
auto parameter setting of step 4.5 or default parameter setting
until K groups of powers have been acquired and stored in the data
file.
[0451] Step 4.9 decides whether or not this individual acquisition
is completed. If decision step 4.9 gives a positive result and,
then in step 4.13 this ith data is saved. Otherwise, the
acquisition will process the steps 4.10 and 4.11 again.
[0452] The step 4.8 decides whether or not a new individual
acquisition is to be initiated. If the entire measurement
acquisition is finished, the step 4.15 saves all individual data
for the overall entire acquisition. If not, the processor resets
k=0 to start a new individual acquisition for steps of 4-9, 4.10,
4.11 and 4.12. Step 4.16 determines whether or not to start another
acquisition.
[0453] At this stage, the measurement parameters and all groups of
powers have been saved in the proper files.
[0454] The decision step 4.17 may launch data processor, step 4.18
may load currently available acquired data from data file, step
4.19 may process them to estimate the DGD value at given center
wavelength or mean DGD or rms DGD (i.e. PMD) value over a
wavelength range for the FUT and step 4.21 may display it.
Optionally step 20 may allow the user to save the processed result,
such as DGD or mean DGD or RMS DGD values versus time.
[0455] Optional decision from step 4.16 then may give the user an
opportunity to initiate another acquisition process for the same
FUT. If the user decides to do so, the program returns to the
parameter setting step 4.3. If not, decision step 4.17 gives the
user the option of exiting acquisition, in which case the data
stored in the data file will be retained for later processing, or
to initiate processing of already acquired and stored data of
powers.
[0456] If processing is initiated, step 4.18 allows the user to
select the data file to be processed in a conventional "open file"
dialog box and the data processor 34 accesses the previously saved
acquisition data comprising detected powers and associated
measurement parameters from the data file, and uses the data to
compute DGD or mean DGD or RMS DGD of the FUT.
[0457] It should be noted that, by employing the method described
hereinbelow, the above steps may be used to obtain one or more of
DGD at a given midpoint wavelength, rms-DGD (i.e. PMD) and DGD as
function of wavelength, the latter enabling rms DGD or mean DGD to
be computed. Such computations may also be included in data
processing step 4.19.
[0458] Note that, for the case of K=1, i.e. the detected light
powers correspond to only one group, i.e. within which the I-SOP,
A-SOP, center-wavelength are the same. Nevertheless, one may still
be able to roughly evaluate the PMD, although this simple case may
not be able to provide a sufficiently accurate and meaningful
result, as there will likely be a very significant associated
uncertainty.
1.15.2 Method of Operation
Single-Ended Overall PMD Measurement
[0459] The method of operation of the tunable OTDR based
single-ended PMD measurement illustrated in FIGS. 3F and 3D will
now be described with reference to the flowcharts shown in FIGS.
6A, 6B and 6C. In step 5.1, the user first installs the application
and inserts the test module in the platform, then starts testing
software to cause the system to initialize the test module,
specifically initializing the tunable pulsed light source 12, the
I/A-SOP controller 14 and the OTDR detection means 22, and the OTDR
processing means 40. Then the fiber under test (FUT) 18 would be
connected to test module (i.e. instrument) and a patch cord with
either a PC connector (such as FC/PC or FC/UPC) or a
fiber-pigtailed mirror 50 is connected to the distal end of the
FUT. This would create a localized reflection at the end of FUT
that is used for the PMD measurement.
[0460] Decision step 5.2 prompts the user to select either manual
parameter setting or automatic parameter setting. Assuming that the
user selects manual parameter setting, the program proceeds to the
manual parameter setting step 5.3 and prompts the user as
follows:
(a) Set a wavelength range [.lamda.min, .lamda.max] for the group
center wavelengths that will be encompassed by the tunable pulsed
laser source 12; (b) Set the step or difference .delta..nu. (or
.delta..lamda.) between the pairs closely-spaced optical
frequencies .nu..sub.U and .nu..sub.L (or wavelengths).
Alternately, the user may enter the anticipated PMD value for the
FUT and leave the processor 34 to select the wavelength step. As an
example, the step can be conveniently set to
.delta..nu.=.alpha..sub..delta..nu.PMD.sup.-1 where
.alpha..sub..delta..nu..about.0.1 to 0.15 and, thus, .delta..lamda.
can be extracted from
.delta..lamda..apprxeq.(c/.nu..sub.c.sup.2).delta..nu. where
.nu..sub.c=(.nu..sub.U+.nu..sub.L)/2. (Note: there is an optimal
step for a given PMD value, as large as possible so as to maximize
signal-to-noise ratio, but small enough to satisfy the above
condition, i.e., PMD.delta..nu.<0.1 to 0.15); (c) Set the number
K of center-wavelengths and/or states of polarization selected by
the I/A-SOP controller 14, i.e., the number (K) of groups of data
to be acquired. For example, K may be set to 200; (d) Set the
averaging time .DELTA.t of each individual power (for example,
.DELTA.t=0.05 or 0.10 second), or set the number of durations of
pulses reflected from the distal end of the FUT to be averaged to
obtain each individual power (for example 50 or 100). Note that
once the averaging time .DELTA.t and the number K of
center-wavelengths and/or states of polarization have been set. a
total acquisition time for PMD measurement may be established; (e)
Select the pulse duration Tp (e.g. 275, 1000, 2500, 5000, 10000,
20000 ns) or, equivalently, the pulse length for OTDR. In order for
the pulse reflected from the selected reflection not to be
superposed in time with some portion of a pulse reflected from
another reflection, the pulse length, L.sub.p, shall be selected
such that L.sub.p<.DELTA.z, where .DELTA.z is the distance along
the FUT between the selected reflection and the nearest of anyone
or all other reflections. Typically, a long pulse length is
selected for the single-ended PMD measurement because it has
advantages of leading to high dynamic range, and/or a high signal
to noise ratio, and/or a short averaging time (thereby a short
overall acquisition time) although a short pulse may still be used;
(f) Set the FUT length, normally the full effective optical length
of the FUT; (g) Optionally, select a high dynamic range or a low
dynamic range according to the optical-fiber length. Typically, in
a normal operation the test module prompts the user to select a
high dynamic range, but it may also allow the user to test a very
short fiber by choosing a low dynamic range for acquisition. With
the low dynamic range mode, the output peak power of the launched
OTDR pulses is reduced, either by inserting an optical attenuator
in the optical path, for example, at a location just before the
output of the test module, or electrically, for example, by
decreasing the bias current of the gain medium of the tunable
pulsed laser; (h) Optionally, enter the cable or fiber name and/or
related relevant information; (i) Save all measurement parameters
to a data file that will be retrieved for data processing by the
data processor 34.
[0461] If, in decision step 5.2, the user selects automatic
parameter setting, the program starts the auto parameter setting
procedure in step 5.4 and carries out the following steps:
(a) Select pre-defined certain default measurement parameters,
namely [0462] (6) The center wavelength range [.lamda.min,
.lamda.max] that will be covered by the tunable pulsed laser source
12; [0463] (7) Number K of (I-SOP, A-SOP) couples and/or center
wavelengths to be set by the I/A-SOP controller 14 (for example,
200) for a real single-ended PMD data acquisition; [0464] (8)
Averaging time .DELTA.t (for example, .DELTA.t=0.05 or 0.1 second)
or the number of duration of pulse reflected from the distal end of
the FUT to be averaged (for example 50 or 100) for each individual
power; and [0465] (9) Pulse duration Tp (or length) for OTDR. It is
noted that these default parameters set in (1), (3) and (4) will
also be used for pre-scan acquisition. (b) The test module will
conduct a pre-scan acquisition using a reduced number of groups,
such as K=50, to obtain estimations of the FUT length, of total
loss from FUT and of optimal wavelength step frequency difference
.delta..nu. (or .delta..lamda.) between the two closely-spaced
optical frequencies .nu..sub.U and .nu..sub.L (or wavelengths
.lamda..sub.U and .lamda..sub.L). The OTDR will launch a standard
OTDR pulse (e.g, 1 or 10 .mu.s) to detect the end of the fiber (or
a user defined localized reflection) so that the FUT length can be
obtained and the pulse repetition period (Tr) can also be deduced
according to the round-trip time through the length of the fiber.
From this OTDR acquisition, a loss of FUT may also be estimated,
otherwise, a saturation situation on photodetectors may be observed
if there is any. Then a decision can automatically be made on
whether or not to reduce the output peak power for the OTDR light
pulses. Pre-scan data acquisition is performed to find the
appropriate step or difference .delta..nu. (frequency) or
.delta..lamda. (wavelength) between the two closely-spaced optical
frequencies .nu..sub.U and .nu..sub.L (or or .lamda..sub.U and
.lamda..sub.L). For example, such data acquisition may be carried
out by using, for each group, four different laser wavelengths to
obtain a total combination of six different frequency or wavelength
steps. The optimally appropriate wavelength step to be used in the
actual single-ended PMD measurement data acquisition may be found
by processing of these pre-scan acquisition data of powers. To save
all automatically-selected measurement parameters to the header of
the data file that will be retrieved for data processing by the
data processor 34. (c) Auto mode may also be designed to
automatically produce cable or fiber name and/or any other relevant
information.
[0466] Once the measurement parameters have been entered, whether
manually or automatically, the program proceeds to step 5.5 and
computes wavelength step .delta..lamda. (or frequency difference
.delta..nu.) if the anticipated total PMD of the FUT has been
specified or estimated via the aforementioned auto-setting
procedure, the repetition period T.sub.r according to the
round-trip time through the length of the fiber, and the
appropriate sequence of wavelengths .lamda.s based on the parameter
settings.
[0467] Finally, all the measurement parameters, whether directly
specified or computed as described above, are stored in the header
of the data file (Step 5.6).
[0468] It should be noted that the linewidth of the tunable pulsed
light source will usually be set, in the factory, to a relatively
small value (e.g. <4 GHz) in order to ensure the ability to
measure a high PMD of the FUT.
[0469] With the group number register initialized to k=0, decision
step 5.7 determines whether the total number of groups of powers
have been acquired. If not, the program proceeds to step 5.8 to
acquire the kth group of powers.
[0470] It should be noted that, conveniently, at each SOP and/or
center wavelength, the frequency difference .delta..nu. (or
wavelength step .delta..lamda.) between the two closely-spaced
optical frequencies .nu..sub.U and .nu..sub.L (wavelengths
.lamda..sub.U and .lamda..sub.L) may remain the same or similar.
Each SOP and/or wavelength may only be set in a short time
period.
[0471] It should be also noted, that it is preferable to acquire
data for several or many SOP couples and different midpoint
wavelengths, in order to determine the overall PMD.
[0472] FIG. 6B shows in more detail of the data acquisition step
5.8 to acquire a kth group of powers. The pre-defined wavelength
step of .delta..lamda. can be used to compute a sequence of
wavelengths as already discussed in step 4.5. The frequencies
.nu..sub.L.sup.(k) and .nu..sub.U.sup.(k are calculated with
satisfaction of .nu..sub.L.sup.(k)-.nu..sub.U.sup.(k)=.delta..nu.
where .delta..nu. is the frequency difference (or when the
wavelength difference .delta..lamda. is used, it satisfies
.lamda..sub.U.sup.(k)-.lamda..sub.L.sup.(k)=.delta..lamda.). The
maximum measurable PMD, PMD.sub.max corresponding to a given step
.delta..nu., can be estimated as
PMD.sub.max.about..alpha..sub.rt(.pi..delta..nu.).sup.-1 and
.delta..lamda. can be extracted from
.delta..lamda..apprxeq.(.lamda..sub.0.sup.2/c).delta..nu. where
.lamda..sub.0=(.lamda..sub.min+.lamda..sub.max)/2. The control unit
30 controls the test module to obtain the kth group of powers as
follows: [0473] Set SOP.sub.k using the I/A-SOP controller (Step of
5.3.1 of FIG. 6B). [0474] Control the tunable pulsed laser 12 to
set the lower wavelength to .lamda..sub.L.sup.(k) (Step of 5.3.2 of
FIG. 6B). Detection and processing unit 36 will acquire data of
powers as P.sub.xL and P.sub.yL (Step of 5.3.3 of FIG. 6B). More
details of this data acquisition are shown in FIG. 4C will be
described below. The same data acquisition process is repeated to
obtain duplicate or repeated powers of P.sub.xL'' and P.sub.yL''
(Step of 5.3.4 of FIG. 6B). [0475] Repeat the same data acquisition
for the upper wavelength .lamda..sub.U.sup.(k) (where the
.lamda..sub.U.sup.(k) is also set by the tunable pulsed laser 12)
while keeping the same (I-SOP, A-SOP) couple. The detection and
processing unit 36 then acquiring data of powers P.sub.xU and
P.sub.yU and duplicates P.sub.xU'' and P.sub.yU'' (Steps of 5.3.5,
5.3.6 and 5.3.7 of FIG. 6B).
[0476] FIG. 6C gives more detail of the data acquisition of step
5.3.3 shown in FIG. 6B for acquiring of P.sub.yL and P.sub.xL in
the kth group of powers. The launched light pulses from the OTDR
are sent into FUT and some fraction of the pulsed light is
reflected from the localized reflector, such as a PC connector of
the patchcord or a fiber-pigtailed mirror connected at the end of
FUT. The reflected light pulses are then returned into the test
module or instrument to be split into two routes--y and x--by
either a PBS or a coupler, for example a 3-dB coupler, with one of
two output arms being connected with a linear polarizer. The split
light pulses entering into routes y and x are detected by two
photodetectors, for example, two APDs such as 22'B and 22'C (Steps
of 5.4.1 and 5.4.2 of FIG. 6C). The "durations" of the response
signals from the light pulses reflected by the distal end of FUT or
at any other locations along fiber are sampled and averaged to
obtain "averaged" mean response pulse signals, such as P.sub.y(t)
and P.sub.x(t) (steps 5.4.3 and 5.4.4 of FIG. 6C). The final
averaged power of P.sub.yL or P.sub.xL are then obtained by
averaging said previously sampled and averaged mean response pulse
signals over its substantial portion of its duration about the
center of the pulse of impulse response signals, Py(t) or Px(t)
(steps 5.4.5 and 5.4.6 of FIG. 6C). The portion of the pulse
duration to be averaged usually depends on the electronic
pre-filtering.
[0477] Once the kth group of powers has been acquired as described
above, in Step 5.9 (see FIG. 6A), the data of group k is saved into
the data file. Step 5.10 then increments the group number
register.
[0478] The data acquisition step 5.8 and group storing step 5.9
will be repeated for different center-wavelengths and/or (I-SOP,
A-SOP) couples selected by the I/A-SOP controller 14 in accordance
with the manual parameter setting step of 5.3 or from auto
parameter setting of step 5.4 until K groups of powers have been
acquired and stored in the data file.
[0479] At this stage, the measurement parameters and all groups of
powers have been saved in the same data file associated with the
header information of measurement parameters.
[0480] During the data acquisition the step 5.20 (optionally) may
load any currently available acquired data from data file and
process them to estimate the RMS DGD (i.e. PMD) value for the FUT
18 and step 5.21 may display it as well as elapsed time of the
acquisition, length and loss of the FUT. Note the estimated PMD
value may frequently be varied until the end of the data
acquisition. Optionally step 5.22 may allow the user to save the
processed result.
[0481] Also at this stage, decision step 5.7 gives a positive
result and, in step 5.11, the program saves and closes the data
file in step 5.11.
[0482] Optional decision from step 5.12 then may give the user an
opportunity to initiate the acquisition of another K groups of
powers for the same FUT. If the user decides to do so, the program
returns to the parameter setting step 5.2. If not, decision step
5.13 gives the user the option of exiting acquisition, in which
case the data stored in the data file will be retained for later
processing, or to initiate processing of already acquired and
stored data of powers.
[0483] If processing is initiated, step 5.14 allows the user to
select the data file to be processed in a conventional "open file"
dialog box, whereupon, in step 5.16, the data processor 34 accesses
the pre-saved acquisition data of powers and associated measurement
parameters from the data file, and uses the data to compute total
rms-DGD (i.e., PMD) of the FUT. On the other hand, box 5.15, which
is not a "step" as such, indicates that the user may launch the
data processing software independently at any time to process any
previously acquired data file. In step 5.17, the data processor 34
saves the result of computed PMD value and measurement parameters
in a file and in step 5.18 displays or otherwise outputs the
measured PMD value with possible other results such as length and
loss of the FUT.
[0484] Note that, for the case of K=1, i.e. the powers of light
backreflection may be obtained in a similar manner for only one
group having both the same (I-SOP, A-SOP) couple and same
center-wavelength, one may also be able to roughly evaluate the PMD
although this simple case may not be able to provide a sufficiently
accurate result, as there may be a significant uncertainty on the
measured result.
[0485] The manner in which the data processing step 5.16 processes
the stored data will be described in the sections below.
[0486] It should note the above step may obtain rms DGD (i.e. PMD),
but it can also obtain DGD as function of optical frequency
(wavelength) and then rms DGD or mean DGD may be computed using the
method described hereinbelow that may also be included in data
processing step 5.16.
1.15.3 Method of Operation
Single-Ended Cumulative PMD Measurement
[0487] The method of operation of the POTDR illustrated in FIG. 4
for measuring cumulative PMD as function of FUT length will now be
described with reference to the flowchart shown in FIGS. 7A and 7B.
In step 6.1, the user causes the system to initialize the POTDR,
specifically initializing the tunable pulsed light source 12, the
I/A-SOP controller 14 and the OTDR detection and processing
section. Decision step 6.2 prompts the user to select either manual
parameter setting or automatic parameter setting. Assuming that the
user selects manual parameter setting, the program proceeds to the
manual parameter setting step 6.3 and prompts the user as
follows:
(a) Set the wavelength range [.lamda.min, .lamda.max] of the group
center wavelengths that will be covered by the tunable pulsed laser
source 12. (b) Set the step or difference .delta..nu. (or
.delta..lamda.) between the pairs of closely-spaced optical
frequencies .nu..sub.U and .nu..sub.L (or wavelengths).
Alternatively, the user may enter the anticipated total PMD value
of the FUT and leave the processor to select the wavelength step.
As an example, the step can be conveniently set to
.delta..nu.=.alpha..sub..delta..nu.PMD.sup.-1 where
.alpha..sub..delta..nu..about.0.1 to 0.15. It should be noted that
the POTDR may be configured to allow the user to select a number M
of steps larger than one; the control program will then select M
steps based on the anticipated total PMD of the FUT, with
appropriate ratios between the steps (note: there is an optimal
step for a given PMD value, as large as possible so as to maximize
signal-to-noise ratio, but small enough to satisfy the above
condition, i.e., PMD.delta..nu.<0.1 to 0.15. But the apparatus
here described must perform the challenging task of measuring
simultaneously a large range of cumulative PMD values as a function
of z, from PMD=0, at z=0, to PMD=Total PMD of the FUT, at z=FUT
length. This is the reason why a few measurements with different
steps in order to measure all different "sections" of the FUT with
similar relative (e.g. in %) accuracy is desirable, or
alternatively as mentioned here and above, use more than two
closely-spaced wavelengths per group, a number N.sub..lamda. of
wavelengths per group leading to a theoretical number of
M=N.sub..lamda.(N.sub..lamda.-1)/2 pairs with different steps in
each scan, so as to save time). (c) Set the number (K) of
center-wavelengths and/or (I-SOP, A-SOP) couples selected by the
I/A-SOP controller 14, i.e., the number (K) of groups of traces to
be acquired. (d) Set the averaging time .DELTA.t of each individual
trace (for example, .DELTA.t=1 or 2 seconds), or set the number
electrical impulse response signals to be averaged to obtain each
individual trace (for example 1250 or 2500). (e) Set the pulse
duration (e.g. Tp=10, 30, 50, 100, 200, 300, 500 ns). (f) Specify
the FUT length, normally the full effective optical length of the
FUT. If, in decision step 6.2, the user selects automatic parameter
setting, the program proceeds to step 6.4 and carries out the
following steps: [0488] Select certain default measurement
parameters, namely [0489] (1) center wavelength range [.lamda.min,
.lamda.max] that will be covered by the tunable pulsed laser source
12, typically the whole wavelength range that the actual tunable
laser can access; [0490] (2) number K of (I-SOP, A-SOP) couples
and/or center wavelengths to be set by the I/A-SOP controller 14,
for example, 100 or 200, for final POTDR data acquisition; [0491]
(3) averaging time .DELTA.t (for example, .DELTA.t=1 or 2 seconds)
or number of electrical impulse response signals to be averaged
(for example 1250 or 2500) for each individual OTDR trace; [0492]
(4) pulse duration (e.g., Tp=10, 30, 50, 100, 200, 300, 500 ns);
and [0493] (5) linewidth of tunable pulsed laser (optional). [0494]
It is noted that these default parameters set in (1), (3), (4) and
(5) will also be used for pre-scan acquisition. [0495] The POTDR
conducts a pre-scan using a reduced number of groups, such as K=20,
to obtain rough estimates of the FUT length and the optimal
wavelength step .delta..lamda. (or frequency difference
.delta..nu.) between the two closely-spaced optical frequencies
.nu..sub.U and .nu..sub.U (or .lamda..sub.U and .lamda..sub.L).
Thus, the OTDR will launch a standard OTDR pulse (e.g. 1 .mu.s) to
detect the end of the fiber so that the FUT length can be obtained
and the pulse repetition period deduced according to the round-trip
time through the length of the fiber. Acquisition of OTDR traces
then will be performed to find the best suited step or difference
.delta..nu. (or .delta..lamda.) between the two closely-spaced
optical frequencies .nu..sub.U and .nu..sub.L (or .lamda..sub.U and
.lamda..sub.L) via a fast estimate of the overall PMD of the FUT.
For example, such acquisition may be carried out by using, for each
group, four different laser wavelengths (N.sub..lamda.=4) to obtain
a total combination of six different wavelength steps (M=6). The
best suited wavelength step to be used in the actual POTDR data
acquisition may be found by processing of these pre-scan data.
[0496] Once the measurement parameters have been entered, whether
manually or automatically, the program proceeds to step 6.5 and
computes wavelength step .delta..lamda. (or frequency difference
.delta..nu.) if the anticipated total PMD of the FUT has been
specified or estimated via the aforementioned auto-setting
procedure, the repetition period T.sub.r according to the
round-trip time through the length of the fiber, and the
appropriate sequence of wavelengths based on the parameter
settings.
[0497] Finally, all the measurement parameters, whether directly
specified or computed as described above, are stored in the header
of the data file (Step 6.6).
[0498] FIG. 7A shows an optional step (following step 6.5) for
setting the laser linewidth, if allowed by the laser light source
12, according to the previously-entered parameters. For example, a
small (large) linewidth may be chosen to measure large (small)
total PMD. In the case where the total PMD is not specified and no
auto-setting procedure has been carried out, the specified
wavelength step (.delta..lamda.) may be used to estimate the total
PMD and then the laser linewidth may also be selected
accordingly.
[0499] With the group number register initialized to k=0, decision
step 6.7 determines whether the total number of groups of traces
have been acquired; if not, the program proceeds to step 6.8 to
acquire the group k of OTDR traces.
[0500] FIG. 7B shows in more detail the trace acquisition step 6.8
to acquire a kth group of OTDR traces. As described previously,
there is at least one pre-defined frequency difference .delta..nu.
(i.e. wavelength step .delta..lamda.) between the two
closely-spaced optical frequencies .nu..sub.U and .nu..sub.L (i.e.
wavelengths), and hence the number of total selected laser
wavelengths must be at least two. If a plurality of different
wavelength steps .delta..lamda. are used, then these wavelength
steps may be selected to optimally measure different ranges of PMD
values. For example, one may choose to have two wavelength steps,
.delta..lamda..sub.1 and .delta..lamda..sub.2, which requires
N.sub..lamda.=3 different wavelengths per group. Furthermore, a
judicious choice of the ratio of said two steps may be, for
example, .delta..lamda..sub.1/.delta..lamda..sub.2=5. The maximum
measurable PMD, PMD.sub.max corresponding to a given step
.delta..nu. can be estimated as
PMD.sub.max.about..alpha..sub.rt(.pi..delta..nu.).sup.-1, and
.delta..lamda. can be extracted from
.delta..lamda.=(.lamda..sub.0.sup.2/c).delta..nu., where
.lamda..sub.0=(.lamda..sub.min+.lamda..sub.max)/2. The control unit
30 controls the POTDR to obtain the kth group of traces as follows:
[0501] Set couple (I-SOP.sub.k, A-SOP.sub.k) by means of the
I/A-SOP controller 14 (step 6.8.1 of FIG. 7B). [0502] Control the
tunable pulsed laser 12 to set wavelength to .lamda..sub.L.sup.(k)
(step 6.8.2 of FIG. 7B) and then launch OTDR light pulses.
Detection and processing unit 36 acquires OTDR traces Px.sub.L and
Py.sub.L (step 6.8.3 of FIG. 7B). The same data acquisition process
is repeated to obtain duplicate or repeated traces Px.sub.L'' and
Py.sub.L'' (step 6.8.4 of FIG. 7B). [0503] Repeat the same data
acquisition for the upper wavelength .lamda..sub.U.sup.(k) while
keeping the same (I-SOP.sub.k, A-SOP.sub.k) couple. The detection
and processing unit 36 then acquires OTDR traces Px.sub.U, Py.sub.U
and duplicates Px.sub.U'', Py.sub.U'' (steps 6.8.9 and 6.8.10 of
FIG. 7B). [0504] Where the group comprises more than one pair of
series of light pulses, to set the wavelength to at least one
additional wavelength .lamda..sub.I.sup.(k) intermediate the lower
and upper wavelengths (step 6.8.5 of FIG. 7B). The processing means
40 acquires OTDR traces Px.sub.I and Py.sub.I (step 6.8.6 of FIG.
7B). The same data acquisition procedure is repeated to obtain the
repeated traces Px.sub.I'' and Py.sub.I'' (step 6.8.7 of FIG.
7B).
[0505] Once the kth group of OTDR traces have been acquired as
described above, in step 6.9 (see FIG. 7A) the group is saved into
the data file. Step 6.10 then increments the group number
register.
[0506] The data acquisition step 6.8 and group storing step 6.9
will be repeated for different center-wavelengths and/or
(I-SOP.sub.k, A-SOP.sub.k) selected by the I/A-SOP controller 14 in
accordance with the parameter setting step 6.2 or 6.3 until K
groups of traces have been acquired and stored in the data
file.
[0507] At this stage, the measurement parameters and all groups of
OTDR traces will have been saved in the same data file.
[0508] Also at this stage, decision step 6.7 gives a positive
result and, in step 6.11, the program closes the data file.
Optional decision step 6.12 then gives the user an opportunity to
initiate the acquisition of another K groups of traces for the same
FUT. If the user decides to do so, the program returns to the
parameter setting step 6.2. If not, decision step 6.13 gives the
user the option of exiting, in which case the data stored in the
data file will be retained for later processing, or initiating
processing of already acquired and stored data.
[0509] If processing is initiated, step 6.14 allows the user to
select the data file to be processed in a conventional "open file"
dialog box, whereupon, in step 6.16, the data processor 32 accesses
the pre-saved acquisition data and associated measurement
parameters from the data file, and uses the data to compute
cumulative PMD as a function of distance (z) along the FUT. On the
other hand, box 6.15, which is not a "step" as such, indicates that
the user may launch the data processing software independently at
any time, even if no acquisition was just completed, to process any
previously acquired data file. In step 6.17, the data processor 32
saves the results (e.g. the cumulative PMD curve as a function of z
and measurement parameters in a file retrievable via spreadsheet
software) and in step 6.18 displays or otherwise outputs the
resulting cumulative PMD curve in a tangible form.
[0510] The manner in which the data processing step 6.16 processes
the stored data will be described in the sections below.
[0511] It should note the above steps may obtain rms DGD (i.e.
PMD), but it can also obtain DGD as function of wavelength and then
rms DGD or mean DGD may be computed as the method described in
below sections that may also be included in data processing step
6.16.
[0512] It should emphasized that it is preferable that the data be
acquired for several or many SOPs and different midpoint
wavelengths.
1.16 Data Processing and Computation
Two-Ended Measurement
1.16.1 Embodiment (1)
Data Processing and Computation for Non-Polarization-Diverse
Measurement
[0513] The manner in which the data processing step 6.19 processes
the stored data will now be described.
1.16.1.1 The Data Structure
[0514] Each measured light power from the FUT, obtained with one
given setting of the wavelength and of the input and analyzer SOP
controllers as described in the Method of Operation for the
two-ended PMD measurement, constitutes an elementary data cell,
i.e. one datum consists of one power value. The next data unit is
one group of four powers (i.e. four data cells), two sets of four
powers for the implementations of FIG. 1D and FIG. 1F where two
powers are obtained simultaneously from photodetectors 22B and 22C,
all obtained with given input and output SOPs as set by I-SOP
scrambler 14A and A-SOP scrambler 14B. The two sets of four powers
forming group k preferably have been obtained in the following
sequence (time flowing from left to right) or other similar means,
such as of two repeated powers being measured at the same time but
with different detectors (such as simultaneously measuring the same
power by two detectors and a coupler), as:
I - SOP k I , A - SOP k O and / or .lamda. k : .lamda. = .lamda. L
( k ) .lamda. = .lamda. U ( k ) P x L ( k ) P x L '' ( k ) P x U (
k ) P x U '' ( k ) P y L ( k ) P y L '' ( k ) P y U ( k ) P y U ''
( k ) ##EQU00047##
where the labels x and y refer to the power obtained simultaneously
or at slightly different time from photodetectors 22B and 22C,
respectively, .lamda..sub.U.sup.(k)-.lamda..sub.L.sup.(k) is equal
to the step .delta..lamda., the midpoint wavelength is defined as
.lamda..sub.k=(.lamda..sub.U.sup.(k)+.lamda..sub.L.sup.(k))/2, and
the double prime denotes repeated powers.
[0515] Finally, the overall data stored in the data file after
acquisition is depicted as a matrix in Eq. (7.1) below, to which we
will refer in all that follows. The matrix comprises K groups each
of four powers of light (two sets of four when two photodetectors
are used):
TABLE-US-00001 ##STR00001##
[0516] The input and output SOPs can each be selected randomly
("macroscopic SOP step") from one to another or undergo slow
continuous SOP scanning, in both cases in such a way that, over
time, each substantially uniformly covers the Poincare Sphere.
1.16.1.2 Auto Calibration of the Relative Gain
[0517] For the PBS-based implementation of FIG. 1F, it is necessary
to perform a calibration procedure described in Section 2.2
hereinafter of the relative gain of the two detectors 22B and 22C
before proceeding with any further computation. The same procedure
is not performed for the other embodiments, e.g. if there is only
one detector.
1.16.1.3 Computation
[0518] The powers are processed to obtain the PMD value as will now
be described. It should be note that, in all that follows, the
symbols refer to the matrix "Data" in equation (17). The labels x
and y refer to the backreflected light powers obtained from
photodetectors 22B and 22C, respectively.
1.16.1.4 The Normalized Powers
[0519] The normalized powers, labelled hereinafter as T, are
computed differently according to the implementation of the
embodiment.
(i) For the implementation of FIG. 1F (two photodetectors with a
PBS), the transmissions (normalized power) are computed as follows
either
T L ( k ) = P x L ( k ) P x L ( k ) + P y L ( k ) T L '' ( k ) = P
x L '' ( k ) P x L '' ( k ) + P y L '' ( k ) T U ( k ) = P x U ( k
) P x U ( k ) + P y U ( k ) T U '' ( k ) = P x U '' ( k ) P x U ''
( k ) + P y U '' ( k ) or ( 7.2 a ) T L ( k ) = 1 2 P x L ( k ) - P
y L ( k ) P x L ( k ) + P y L ( k ) T L '' ( k ) = 1 2 P x L '' ( k
) - P y L '' ( k ) P x L '' ( k ) + P y L '' ( k ) T U ( k ) = 1 2
P x U ( k ) - P y U ( k ) P x U ( k ) + P y U ( k ) T L '' ( k ) =
1 2 P x U '' ( k ) - P y U '' ( k ) P x U '' ( k ) + P y U '' ( k )
( 7.2 b ) ##EQU00048##
where it should be appreciated that the different Py powers have
been pre-multiplied by the measured relative gain, g.sub.Forward,
as indicated in the description of the auto-calibration procedure,
before they are used in equations (7.2a) and (7.2b). (ii) For the
implementation of FIG. 1D (two photodetectors with a coupler), the
ratio of trace Px over trace Py is first computed as,
R L ( k ) = P x L ( k ) P y L ( k ) R L '' ( k ) = P x L '' ( k ) P
y L '' ( k ) R U ( k ) = P x U ( k ) P y U ( k ) R U '' ( k ) = P x
U '' ( k ) P y U '' ( k ) ( 7.2 c ) ##EQU00049##
and then the above ratio is normalized with respect to its average
over the K groups as,
T L ( k ) = u o R L ( k ) R L SOP T L '' ( k ) = u o R L '' ( k ) R
L SOP T U ( k ) = u o R U ( k ) R U SOP T U '' ( k ) = u o R U '' (
k ) R U SOP ( 7.2 d ) ##EQU00050##
where the reference mean-value is u.sub.o=1/2 and the average ratio
R is defined as,
R L SOP = 1 2 K k ( R L ( k ) + R L '' ( k ) ) R U SOP = 1 2 K k (
R U ( k ) + R U '' ( k ) ) ( 7.2 e ) ##EQU00051##
or, when changes of the coupler ratio as a function of wavelength
are negligible within a prescribed wavelength range, then
R.sub.L.sub.SOP and R.sub.U.sub.SOP can be replaced by:
R SOP ; v = 1 4 K k ( R L ( k ) + R L '' ( k ) + R U ( k ) + R U ''
( k ) ) ( 7.2 f ) ##EQU00052##
[0520] Here, the auto calibration procedure is not required, i.e.
above mentioned pre-multiplication of the powers Py by the measured
relative gain may be skipped.
(iii) For the embodiment of FIG. 1B (single photodetector), the
only available powers are the Px powers (obtained here from
photodetector 22A). The normalized power is obtained as in (7.2d)
but without computing the ratio of power x over power y first,
i.e.
T L ( k ) = u o P x L ( k ) P L SOP T L '' ( k ) = u o P x L '' ( k
) P L SOP T U ( k ) = u o P x U ( k ) P U SOP T U '' ( k ) = u o P
x U '' ( k ) P U SOP ( 7.2 g ) ##EQU00053##
where the average power is defined as,
P L SOP = 1 2 K k ( P x L ( k ) + P x L '' ( k ) ) P U SOP = 1 2 K
k ( P x U ( k ) + P x U '' ( k ) ) ( 7.2 h ) ##EQU00054##
[0521] Here, the detected power is assumed to be roughly constant
during the time period for measurement of the initial and repeated
powers.
(iv) For the embodiment of FIG. 1C with two photodetectors combined
with a coupler after the polarizer 20A (serving as an analyzer),
two powers of the Px and Px'' powers are obtained from
photodetectors 22B and 22C, respectively. The normalized powers are
now obtained as,
T L ( k ) = u o P x L ( k ) P x L SOP T L '' ( k ) = u o P x L '' (
k ) P x L '' SOP T U ( k ) = u o P x U ( k ) P x U SOP T U '' ( k )
= u o P x U '' ( k ) P x U '' SOP ( 7.2 i ) ##EQU00055##
where the average power is defined as,
Px L SOP = 1 K k Px L ( k ) Px L '' SOP = 1 K k Px L '' ( k ) Px U
SOP = 1 K k Px U ( k ) Px U '' SOP = 1 K k Px U '' ( k ) ( 7.2 j )
##EQU00056##
[0522] Here the auto-calibration procedure is also not required.
Note that this embodiment has the advantage of only requiring
approximately half the acquisition time of other embodiments.
[0523] Note for the normalization procedure described in (iii) and
(iv) above, the light power exiting FUT 18 during measurement must
be stable. Also, if the power is constant for all wavelengths
within a prescribed wavelength range, .sub.SOP can be averaged over
either SOP or wavelength, or both SOP and wavelength.
[0524] Fundamentally all of these relationships are valid in all
cases if sufficiently random input and output SOP scrambling is
applied, giving the correct value of the DGD at one particular
midpoint wavelength, and then it is possible to obtain DGD against
midpoint wavelength. Therefore, one can also compute a mean DGD or
rms DGD value for a given wavelength range.
[0525] It should be appreciated that scanning the midpoint
wavelength serves the purpose of averaging DGD over wavelength as
per the definition of the statistical PMD value so as to obtain a
rms DGD value (not a mean DGD). On the contrary, as discussed
earlier, averaging only over wavelength while keeping the input and
analyzer SOPs unchanged requires that assumptions about the FUT be
met, and also requires a large value of the product PMD.DELTA..nu..
The same remarks apply for the equations presented hereinafter.
1.16.1.4.1 Noise Variance
[0526] The second motivation for sampling repeated traces, which
are substantially identical in the absence of noise for each
setting of SOP and midpoint wavelength .lamda..sub.mid, is the
ability to obtain an accurate estimate of the variance noise from
variations of light polarization and/or laser frequency and/or
power (intensity). If this noise variance is known, it may be
subtracted. Thanks to the repeated traces, the variance from
polarization noise and/or laser frequency and/or power noise and/or
any other noises etc. can be estimated independently as
follows:
.sigma. ( v ) noise 2 = ( 1 .sigma. 20 ) 2 ( T L ( v ) - T L '' ( v
) ) ( T U ( v ) - T U '' ( v ) ) SOP ( 7.3 a ) ##EQU00057##
which is particularly appropriate for determining a DGD estimate at
a given wavelength; and
.sigma. noise 2 = ( 1 .sigma. 20 ) 2 ( T L - T L '' ) ( T U - T U
'' ) SOP ; v ( 7.3 b ) ##EQU00058##
which is particularly appropriate for determining a PMD estimate;
and where, for both cases, .sigma..sub.20.sup.2= 1/12.
[0527] It should be noted that this "noise variance" could arise
from a randomly varied input and output SOP (such as might be
induced by a swaying aerial cable, for instance), and/or an
instability of laser frequency and intensity, or any other noise
sources.
[0528] In order to obtain a reliable measurement result, the
variance noise, e.g. from polarization variation and similar other
effects, such as instability of laser frequency and intensity,
should be less than few percent (e.g. of <2%) compared to the
mean-square difference.
1.16.1.4.2 Relative Variance
[0529] The relative variance, for example mainly due to
un-polarized ASE light from optical amplifiers in the test link (or
any other depolarizing effects), as used in equations (6.8) and
(6.9), is computed here as the average of the two available
estimates, i.e.,
.sigma. r '2 ( v ) = ( 1 .sigma. 20 ) 2 [ .delta. ( T L ( v ) ) +
.delta. ( T U ( v ) ) 2 ] ( 7.4 a ) .sigma. r '2 = ( 1 .sigma. 20 )
2 [ .delta. ( T L ) + .delta. ( T U ) 2 ] ( 7.4 b )
##EQU00059##
where .sigma..sub.20.sup.2= 1/12, and the function ".delta." is
defined as,
.delta.(T.sub.L(.nu.))=.left
brkt-bot.T.sub.L(.nu.)T.sub.L''(.nu.).sub.SOP-T.sub.L(.nu.).sub.SOP.sup.2-
.right brkt-bot.
.delta.(T.sub.U(.nu.))=.left
brkt-bot.T.sub.U(.nu.)T.sub.U''(.nu.).sub.SOP-T.sub.U(.nu.).sub.SOP.sup.2-
.right brkt-bot.
.delta.(T.sub.L)=.left
brkt-bot.T.sub.LT.sub.L''.sub.SOP;.nu.-T.sub.L.sub.SOP;.nu..sup.2.right
brkt-bot.
.delta.(T.sub.U)=.left
brkt-bot.T.sub.UT.sub.U''.sub.SOP;.nu.-T.sub.U.sub.SOP;.nu..sup.2.right
brkt-bot.
[0530] Alternatively, the relative variance can also be computed
via polarization component s.sub.p, for example,
.sigma. r '2 ( v ) = ( 1 .sigma. 20 ) 2 [ s p L ( v ) s p L '' ( v
) SOP + s p U ( v ) s p U '' ( v ) SOP 2 ] ( 7.4 c ) .sigma. r '2 =
( 1 .sigma. 20 ) 2 [ s p L s p L '' SOP : v + s p U s p U '' SOP :
v 2 ] ( 7.4 d ) ##EQU00060##
where .sigma..sub.s0.sup.2=1/3, and s.sub.p as,
s.sub.pL=2T.sub.L-1 s.sub.pL''=2T.sub.L''-1
s.sub.pU=2T.sub.U-1 s.sub.pU''=2T.sub.U''-1
[0531] A relative variance computed from equation (7.4b) cannot be
applied to any above- or below-mentioned "relative power" related
computation for extracting DGD or PMD, i.e. the measured power must
be normalized properly.
[0532] It should be noted that above equation is valid under the
condition of uniformly distributed I-SOPs and A-SOPs on Poincare
Sphere from either or both input and output polarization
controllers. It can be only averaged over SOP or averaged over both
SOP and wavelength.
[0533] The noise variance (equation 7.3) is then subtracted from
the first estimation of the relative variance (equation 7.4a) in
the computation, and a final relative variance is as follows,
.sigma..sub.r.sup.2(.nu.)=.sigma.'.sub.r.sup.2(.nu.)-.sigma..sub.noise.s-
up.2(.nu.) (7.5a)
which is particularly appropriate for determining a DGD estimate at
a particular wavelength; and
.sigma..sub.r.sup.2=.sigma.'.sub.r.sup.2-.sigma..sub.noise.sup.2
(7.5b)
which is particularly appropriate for determining a PMD estimate at
a particular wavelength.
1.16.1.4.3 Mean-Square Differences
[0534] The calculation here differs from the simple mean-square
found in equations (6.8) and (6.9) which, for greater clarity, did
not take into account the noise. Instead, the product of the
repeated differences between normalized power at .lamda..sub.U and
.lamda..sub.L is averaged as follows,
.DELTA. T 2 ( v ) SOP = ( T U ( v ) - T L ( v ) ) ( T U '' ( v ) -
T L '' ( v ) ) SOP = 1 K k ( T U ( k ) ( v ) - T L ( k ) ( v ) ) (
T U '' ( k ) ( v ) - T L '' ( k ) ( v ) ) ( 7.6 a ) .DELTA. T 2 ( v
) SOP ; v = ( T U - T L ) ( T U '' - T L '' ) SOP ; v = 1 K k ( T U
( k ) - T L ( k ) ) ( T U '' ( k ) - T L '' ( k ) ) ( 7.6 b )
##EQU00061##
[0535] In conventional mathematical terms, each of equations (7.6)
may be referred to as the second-order joint moment of the repeated
differences.
[0536] Doing so, the noise averages to zero instead of being
"rectified", because the noise superimposed on a given trace is not
correlated with the noise superimposed on the corresponding
repeated power. That is the first motivation for acquiring repeated
data.
[0537] Note that .sub.SOP in Eq. (7.6a) can refer to averaging over
the SOP at a given midpoint frequency (.nu..sub.mid) (i.e. midpoint
wavelength, .lamda..sub.mid), i.e., only changing the SOP from one
group of powers to other, which is particularly appropriate for
determining the DGD at this wavelength, and .sub.SOP;.nu. in Eq.
(7.6b) indicates averages taken over both the SOP and the midpoint
frequencies (.nu..sub.mid) (i.e. midpoint wavelength
.lamda..sub.mid). Thus, both SOP and optical frequency are changed
from one group of powers to other, which is particularly
appropriate for determining the PMD over a particular wavelength
range.
1.16.1.4.4 Computation of the DGD or PMD Value
[0538] The DGD or rms DGD (i.e. PMD) then is computed according to
the arcsine formula as,
D G D ( v ) = 1 .pi. .delta. v arcsin ( .alpha. ds .DELTA. T 2 ( v
) SOP .sigma. r 2 ( v ) ) ( 7.7 ) ##EQU00062##
where .sub.SOP refers to averaging over the SOP only.
P M D = 1 .pi. .delta. v arcsin ( .alpha. ds .DELTA. T 2 ( v ) SOP
; v .sigma. r 2 ) ( 7.8 ) ##EQU00063##
where .sub.SOP;.nu. refers to averaging over both the SOP and
optical frequency (wavelength), and a theoretical constant
.alpha. ds = 9 2 . ##EQU00064##
[0539] It should be appreciated that the arcsine formula, in
equations (7.7) and (7.8), is not the only possible one. The
purpose of using this formula is to obtain a result that is
unbiased even if using a relatively large step, such that
PMD.delta..nu..about.0.2, without introducing a significant error;
this in order to maximize the signal-to-noise ratio and therefore
the dynamic range of the instrument. Although applicable to any
step size, if one were not concerned with maximizing the dynamic
range, one could select a small step, in which case the following
simpler differential formula is valid:
D G D ( v ) = .alpha. ds .pi. .delta. v .DELTA. T 2 ( v ) SOP
.sigma. r 2 ( v ) ( 7.7 a ) P M D = .alpha. ds .pi. .delta. v
.DELTA. T 2 ( v ) SOP ; v .sigma. r 2 ( 7.8 a ) ##EQU00065##
[0540] This is not to infer that these formulas are better or
particularly advantageous, but merely that it may conveniently be
used if the step is much smaller, i.e., satisfying the condition
PMD.delta..nu.<0.01.
[0541] It should be noted that in an ideal situation where there is
no ASE from optical amplifiers, depolarization effects, or other
"noise" related to variations in light polarization, frequency and
intensity etc., then .sigma..sub.r.sup.2=1, the above equations
(7.7) and (7.8) simplify to,
D G D ( v ) = 1 .pi. .delta. v arcsin ( .alpha. ds .DELTA. T 2 ( v
) SOP ) ( 7.9 ) P M D = 1 .pi. .delta. v arcsin ( .alpha. ds
.DELTA. T 2 ( v ) SOP ; v ) ( 7.10 ) ##EQU00066##
and their corresponding simpler differential formulas are,
D G D ( v ) = .alpha. ds .pi. .delta. v .DELTA. T 2 ( v ) SOP ( 7.9
a ) P M D = .alpha. ds .pi. .delta. v .DELTA. T 2 ( v ) SOP ; v (
7.10 a ) ##EQU00067##
[0542] Note that a mean DGD or rms DGD may be computed from
averaging DGD(.nu.) from many different midpoint wavelengths over a
prescribed wavelength range, such as
RMS DGD = DGD 2 ( v ) v ( 7.11 ) mean DGD = DGD ( v ) v ( 7.12 )
##EQU00068##
[0543] As shown in the equations (7.7) and (7.8), if the DGD(.nu.)
and PMD calculation involves the use of the relative variance,
.sigma..sub.r.sup.2(.nu.) and .sigma..sub.r.sup.2 respectively, of
the normalized power (T), then the normalized power need not be
necessarily computed to lie between 0 and 1. In other words, some
steps of above normalization procedure may be skipped.
[0544] For example, for the implementation of FIG. 1D (two
photodetectors with a coupler), the relative power (P.sub.R) can
simply be obtained from the ratio of trace Px over trace Py as,
P RL ( k ) = Px L ( k ) Py L ( k ) P RL '' ( k ) = Px L '' ( k ) Py
L '' ( k ) P RU ( k ) = Px U ( k ) Py U ( k ) P RU '' ( k ) = Px U
'' ( k ) Py U '' ( k ) ( 7.13 ) ##EQU00069##
[0545] For the implementation of FIG. 1F (two photodetectors with a
PBS) and in FIG. 1D (two photodetectors with a coupler), the
relative power (P.sub.R) may be obtained without recourse to the
aforementioned reference constants and averaging over SOP and/or
wavelength in order to obtain a normalized power. Then DGD and PMD
may be computed by means of the following arcsine formula as,
D G D ( v ) = 1 .pi. .delta. v arcsin ( .alpha. ds .DELTA. P R 2 (
v ) SOP .sigma. R 2 ( v ) ) ( 7.14 ) ##EQU00070##
where .sub.SOP refers to averaging over SOP only.
P M D = 1 .pi. .delta. v arcsin ( .alpha. ds .DELTA. P R 2 ( v )
SOP ; v .sigma. R 2 ) ( 7 , 15 ) ##EQU00071##
where .sub.SOP;.nu. refers to averaging over both the SOP and
wavelength.
[0546] Here mean-square .DELTA.P.sub.R.sup.2(.nu.).sub.SOP and
.DELTA.P.sub.R.sup.2(.nu.).sub.SOP;.nu. can be found as
follows,
.DELTA. P R 2 ( v ) SOP = ( P RU ( v ) - P RL ( v ) ) ( P RU '' ( v
) - P RL '' ( v ) ) SOP = 1 K k ( P RU ( k ) ( v ) - P RL ( k ) ( v
) ) ( P RU '' ( k ) ( v ) - P RL '' ( k ) ( v ) ) ( 7.16 a )
.DELTA. P R 2 ( v ) SOP ; v = ( P RU - P RL ) ( P RU '' - P RL '' )
SOP ; v = 1 K k ( P RU ( k ) - P RL ( k ) ) ( P RU '' ( k ) - P RL
'' ( k ) ) ( 7.16 b ) ##EQU00072##
and the relative variance, .sigma..sub.R.sup.2, is computed here as
the average of the four available estimates, i.e.,
.sigma. R 2 ( v ) = ( 1 .sigma. 20 ) 2 [ .delta. ( P RL ( v ) ) +
.delta. ( P RU ( v ) ) 2 ] ( 7.16 c ) .sigma. R 2 = ( 1 .sigma. 20
) 2 [ .delta. ( P RL ) + .delta. ( P RU ) 2 ] ( 7.16 d )
##EQU00073##
where .sigma..sub.20.sup.2= 1/12, and the function ".delta." is
defined as,
.delta.(P.sub.RL(.nu.))=.left
brkt-bot.P.sub.RL(.nu.)P.sub.RL''(.nu.).sub.SOP-P.sub.RL(.nu.).sub.SOP.su-
p.2.right brkt-bot.
.delta.(P.sub.RU(.nu.))=.left
brkt-bot.P.sub.RU(.nu.)P.sub.RU''(.nu.).sub.SOP-P.sub.RU(.nu.).sub.SOP.su-
p.2.right brkt-bot.
.delta.(P.sub.RL)=.left
brkt-bot.P.sub.RLP.sub.RL''.sub.SOP;.nu.-P.sub.RL.sub.SOP;.nu..sup.2.righ-
t brkt-bot.
.delta.(P.sub.RU)=.left
brkt-bot.P.sub.RUP.sub.RU''.sub.SOP;.nu.-P.sub.RU.sub.SOP;.nu..sup.2.righ-
t brkt-bot.
[0547] Note that .sub.SOP;.nu. can refer to averaging over either
the SOP, or the optical frequency (wavelength), or over both, i.e.,
changing both SOP and optical frequency from one group of powers to
the next.
[0548] If one selected a small step, the arcsine formula, in
equations (7.14) and (7.15) may be written as a simpler
differential formula:
D G D ( v ) = .alpha. ds .pi. .delta. v .DELTA. P R 2 ( v ) SOP
.sigma. R 2 ( v ) ( 7.14 a ) P M D = .alpha. ds .pi. .delta. v
.DELTA. P R 2 ( v ) SOP ; v .sigma. R 2 ( 7.15 a ) ##EQU00074##
[0549] For the case where the tunable light source has a relatively
large linewidth and a high-PMD fiber is under test, a further
linewidth "correction factor" may be applied in equations in order
to extract a DGD or PMD value of the FUT having a greater
accuracy.
[0550] It should be appreciated noted that the above-computed
forward DGD or PMD for two-ended PMD measurement is in fact the DGD
or PMD of FUT.
[0551] It should also be noted that repeated powers may be obtained
from two or more measurements at different times using the same
detectors, or from measurements using different detectors, e.g.
after the light power has been split by a coupler (FIG. 1C) and the
resulting apportioned powers detected by respective detectors
contemporaneously.
1.16.2 Two-Ended DGD and PMD
Data Processing and Computation Using Two Detected Polarization
Components with Rapid Wavelength Sweeping
1.16.2.1 The Data Structure
[0552] The data structure for the exemplary polarization-diverse
detection implementations depicted in FIGS. 1K and 1G, where the
wavelength of the detected light is rapidly swept over a prescribed
wavelength range, differs somewhat from the other embodiments. Each
light power from the FUT 18, obtained with either one given setting
of the wavelength from tunable filter A 27B and tunable filter B
27C (FIG. 1K) or from swept tunable laser source 12A (FIG. 1G) and
of the SOP couple (I-SOP; A-SOP), as described in the Method of
Operation for the two-ended PMD measurement provided hereinafter,
constitutes an elementary data cell, i.e. one datum consists of one
power value. The data unit is one group of N powers, two sets of N
powers for the embodiments of FIGS. 1K and 1G where two powers are
obtained simultaneously from photodetectors 22B and 22C, all
obtained with given approximately same SOP couples as set by I-SOP
scrambler 14A and A-SOP scrambler 14B. Preferably, the I-SOP
scrambler 14A operates in a slow "continuous scanning" mode,
randomly scanning its input SOP, while the A-SOP scrambler 14B sets
one analyzer SOP for one group data with N powers.
[0553] By "slow" continuous scanning, one means that the I-SOP
scrambler 14A scans sufficiently slowly that, in the absence of DGD
or PMD from the FUT, the mean-squared equalized transmission
(equalized normalized power) difference over a large number of SOPs
caused by the input SOP changing is much smaller (e.g. less than
few percent) than that (i.e. a mean-squared equalized transmission
difference) generated from a given DGD of the FUT for one set
optical frequency difference between two closely-spaced frequencies
that is used to compute the DGD or PMD of the FUT as used in
equations (6.8) and (6.9). The two sets of N powers forming group k
preferably have been obtained in the following sequence (time
flowing from left to right), for I-SOP.sub.k.sup.I,
A-SOP.sub.k.sup.O and .nu..sub.1 to .nu..sub.N, as:
P x ( k ) ( v 1 ) P x ( k ) ( v 2 ) P x ( k ) ( v i ) P x ( k ) ( v
N ) P y ( k ) ( v 1 ) P y ( k ) ( v 2 ) P y ( k ) ( v i ) P y ( k )
( v N ) ##EQU00075##
where the labels x and y refer to the power obtained approximately
simultaneously photodetectors 22B and 22C, respectively,
.delta..nu.=.nu..sub.i+n-.nu..sub.i is an optical frequency
difference (wavelength step) between two closely-spaced optical
frequencies, and its midpoint optical frequency (wavelength) is
defined as
v i , mid = v i + v i + n 2 ( .lamda. i , mid = 2 .lamda. i .lamda.
i + n .lamda. i + .lamda. i + n ) ##EQU00076##
(where n is an acquired data number difference for the optical
frequency difference, .delta..nu., between two closely-spaced
optical frequencies (wavelengths)).
[0554] Typically an optical frequency being scanned from .nu..sub.1
to .nu..sub.N is actually incrementally or decrementally stepped
in, preferably approximately equal, small optical frequency
(wavelength) steps, for example, .about.125-1250 MHz (.about.1-10
pm). The precise value of each step need not be known. Also it
should be noted that as long as knowing accurate optical frequency,
for example optical frequency being measured by a wavelength meter
during data acquisition, a step from one frequency to next may be
different. However, it is desirable for equations (6.8) and (6.9),
for the sake of convenience, to use approximately equal optical
frequency differences to calculate a rms DGD or PMD.
[0555] The overall data can be acquired by many scans over
wavelength (e.g. 3-10,000 scans) for which the input and analyzer
SOPs are different, that can be either achieved by tunable filter
means 27 or tunable laser 12A. A desirable tunable filter means
(FIG. 1K) may be based on a polarization-diverse two-channel
scanning monochromator, such as comprised within a commercial
optical spectrum analyzer such as the model FTB-5240, manufactured
by EXFO Inc.
[0556] The acquired data are stored in the data file as above
matrix (34). The matrix comprises K groups each of 2.times.N light
powers (i.e. two sets of N) are acquired from two photodetectors
22B and 22C (FIGS. 1K and 1G):
SOP 0 I , SOP 0 O P x ( 0 ) ( v 1 ) P x ( 0 ) ( v 2 ) P x ( 0 ) ( v
i ) P x ( 0 ) ( v N ) P y ( 0 ) ( v 1 ) P y ( 0 ) ( v 2 ) P y ( 0 )
( v i ) P y ( 0 ) ( v N ) SOP 1 I , SOP 1 O P x ( 1 ) ( v 1 ) P x (
1 ) ( v 2 ) P x ( 1 ) ( v i ) P x ( 1 ) ( v N ) P y ( 1 ) ( v 1 ) P
y ( 1 ) ( v 2 ) P y ( 1 ) ( v i ) P y ( 1 ) ( v N ) SOP k I , SOP k
O P x ( k ) ( v 1 ) P x ( k ) ( v 2 ) P x ( k ) ( v i ) P x ( k ) (
v N ) P y ( k ) ( v 1 ) P y ( k ) ( v 2 ) P y ( k ) ( v i ) P y ( k
) ( v N ) SOP K - 1 I , SOP K - 1 O P x ( K - 1 ) ( v 1 ) P x ( K -
1 ) ( v 2 ) P x ( K - 1 ) ( v i ) P x ( K - 1 ) ( v N ) P y ( K - 1
) ( v 1 ) P y ( K - 1 ) ( v 2 ) P y ( K - 1 ) ( v i ) P y ( K - 1 )
( v N ) ( 7.17 ) ##EQU00077##
1.16.2.2 Auto Calibration of the Relative Gain
[0557] For the implementations of FIGS. 1K and 1G, it is necessary
to perform the below described calibration procedure of the
relative gain of the two detectors 22B and 22C before proceeding
with any further computation. The same procedure is not performed
for the other implementations, e.g. if there is only one
detector.
[0558] The calibration principle is predicated upon the fact that,
when input and output SOP scramblers are used to generate a
sufficiently large number of SOPs so as to substantially cover the
Poincare Sphere, the average power of the light from the FUT 18
will exit from the two ports of the PBS with a 1:1 ratio (equal).
Hence, any observed deviation from this 1:1 ratio for the observed
detector powers can be quantified and taken into account, as
follows.
[0559] After data acquisition is completed, K groups of 2.times.N
light powers obtained from both photodetectors have been stored,
i.e., a total number of KN powers (data) from detector 22B and also
KN powers from detector 22C, as depicted in matrix (7.17). The
i.sup.th powers at optical frequency .nu..sub.i (ideally where the
optical frequency is selected to correspond to approximately
maximum transmitted power or to be in spectral proximity to the
central frequency of the test channel or device under test or FUT)
from 22B and 22C are referred to below as P.sub.x(.nu..sub.i) and
P.sub.y(.nu..sub.i), respectively. If the overall losses in the two
arms of the PBS were identical and the gains of both photodetectors
and associated electronics were also equal, the ratio of the powers
P.sub.x(.nu..sub.i) and P.sub.y(.nu..sub.i) after averaging over
all K, i.e. all input and analyzer SOPs, would be
P x ( v i ) P y ( v i ) .ident. K P x k ( v i ) K P y k ( v i ) = 1
( 7.18 ) ##EQU00078##
[0560] In practice, the ratio obtained from the average of the
measured powers for P.sub.x(.nu..sub.i) and P.sub.y(.nu..sub.i)
does not equal 1 because of different losses in the arms of the PBS
and different "effective" gains of the photodetectors, which
includes the photodiode responsivity as well as the overall gains
of the following electronics, amplifiers and sampling circuitry.
(Note that it is not necessary to determine the individual gains
separately.) Therefore, before proceeding with the rest of the
computations, all the KN powers obtained from photodetector 22C,
i.e. all the P.sub.y.sup.(k)(.nu..sub.i) (i=1, 2 . . . N; and k=1,
2, . . . K), are multiplied as follows:
P y ( k ) ( v i ) .ident. g Forward P y ( k ) ( v i ) where g
Forward = P x ( v i ) P y ( v i ) .ident. K P x k ( v i ) K P y k (
v i ) ( 7.19 ) ##EQU00079##
[0561] It should be noted that above auto-calibration assumes the
relative gain to have negligible wavelength (optical frequency)
dependence. Indeed it holds for a narrow wavelength range,
especially for a narrow DWDM channel under test. However, if a wide
optical frequency range is used for the test, e.g. either the C, L
or C+L band, an auto calibration for the relative gain may be
performed at every optical frequency. The calibration process may
need only be carried out once per PMD measurement sequence.
1.16.2.3 Computation for Implementations Employing Two Orthogonal
Polarization Analyzers with a Polarization Beam Splitter
[0562] The powers are processed to obtain the DGD(.nu.) and PMD
values using detected two "physically" orthogonal (i.e. 180 degrees
on the Poincare sphere) polarization components from a polarization
beam splitter by rapid wavelength sweeping of either tunable filter
means or swept tunable laser, as will now be described. The labels
x and y refer to the probed light powers obtained from
photodetectors 22B and 22C, respectively.
1.16.2.3.1 The Normalized Powers
[0563] The transmissions (normalized powers), labeled as T.sub.x
and T.sub.y, are computed for the implementations of FIGS. 1K and
1G for two photodetectors with a PBS as follows either
T x ( k ) ( v ) = P x ( k ) ( v ) P x ( k ) ( v ) + P y ( k ) ( v )
SOP T y ( k ) ( v ) = P y ( k ) ( v ) P x ( k ) ( v ) + P y ( k ) (
v ) SOP or ( 7.20 a ) T x ( k ) ( v ) = P x ( k ) ( v ) u 0 P x ( k
) ( v ) SOP T y ( k ) ( v ) = P y ( k ) ( v ) u 0 P y ( k ) ( v )
SOP ( 7.20 b ) ##EQU00080##
where .sub.SOP is referred to average over all or many input and
analyzer SOPs at a given optical frequency .nu., and the reference
mean-value is u.sub.o=1/2. Equations (7.20a) and (7.20b) assume a
measured overall total power, i.e. the sum of the two measurements
from, respectively, A 22B and detector B 22C, is stable over the
entire measurement time.
[0564] If a measured overall total power, i.e. sum of the two
measurements from, respectively, detector A 22B and detector B 22C,
has negligible noise (which typically holds for most commercial
instruments, such as a power meter or an optical spectrum analyzer,
if the incident light power is not too low), the transmissions
(normalized powers) can then be written as:
T x ( k ) ( v ) = P x ( k ) ( v ) P x ( k ) ( v ) + P y ( k ) ( v )
T y ( k ) ( v ) = P y ( k ) ( v ) P x ( k ) ( v ) + P y ( k ) ( v )
( 7.20 c ) ##EQU00081##
[0565] Advantageously, the transmissions (normalized powers) being
obtained in the way as described in equation (7.20c) have
negligible dependence on the test light source stability, which
otherwise might be important for a test being performed in a live
DWDM network where there may be many live channels being operated
during the data acquisition.
[0566] It should be noted that above normalized power is computed
at each optical frequency (.nu.), i.e. from one wavelength to
another, for the entire optical frequency range. This is because
there may be different measured light power levels and light noise
(i.e. ASE) levels at different optical frequencies (wavelengths),
especially if the measurement is performed in a narrow optical
channel, e.g. a DWDM channel, so that their relative variance may
be different from one optical frequency to another.
1.16.2.3.2 Relative Variance
[0567] The relative variance, for example mainly due to
un-polarized ASE light from optical amplifiers in the test network
fiber link or any other depolarizing effects, as used in equations
(7) below, is computed at each optical frequency as
.sigma. r 2 ( v ) = ( 1 .sigma. 20 ) 2 [ - 1 T x ( v ) T y ( v )
SOP + 1 4 T x ( v ) + T y ( v ) SOP 2 ] or ( 7.21 a ) .sigma. r 2 (
v ) = ( 1 .sigma. 20 ) 2 [ - 1 T x ( v ) T y ( v ) SOP + T ( v )
SOP 2 ] ( 7.21 b ) ##EQU00082##
where .sigma..sub.20.sup.2= 1/12, .sub.SOP refers to an average
over all or many (I-SOP, A-SOP) couples at each given optical
frequency .nu., and T(.nu.).sub.SOP refers to an average over all
or many input and output SOP couples at each given optical
frequency, .nu., for these transmissions (normalized powers)
measured from two photodetectors.
[0568] Advantageously, the above computed relative variance exhibit
negligible or minimal dependence on noise in the detected powers.
However, under an assumption of negligible noise from the measured
powers for each individual detectors of A and B (22B and 22C), a
relative variance may be obtained as
.sigma. r 2 ( v ) = ( 1 .sigma. 20 ) 2 [ T x 2 ( v ) SOP + T y 2 (
v ) SOP - 2 T ( v ) SOP 2 2 ] ( 7.22 a ) .sigma. r , x 2 ( v ) = (
1 .sigma. 20 ) 2 [ T x 2 ( v ) SOP - T x ( v ) SOP 2 ] ( 7.22 b )
.sigma. r , y 2 ( v ) = ( 1 .sigma. 20 ) 2 [ T y 2 ( v ) SOP - T y
( v ) SOP 2 ] ( 7.22 c ) ##EQU00083##
[0569] It should be noted that Equation 7.22b) or (7.22c) can be
applied to the implementations of FIGS. 1K and 1G where the PBS is
replaced by a linear polarizer 20A (as shown in FIGS. 1I and 1B)
and only one photodetector 22A is used.
[0570] Also note that after averaging over sufficient large number
of input and output SOP couples, relative variances being obtained
from equations (7.22a), (7.22b) and (7.22c) are equal, i.e.
.sigma..sub.r.sup.2(.nu.)=.sigma..sub.r,x.sup.2(.nu.)=.sigma..sub.r,y.sup-
.2(.nu.).
1.16.2.3.3 Equalization of Normalized Powers
[0571] The transmissions (or normalized powers) computed above
normally do not include equalization, i.e. they may be affected by
ASE and any depolarization effects, etc., therefore they may not be
equalized between 0 and 1 even with uniformly distributed input and
analyzer SOPs. However, to compute the DGD and PMD as defined in
equations (6.8) and (6.9) hereinbefore, one must equalize the
measured transmissions (or normalized powers) so that they have a
uniform distribution between 0 and 1 if the input and analyzer SOPs
are uniformly distributed. The purpose of the equalization
procedure for the normalized powers is to remove these
"depolarization" effects on the polarized test light source, and
thereby enable these equalized transmissions (or equalized
normalized powers) to be directly used to calculate the mean-square
difference for the DGD and PMD computation.
[0572] The equalized transmissions (or equalized normalized
powers), labelled as T.sub.e,x and T.sub.e,y, are computed for the
implementations of FIGS. 1K and 1G for two photodetectors with a
PBS as follows
T e , x ( k ) ( v ) = T x ( k ) ( v ) .sigma. r ( v ) - 1 2 ( 1
.sigma. r ( v ) - 1 ) T e , y ( k ) ( v ) = T y ( k ) ( v ) .sigma.
r ( v ) - 1 2 ( 1 .sigma. r ( v ) - 1 ) ( 7.23 a ) ##EQU00084##
where .sigma..sub.r(.nu.) can be obtained from equation (6.7).
[0573] Under the assumption of negligible noise from the measured
powers for each individual detectors of A and B (22B and 22C) the
equalized transmissions (or equalized normalized powers) can also
be expressed as
T e , x ( k ) ( v ) = T x ( k ) ( v ) .sigma. r , x ( v ) - 1 2 ( 1
.sigma. r ( v ) - 1 ) T e , y ( k ) ( v ) = T y ( k ) ( v ) .sigma.
r , y ( v ) - 1 2 ( 1 .sigma. r , y ( v ) - 1 ) ( 7.23 b )
##EQU00085##
where .sigma..sub.r,x(.nu.) and .sigma..sub.r,y(.nu.) can be
obtained from equation (6.7).
[0574] Note that Equation (7.23b) can be applied to the embodiments
of FIGS. 1K and 1G in which the PBS is replaced by a linear
polarizer 20A (e.g. implementations shown in FIGS. 1I and 1B) and
only one photodetector 22A is used.
[0575] It should be noted that the equalization for transmissions
(or normalized powers) needs to be performed at each optical
frequency. This is because a relative variance may be different at
different optical frequency (wavelength), especially for a narrow
bandwidth channel of the DWDM network system under test with ASE
from optical amplifiers. However, if there is no difference for
relative variance against optical frequency (wavelength), one or an
averaged relative variance may be calculated.
1.16.2.3.4 Mean-Square Differences
[0576] The calculation of mean-square differences using equalized
transmissions (or equalized normalized powers), T.sub.e,x and
T.sub.e,y, from two photodetectors with a PBS for the
implementations of FIGS. 1K and 1G, can be found as
.DELTA. T e 2 ( v ) SOP = - 1 ( T e , x ( k ) ( v + 1 2 .delta. v )
- T e , x ( k ) ( v - 1 2 .delta. v ) ) ( T e , y ( k ) ( v + 1 2
.delta. v ) - T e , y ( k ) ( v - 1 2 .delta. v ) ) SOP = - 1 K k (
T e , x ( k ) ( v + 1 2 .delta. v ) - T e , x ( k ) ( v - 1 2
.delta. v ) ) ( T e , y ( k ) ( v + 1 2 .delta. v ) - T e , y ( k )
( v - 1 2 .delta. v ) ) ( 7.24 a ) .DELTA. T e 2 ( v ) SOP , v = -
1 ( T e , x ( k ) ( v + 1 2 .delta. v ) - T e , x ( k ) ( v - 1 2
.delta. v ) ) ( T e , y ( k ) ( v + 1 2 .delta. v ) - T e , y ( k )
( v - 1 2 .delta. v ) ) SOP , v = - 1 K N ' k , n ( T e , x ( k ) (
v + 1 2 .delta. v ) - T e , x ( k ) ( v - 1 2 .delta. v ) ) ( T e ,
y ( k ) ( v + 1 2 .delta. v ) - T e , y ( k ) ( v - 1 2 .delta. v )
) ( 7.24 b ) ##EQU00086##
where K is the total number of input and output SOP couples and N'
is the total number of midpoint optical frequencies.
[0577] As shown in equations (7.24a) and (7.24b), by using
equalized transmissions (or equalized normalized powers), T.sub.e,x
and T.sub.e,y, to compute the mean-square difference for the
PBS-based implementations of FIGS. 1K and 1G with two
photodetectors, the noise averages to zero instead of being
"rectified", because the noise superimposed on a measured power by
one detector is not correlated with the noise superimposed on the
measured power by a different detector. That is achieved by
acquiring data with different detectors A and B (22B and 22C) in
the exemplary implementations of FIGS. 1K and 1G.
[0578] Equalized transmissions (or equalized normalized powers)
obtained from one photodetector connected either after one of two
ports of a PBS or after a linear polarizer, for example for
implementations in FIGS. 1I and 1B where only one photodetector 22A
is used, can also be used to calculate mean-square difference
as,
.DELTA. T e 2 ( v ) SOP = ( T e , x ( k ) ( v + 1 2 .delta. v ) - T
e , x ( k ) ( v - 1 2 .delta. v ) ) 2 SOP = 1 K k ( T e , x ( k ) (
v + 1 2 .delta. v ) - T e , x ( k ) ( v - 1 2 .delta. v ) ) 2 (
7.25 a ) .DELTA. T e 2 ( v ) SOP = ( T e , y ( k ) ( v + 1 2
.delta. v ) - T e , y ( k ) ( v - 1 2 .delta. v ) ) 2 SOP = 1 K k (
T e , y ( k ) ( v + 1 2 .delta. v ) - T e , y ( k ) ( v - 1 2
.delta. v ) ) 2 and ( 7.25 b ) .DELTA. T e 2 ( v ) SOP , v = ( T e
, x ( k ) ( v + 1 2 .delta. v ) - T e , x ( k ) ( v - 1 2 .delta. v
) ) 2 SOP , v = 1 K N ' k , n ( T e , x ( k ) ( v + 1 2 .delta. v )
- T e , x ( k ) ( v - 1 2 .delta. v ) ) 2 ( 7.26 a ) .DELTA. T e 2
( v ) SOP , v = ( T e , y ( k ) ( v + 1 2 .delta. v ) - T e , y ( k
) ( v - 1 2 .delta. v ) ) 2 SOP , v = 1 K N ' k , n ( T e , y ( k )
( v + 1 2 .delta. v ) - T e , y ( k ) ( v - 1 2 .delta. v ) ) 2 (
7.26 b ) ##EQU00087##
where K is total input and analyzer SOP couples and N' is total
midpoint optical frequency number. Equations (9) and (10) assume
that there is negligible noise for the measured powers for each
individual detectors of A or B (22B and 22C) or photodetector 22A
of FIGS. 1I and 1B.
[0579] Note that .sub.SOP in above equations refers only to an
average taken over the SOP at a given midpoint frequency
(.nu..sub.i,mid) (or midpoint wavelength, .lamda..sub.i,mid), i.e.,
only changing the (I-SOP, A-SOP) couples from one group of powers
to other, and .sub.SOP,.nu. in above equations refers to an average
taken over the (I-SOP, A-SOP) couples and midpoint frequencies
(.nu..sub.i,mid).
1.16.2.3.5 Computation of the DGD and PMD Value Using Mean-Square
Differences of Equalized Transmissions
[0580] The DGD(.nu.) is computed according to the arcsine formula
from calculated mean-square differences using equalized
transmissions (or equalized normalized powers) in equation (7.25)
or (7.26) for the implementations of FIGS. 1K and 1G with PBS and
two photodetectors as,
D G D ( v ) = 1 .pi..delta. v arcsin ( .alpha. ds .DELTA. T e 2 ( v
) SOP ) ( 7.27 a ) ##EQU00088##
where .sub.SOP refers to average over the (I-SOP, A-SOP) couples
only.
[0581] A rms DGD can be written as
rms D G D = 1 .pi..delta. v arcsin ( .alpha. ds .DELTA. T e 2 ( v )
SOP ; v ) ( 7.28 a ) ##EQU00089##
where .sub.SOP;.nu. refers to averaging over both the (I-SOP,
A-SOP) couples and optical frequency (i.e. wavelength), and a
theoretical constant
.alpha. ds = 9 2 , ##EQU00090##
and, .delta..nu.=.nu..sub.i+n-.nu..sub.i, an optical frequency
difference between two closely-spaced optical frequencies,
.nu..sub.i and .nu..sub.i+n, is used for computing DGD and PMD.
[0582] It should be appreciated that the arcsine formula, in above
equations, is not the only possible one. The purpose of using this
formula is to obtain a result that is unbiased even if using a
relatively large step, such that PMD.delta..nu..about.0.2, without
introducing a significant error; thereby to maximize the
signal-to-noise ratio and therefore the dynamic range of the
instrument. Although applicable to any step size, if one were not
concerned with maximizing the dynamic range, one could select a
small step and apply the following simpler differential formulae,
which represent the limiting cases of Equations (7.27a) and (7.28a)
as the small optical-frequency difference approaches zero:
DGD ( v ) = 1 .pi. .delta. v ( .alpha. ds .DELTA. T e 2 ( v ) SOP )
( 7.27 b ) RMS DGD = 1 .pi. .delta. v ( .alpha. ds .DELTA. T e 2 (
v ) SOP ; v ) ( 7.28 b ) ##EQU00091##
[0583] This is not to infer that these formulae are better or
particularly advantageous, but merely that it may conveniently be
used if the step is much smaller, i.e., satisfying the condition
DGD.delta..nu. or rms DGD.delta..nu.<0.01.
[0584] For the equations (7.27) and (7.28), an optical frequency
difference, .delta..nu., is the same or approximately the same for
all midpoint optical frequencies.
[0585] Note that the relationships in equations (7.27a) and (7.28a)
hold for DGD.delta..nu.<0.5 or PMD.delta..nu.<0.2 for the
two-ended measurement configuration, thus clarifying the meaning of
"closely-spaced optical frequencies".
[0586] Also note that in equation (7.28b) an averaging optical
frequency range can be small, for example as small as of <20
GHz, or very wide, for example close to 10 THz.
[0587] It should also be noted that above equations can be used for
any situation where there is no ASE where the ASE arising from
optical amplifiers is significant, for example for which the
signal-to-noise ratio may be as low as of .about.3 dB, and
accompanied by other depolarization effects etc. This is because
the equalization for transmissions (or normalized powers) will have
already been performed.
[0588] A mean DGD or rms DGD may be computed by averaging DGD(.nu.)
(obtained from equation (7.27a) or (7.27b)) from many different
midpoint optical frequencies over a prescribed optical frequency
range, such as
R M S D G D = D G D 2 ( v ) v ( 7.29 a ) mean D G D = D G D ( v ) v
( 7.29 b ) ##EQU00092##
1.16.2.4 Computation for Implementations Using Two Polarization
Analyzers Having an Arbitrary Relative Orientation
[0589] The powers are processed, for exemplary rapid
wavelength-sweeping implementations employing either a tunable
filter or a swept laser, to obtain the DGD(.nu.) and PMD values,
for the more general case where the two analyzers have a relative
angle of .theta. (as measured on the Poincare sphere), without
restricting .theta. to be 0 degrees (e.g. from a 50/50
polarization-independent splitter) or 180 degrees (e.g. from a
PBS). As will become apparent, the relative angle must not be 90 or
270 degrees (as measured on the Poincare sphere). The labels x and
y refer to the measured light powers obtained by two photodetectors
followed two polarization analyzers.
1.16.2.4.1 The Normalized Powers
[0590] The transmissions (normalized powers) can be written as
T x ( k ) ( v ) = P x ( k ) ( v ) u 0 P x ( k ) ( v ) SOP T y ( k )
( v ) = P y ( k ) ( v ) u 0 P y ( k ) ( v ) SOP ( 7.30 )
##EQU00093##
where .sub.SOP refers to an average over all or many (I-SOP, A-SOP)
couples at a given optical frequency .nu., and the reference
mean-value is u.sub.o=1/2. Equation (7.30) assumes that the overall
total power is stable over entire measurement time.
1.16.2.4.2 Relative Variance
[0591] The relative variance, for example mainly due to
un-polarized ASE light from optical amplifiers in the test network
fiber link or any other depolarizing effects, as used in equation
(49) below, is computed at each optical frequency as
.sigma. r 2 ( v ) = ( 1 .sigma. 20 ) 2 [ T x ( v ) T y ( v ) SOP -
1 4 T x ( v ) + T y ( v ) SOP 2 cos .theta. ] or ( 7.31 a ) .sigma.
r 2 ( v ) = ( 1 .sigma. 20 ) 2 [ T x ( v ) T y ( v ) SOP - T ( v )
SOP 2 cos .theta. ] ( 7.31 ) ##EQU00094##
where .theta. is an angle between two polarization analyzers (not
90 or 270 degree (in Poincare sphere)), .sigma..sub.20.sup.2= 1/12,
.sub.SOP refers to an average over all or many (I-SOP, A-SOP)
couples at each given optical frequency .nu., and T(.nu.).sub.SOP
refers to an average over all or many (I-SOP, A-SOP) couples at
each given optical frequency, .nu., for these transmissions
(normalized powers) measured from two photodetectors.
Advantageously, the above computed relative variance exhibits
negligible or very small dependence on noise in the detected
powers.
1.16.2.4.3 Equalization of Normalized Powers
[0592] The equalized transmissions (or equalized normalized
powers), labelled as T.sub.e,x and T.sub.e,y, are computed for two
photodetectors from two analyzers in the same way as in equation
(40a) as follows
T e , x ( k ) ( v ) = T x ( k ) ( v ) .sigma. r ( v ) - 1 2 ( 1
.sigma. r ( v ) - 1 ) T e , y ( k ) ( v ) = T y ( k ) ( v ) .sigma.
r ( v ) - 1 2 ( 1 .sigma. r ( v ) - 1 ) ( 7.32 a ) ##EQU00095##
where .delta..sub.r(.nu.) can be obtained from equation (7.31).
1.16.2.4.4 Mean-Square Differences
[0593] The calculation of mean-square differences using equalized
transmissions (or equalized normalized powers) from two
photodetectors with two arbitrary orientated polarization analyzers
having an angle, .theta., but not 90 or 270 degrees on the Poincare
sphere) between them can be found as
.DELTA. T e 2 ( v ) SOP = ( T e , x ( k ) ( v + 1 2 .delta. v ) - T
e , x ( k ) ( v - 1 2 .delta. v ) ) ( T e , y ( k ) ( v + 1 2
.delta. v ) - T e , y ( k ) ( v - 1 2 .delta. v ) ) SOP = 1 K k ( T
e , x ( k ) ( v + 1 2 .delta. v ) - T e , x ( k ) ( v - 1 2 .delta.
v ) ) ( T e , y ( k ) ( v + 1 2 .delta. v ) - T e , y ( k ) ( v - 1
2 .delta. v ) ) ( 7.33 a ) .DELTA. T e 2 ( v ) SOP , v = ( T e , x
( k ) ( v + 1 2 .delta. v ) - T e , x ( k ) ( v - 1 2 .delta. v ) )
( T e , y ( k ) ( v + 1 2 .delta. v ) - T e , y ( k ) ( v - 1 2
.delta. v ) ) SOP , v = - 1 K N ' k , n ( T e , x ( k ) ( v + 1 2
.delta. v ) - T e , x ( k ) ( v - 1 2 .delta. v ) ) ( T e , y ( k )
( v + 1 2 .delta. v ) - T e , y ( k ) ( v - 1 2 .delta. v ) ) (
7.33 b ) ##EQU00096##
where K is the total number of (I-SOP, A-SOP) couples and N' is the
total number of midpoint optical frequencies.
[0594] As shown in equations (7.33a) and (7.33b), by using
equalized transmissions (or equalized normalized powers), T.sub.e,x
and T.sub.e,y, to compute the mean-square difference from two
polarization analyzers followed by two tunable filters and two
photodetectors (for the implementation using broadband source) or
two photodetectors (for the implementation using tunable laser
source), the noise averages to zero instead of being "rectified",
because the noise superimposed on a given measured power from one
detector is not correlated with the noise superimposed on the
another power measured by a different detector.
1.16.2.4.5 Computation of the DGD and PMD Value Using Mean-Square
Differences of Equalized Transmissions
[0595] If the two polarization analyzers have an arbitrary mutual
angle .theta. that is substantially not equal to 90 or 270 degrees
on the Poincare sphere, the DGD(.nu.) may be computed according to
the following arcsine formula from calculated mean-square
differences using equalized transmissions (or equalized normalized
powers) as defined in equation (49) and as measured by two
photodetectors:
DGD ( v ) = 1 .pi. .delta. v arcsin ( .alpha. ds .DELTA. T e 2 ( v
) SOP cos .theta. ) ( 7.34 a ) ##EQU00097##
where .sub.SOP refers to an average over the (I-SOP, A-SOP) couples
only.
[0596] A rms DGD can be written as
rms DGD = 1 .pi. .delta. v arcsin ( .alpha. ds .DELTA. T e 2 ( v )
SOP ; v cos .theta. ) ( 7.35 a ) ##EQU00098##
where .sub.SOP;.nu. refers to an average over both the (I-SOP,
A-SOP) couples and optical frequency (i.e. wavelength), and a
theoretical constant
.alpha. ds = 9 2 , ##EQU00099##
and, .delta..nu.=.nu..sub.i+n-.nu..sub.i, an optical-frequency
difference between two closely-spaced optical frequencies,
.nu..sub.i and .nu..sub.i+n, is used for computing DGD and PMD.
[0597] It should be appreciated that the arcsine formula, in above
equations, is not the only possible one. For a small step, i.e.
satisfying the condition DGD.delta..nu. or rms
DGD.delta..nu.<0.01, the small-step limit of equations (7.34a)
and (7.35a) tend to the following simpler differential
formulas:
DGD ( v ) = 1 .pi. .delta. v ( .alpha. ds .DELTA. T e 2 ( v ) SOP
cos .theta. ) ( 7.34 b ) RMS DGD = 1 .pi. .delta. v ( .alpha. ds
.DELTA. T e 2 ( v ) SOP ; v cos .theta. ) ( 7.35 b )
##EQU00100##
[0598] A mean DGD or rms DGD may be computed by averaging DGD(.nu.)
(obtained from equations (6.1) or (6.8)) over many different
midpoint optical frequencies across a prescribed optical frequency
range, such as
rms D G D = D G D 2 ( v ) v ( 7.36 a ) mean D G D = D G D ( v ) v (
7.36 b ) ##EQU00101##
[0599] It should be noted that the two analyzer axes may also be
oriented in exactly the same direction or even replaced by only one
polarization analyzer followed by a coupler 21 and two detectors A
and B (22B and 22C) as shown in the implementation of FIG. 1C.
1.17 Embodiment (2)
Partial DGD Measurement and PMD Estimation Therefrom
1.17.1 Method of Operation
[0600] The method of operation for the instrument for DGD.sub.P
measurement and PMD measurement, illustrated schematically in FIG.
2K, will now be described in more detail.
[0601] The user first inserts the test modules in the platforms,
then starts testing software to cause the system to initialize the
test modules, specifically initializing the analyzing means, the
detection and processing sections. Then the analyzer-and-detection
module (e.g. FTB-5240BP Optical Spectrum Analyzer sold by EXFO
Inc., comprising a polarization controller just "downstream" from
its input 10) is connected to a point in the optical link that is
usually tapped from a network transmission line (i.e. a monitor
port 26 or 27) or at the distal end of an optical path (i.e. at a
receiver (Rx) side 28) by patch cords with either a PC or an APC
connector (such as FC/PC or FC/APC), or direct bulkhead connectors,
are used to connect the modules 10. Most instrument parameters will
usually be factory set according to customer requirements, but the
user may manually select parameters for analyzer in its application
interface. Assuming that the user selects manual parameter setting,
the program proceeds to the manual parameter setting and prompts
the user as follows:
(a) To set a scan wavelength range, e.g. C-band. (b) To set the
number K of OSA scans or states of polarization (A-SOP). For
example, K may be set as 3 to 10,000. (c) Set an overall total
acquisition number of DGD.sub.P monitoring and PMD measurement as
well as its waiting time between any two monitoring and
measurements. (d) Set a SUT bandwidth, e.g. 1, or 3, or 10, or 20
dB, or 30 dB, for a computation of weighting average of DGD.sub.P
value over a SUT bandwidth from measured DGD.sub.P(.lamda.) and
signal spectrum S(.lamda.) (i.e. set a SUT bandwidth for
DGD.sub.P(.lamda.) and S(.lamda.) monitoring and measurement).
[0602] If, in decision step, the user selects automatic parameter
setting, the program starts the auto parameter setting procedure
and carries out the following steps. Auto mode may also be designed
to automatically produce cable or fiber name and/or with relevant
information.
[0603] Once the measurement parameters have been entered, whether
manually or automatically, the program proceeds and computes
wavelength step .delta..lamda. (or frequency difference
.delta..nu.) if the anticipated DGD.sub.P, PMD-induced penalty, and
total PMD values have been specified or estimated via the
aforementioned auto-setting procedure, and the appropriate sequence
of wavelengths .lamda.s based on the parameter settings.
[0604] For the case of estimating a PMD penalty, user may also need
to select or set the dimensionless parameter(s) (e.g. the factor A
in Equation (6)) according to experiment (reference/calibration) or
simulations for the SUTs.
[0605] Finally, all the measurement parameters, whether directly
specified or computed as described above, are stored in the header
of the data file or instrument.
[0606] It should be noted that the spectral resolution bandwidth
(RBW) of the tunable optical filters will usually be set, in the
factory or by design, and will normally be quite small (e.g. of 20
to 80 pm) in order to ensure the ability to measure a high
DGD.sub.P or PMD.
[0607] It should be noted that, conveniently, at each SOP and/or
center wavelength, the frequency difference .delta..nu. (or
wavelength step .delta..lamda.) between the two closely-spaced
optical frequencies .nu..sub.U and .nu..sub.L (wavelengths
.lamda..sub.U and .lamda..sub.L) may remain the same or similar.
Each SOP and/or wavelength may only be set in a short time
period.
[0608] It should be re-emphasized, that in order to obtain a
reliable DGD.sub.P measurement for a SUT 60 and PMD measurement of
the optical link 24, it is preferable that the acquisition should
be undertaken for several or many A-SOPs, and/or different center
(i.e. midpoint) wavelengths. Preferably, for PMD measurement of an
optical fiber link, the acquisition may also be undertaken over an
extended duration (encompassing environmental changes and
perturbations) so as to improve the PMD measurement accuracy and it
is especially critical if the measurement is undertaken with a very
limited number of SUTs, e.g. only one SUT being available.
[0609] It should note the above steps may obtain DGD.sub.P at given
midpoint wavelength or DGD.sub.P as function of wavelength or as
well as to obtain rms DGD.sub.P over a multiplicity of SUTs (and
thereby a PMD estimate) that may be computed as the method
described in below sections that may also be included in data
processing step.
1.17.2 Data Processing and Computation
[0610] The powers are processed to obtain the DGD.sub.P of a SUT 60
and PMD value of a lightpath 24 in a DWDM optical network as will
now be described. It should be noted that, in all that follows, the
symbols refer to the matrix "Data". The labels x and y refer to the
light powers obtained from photodetectors PD.sub.x 18A and PD.sub.y
18B, respectively.
1.17.2.1 Using Two Repeated Powers
1.17.2.1.1 Normalized Powers
[0611] The normalized powers, labelled hereinafter as T, are
computed differently according to the particular embodiment.
(i) For the embodiment of FIG. 2K (two tunable filters TF.sub.x 16A
and TF.sub.y 16B and two photodetectors PD.sub.x 18A and PD.sub.y
18B with a PBS 14), the transmission values (normalized power) are
computed as follows either
T L ( k ) = Px L ( k ) Px L ( k ) + Py L ( k ) T L '' ( k ) = Px L
'' ( k ) Px L '' ( k ) + Py L '' ( k ) T U ( k ) = Px U ( k ) Px U
( k ) + Py U ( k ) T U '' ( k ) = Px U '' ( k ) Px U '' ( k ) + Py
U '' ( k ) or ( 7.37 a ) T L ( k ) = 1 2 Px L ( k ) - Py L ( k ) Px
L ( k ) + Py L ( k ) T L '' ( k ) = 1 2 Px L '' ( k ) - Py L '' ( k
) Px L '' ( k ) + Py L '' ( k ) T U ( k ) = 1 2 Px U ( k ) - Py U (
k ) Px U ( k ) + Py U ( k ) T U '' ( k ) = 1 2 Px U '' ( k ) - Py U
'' ( k ) Px U '' ( k ) + Py U '' ( k ) ( 7.37 b ) ##EQU00102##
where it should be appreciated that the different P.sub.y powers
have been pre-multiplied by a factory calibration factor or a
measured relative gain using many measured powers for a large
number of A-SOPs, before they are used in equations (7.37a) and
(7.37b). (ii) For the embodiment of FIG. 2I (single tunable filter
16 and single photodetector 18 with linear polarizer 15), the only
available powers are the Px powers (obtained here from
photodetector 18). The normalized power is obtained as in (7.37c)
but without computing the ratio of power x over power y first,
i.e.
T L ( k ) = u o Px L ( k ) P L SOP T L '' ( k ) = u o Px L '' ( k )
P L SOP T U ( k ) = u o Px U ( k ) P U SOP T U '' ( k ) = u o Px U
'' ( k ) P U SOP ( 7.37 c ) ##EQU00103##
where u.sub.0=1/2, and the average power is defined as,
P L SOP = 1 2 K k ( Px L ( k ) + Px L '' ( k ) ) P U SOP = 1 2 K k
( Px U ( k ) + Px U '' ( k ) ) ( 7.37 d ) ##EQU00104##
[0612] Here, the detected power is assumed to be roughly constant
during the time period for measurement of the initial and repeated
powers and the same requirement for the above (i)
normalization.
[0613] Fundamentally all of these relationships are valid if
sufficiently random output SOP scrambling is applied, yielding an
accurate estimate of DGD.sub.P at one particular midpoint
wavelength, and then it is possible to obtain DGD.sub.P against
midpoint wavelength within a SUT bandwidth. Therefore, one can also
compute a spectral-power-weighted mean DGD.sub.P or rms DGD.sub.P
value for SUT 60.
1.17.2.1.2 Signal Power Spectrum
[0614] In order to monitor a traffic signal (SUT 60) PMD penalty,
one must compute the "signal-only" power as a function of
frequency, i.e. S(.nu.), and it is computed differently according
to the embodiment.
(i) For the embodiment of FIG. 2K (two tunable filters 16A and 16B
and two photodetectors 18A and 18B with a PBS 14), the transmitted
signal power as a function of frequency, .nu., is computed as
follows
S ( v ) = Px ( v ) - Py ( v ) SOP S ( v ) = Px '' ( v ) - Py '' ( v
) SOP or ( 7.38 a ) S ( v ) = ( Px ( v ) - Py ( v ) ) 2 SOP S ( v )
= ( Px '' ( v ) - Py '' ( v ) ) 2 SOP ( 7.38 b ) ##EQU00105##
or, alternatively, a transmitted signal power may be calculated
maximum and minimum power measurements for a large number of A-SOPs
as
S(.nu.)=max[Px(.nu.),Py(.nu.),Px''(.nu.),Py''(.nu.)]-min[Px(.nu.),Py(.nu-
.),Px''(.nu.),Py''(.nu.)] (7.38c)
[0615] If there is a negligible ASE, for example an OSNR>20 dB,
the S(.nu.) of the signal power spectrum may be calculated from an
average over two measured optical power at each wavelength from two
detectors for any A-SOP as:
S(.nu.)=Px(.nu.)+Py(.nu.) (7.38d)
or averaging a number of A-SOPs as:
S(.nu.)=Px(.nu.)+Py(.nu.).sub.SOP (7.38d')
[0616] (ii) For the embodiment of FIG. 2I (single tunable filter 16
and single photodetector 18 with linear polarizer 15), the only
available powers are the Px powers (obtained here from
photodetector 18). The transmitted signal power as a function of
frequency, .nu., is computed as follows
S ( v ) = Px ( v ) SOP - Px ( v ) SOP ' SOP or ( 7.38 e ) S ( v ) =
( Px ( v ) SOP - Px ( v ) SOP ' ) 2 SOP ( 7.38 f ) ##EQU00106##
where Px(.nu.).sub.SOP-Px(.nu.).sub.SOP' is a power difference
value between two measured powers from two power measurements for
two different A-SOPs by single photodetector 18.
[0617] Alternatively, a transmitted signal power may be calculated
maximum and minimum power measurements for a large number of A-SOPs
as
S(.nu.)=max[Px(.nu.),Px''(.nu.)]-min[Px(.nu.),Px''(.nu.)]
(7.38g)
[0618] If there is a negligible ASE, for example where the
OSNR>20 dB (e.g. as defined, by convention, in a bandwidth of
0.1 nm), the S(.nu.) of the signal power spectrum may be calculated
from an average over at least one preferably over a large of number
of measured optical powers at each wavelength as:
S(.nu.)=P(.nu.).sub.SOP (7.38h)
[0619] It should be appreciated that the calculated spectral power,
S(.nu.), in equations (11a-h) may be multiplied by any factor that
is constant for all optical frequencies within an optical-frequency
range of interest.
[0620] It should be also appreciated that S(.nu.) is a calculated
signal-related intensity (spectrum) at each midpoint wavelength or
frequency. Or, otherwise, such P(.nu.) must be measured in order to
compute an accurate signal power (intensity) spectrum, S(.nu.).
1.17.2.1.3 Relative Variance
[0621] The relative variance, for example arising from un-polarized
ASE from optical amplifiers and/or nonlinear effect (e.g. XPM)
induced signal depolarization in the optical path (or any other
depolarizing effects) is computed here as the average of the two
available estimates, i.e.,
.sigma. r 2 ( v ) = 12 [ .delta. ( T L ( v ) ) + .delta. ( T U ( v
) ) 2 ] ( 7.39 ) ##EQU00107##
where
.delta.(T.sub.L(.nu.))=.left
brkt-bot.T.sub.L(.nu.)T.sub.L''(.nu.).sub.SOP-T.sub.L(.nu.).sub.SOP.sup.2-
.right brkt-bot.
.delta.(T.sub.L(.nu.))=.left
brkt-bot.T.sub.U(.nu.)T.sub.U''(.nu.).sub.SOP-T.sub.U(.nu.).sub.SOP.sup.2-
.right brkt-bot.
These equations are valid when the A-SOPs are approximately
uniformly distributed on the Poincare Sphere.
[0622] It should be noted that noise variance may also be
calculated by using the above-obtained normalized power and is then
subtracted from the above estimation of the relative variance
(equation 7.39) to obtain a noise-free relative variance.
1.17.2.1.4 Mean-Square Differences
[0623] The calculation here differs from the simple mean-square
found in equations (2a) which, for greater clarity, did not take
into account the noise. Instead, the product of the repeated
differences between normalized power at .lamda..sub.U and
.lamda..sub.L is averaged as follows,
.DELTA. T 2 ( v ) SOP = ( T U ( v ) - T L ( v ) ) ( T U '' ( v ) -
T L '' ( v ) ) SOP = 1 K k ( ( T U ( k ) ( v ) - T L ( k ) ( v ) )
( T U '' ( k ) ( v ) - T L '' ( k ) ( v ) ) ) ( 7.40 )
##EQU00108##
[0624] In conventional mathematical terms, equations (7.40) may be
referred to as the second-order joint moment of the repeated
differences.
[0625] The formula of Equation (7.40) leads to the noise being
averaged to zero instead of being "rectified", since the noise
superimposed on a given trace is not correlated with the noise
superimposed on the corresponding repeated power. That is the first
motivation for acquiring repeated data.
[0626] It should be noted that .sub.SOP in Eq. (7.40) refers to an
average over the A-SOP at a given midpoint frequency (.nu..sub.mid)
(i.e. midpoint wavelength, .lamda..sub.mid), i.e., only changing
the output SOP from one group of powers to other, which is
particularly appropriate for determining the DGD.sub.P at this
wavelength.
1.17.2.1.5 Computation of the DGD.sub.P Value of a SUT
[0627] The DGD.sub.P as a function optical frequency for a fixed
given launched polarization of a SUT can be calculated according to
the arcsine formula as,
.tau. PB ( v ) = 1 .pi..delta. v arcsin ( 3 .DELTA. T 2 ( v ) SOP
.sigma. r 2 ( v ) ) ( 7.41 ) ##EQU00109##
where .sub.SOP refers to an average taken over A-SOP only.
[0628] To obtain the DGD.sub.P parameter to estimate a PMD penalty,
an average over computed DGD.sub.P in equation (15) over signal
(SUT 60) bandwidth with the spectral intensity (density) weighting
can be expressed as:
.tau. _ PB SUT = .intg. v S ( v ) .tau. PB ( v ) v .intg. v S ( v )
v ( 7.42 a ) ##EQU00110##
[0629] The light power spectral weighting average in equation
(7.42a) can be performed over any pre-defined SUT bandwidth, e.g.
-3 dB to -10 dB, or as wide as possible, however, in practice, for
example, a -20 dB or -10 dB or -3 dB bandwidth may be chosen. It
should be noted that in practice it is preferably to use a signal
spectral `mean` averaging shown equation (7.42a).
[0630] Alternatively, if S(.nu.) is set to equal to a constant
value (e.g. 1) for above equations (7.42a), a mean DGD.sub.P value
over a specified wavelength range of a SUT bandwidth is expressed
as:
.tau..sub.PB.sub.SUT=.tau..sub.PB(.nu.).sub..nu. (7.42b)
or alternatively an rms DGD.sub.P value as:
.tau. _ PB SUT = .tau. PB 2 ( v ) v ( 7.42 c ) ##EQU00111##
where .sub..nu. is to average over a specified wavelength range,
e.g. of a SUT bandwidth.
[0631] It should be appreciated that the arcsine formula, in
equation (7.41), is not the only possible one. The purpose of using
this formula is to obtain a result that is unbiased even if using a
relatively large step (e.g. such that
DGD.sub.P.delta..nu..about.0.20), without introducing a significant
error; this in order to maximize the signal-to-noise ratio and
therefore the dynamic range of the instrument. Although applicable
to any step size, if one were not concerned with maximizing the
dynamic range, one could select a small step, in which case the
following simpler differential formula is valid:
.tau. PB ( v ) = 1 .pi. .delta. v 3 .DELTA. T 2 ( v ) SOP .sigma. r
2 ( v ) ( 7.41 a ) ##EQU00112##
[0632] This is not to infer that this formula is better or
particularly advantageous, but merely that it may conveniently be
used if the step is much smaller, i.e., satisfying the condition
DGD.sub.P.delta..nu.<0.01.
[0633] It should be noted that in an ideal situation where there is
no depolarization (i.e. no ASE or other depolarizing phenomena) and
no effective depolarization due to rapid temporal fluctuations
(e.g. due to rapidly moving aerial cable), then
.sigma..sub.r.sup.2=1 can be used in equations (7.41) and (7.41a)
above (and, in analogous fashion, in equations (7.44b) and (7.44c)
in section 1.6).
[0634] For the case where the tunable filter(s) has/have a
relatively large bandwidth(s) (i.e. RBW) and a high-DGD.sub.P is
being monitored, a further RBW `correction factor` may be applied
in equations in order to extract a DGD.sub.P value of the SUT
60.
[0635] It should also be noted that repeated powers may be obtained
from two or more measurements at different times using the same
detectors, or from measurements using different detectors, e.g.
after light power being split by an optical coupler, where the
powers detected by the different detectors are measured
contemporaneously.
1.17.2.1.6 Computation of the PMD Penalty of a SUT from an Average
DGD.sub.P Value Over a Signal Bandwidth
[0636] Based on above computed average DGD.sub.P value over a
specified wavelength range, (typically corresponding to the SUT
bandwidth) in equations (7.42a), (7.42b), (7.42c) or (7.42d), a
PMD-induced impairment of a SUT due to pulse broadening from a
relative time delay of two orthogonally polarization components
propagating along the lightpath may be expressed as a PMD-induced
power penalty, .eta., as:
.eta. = A ( .tau. _ PB SUT 2 B ) 2 ( 7.43 ) ##EQU00113##
where a PMD power penalty, .eta., is expressed in dB, which is
assumed small, and B is a bit interval, i.e. bit period, and A may
be a predetermined dimensionless parameter that may depend on
modulation format, pulse shape, network characteristics (e.g.
optical noise, optical filter, etc.), and receiver characteristics
(e.g. electric filter, noise, etc.).
[0637] It should be appreciated that the above equation (7.43) is
not the only possible one, and it may be expressed as any other
formula.
1.17.2.1.7 Computation of the PMD Value of a Fiber Link
[0638] From above computed DGD.sub.P at each wavelength as
described above section 1.5, a link PMD in a network may also be
determined, specifically estimated, by averaging DGD.sub.P over a
prescribed wavelength range encompassing the central wavelengths of
a multiplicity of SUTs (e.g. DWDM signals) as,
PMD = 3 2 .tau. PB 2 ( v ) v or ( 7.44 a ) PMD = 1 .pi. .delta. v
arcsin ( 9 2 .DELTA. T 2 ( v ) .sigma. r 2 ( v ) SOP ; v ) ( 7.74 b
) ##EQU00114##
where equation (7.44a) is averaged measured DGD.sub.P over a large
number of SUT bandwidths and equation (7.44b) is a (directly)
average from measured normalized power difference over both A-SOP
and optical frequency.
[0639] It should be appreciated that the arcsine formula, in
equation (7.43), is not the only possible one. The purpose of using
this formula is to obtain a result that is unbiased, i.e. does not
introduce significant error, even if the separation between the
above-described closely-spaced optical frequencies is relatively
large step, e.g. such that PMD.delta..nu..about.0.15. However, if a
much smaller step is selected, the following alternative and
simpler differential formula is valid and may be applied:
PMD = 1 .pi. .delta. v 9 2 .DELTA. T 2 ( v ) .sigma. r 2 ( v ) SOP
; v ( 7.44 c ) ##EQU00115##
[0640] This is not to infer that these formulas are better or
particularly advantageous, but merely that it may conveniently be
used if the step is much smaller, i.e., satisfying the condition
PMD.delta..nu.<0.01.
[0641] Alternatively, PMD of the link may be roughly estimated by
averaging these measured DGD.sub.P from a single channel signal
(SUT) over a time period sufficiently long that environmental
fluctuations may be significant. Such fluctuations may lead to
variation of SUT polarization at the input or along the length of
the lightpath, and/or variation of PSP axis of the lightpath,
and/or DGD variations. In such a case, the PMD may be estimated
as:
PMD = 3 2 .tau. PB 2 ( v ) ( t , v ) ( 7.44 a ' ) ##EQU00116##
where .sub.(t,.nu.) indicates an average over time (t), and/or
signal light polarization fluctuation, and or wavelength (optical
frequency) over the SUT bandwidth.
[0642] It should also be noted that a measured PMD accuracy can be
further improved if equations (7.44a), (7.44b) and (7.44c) are
further averaged over one or more of time and over possible random
variations of the launched SOP of the SUT (i.e. .phi.) and/or
possible variations of the SOP along the link caused by cable
movement, etc.
1.17.2.2 Employing Two Physically Orthogonal Polarization Analyzers
from a Polarization Beam Splitter with Rapid Wavelength
Sweeping
[0643] In practice, an instrument can be designed in accordance
with the configuration illustrated in FIG. 2K, employing
polarization-diverse detection and rapid wavelength sweeping, where
the wavelength of the detected light is swept over a prescribed
wavelength range, e.g. by tunable filters. Each light powers from
the SUT, obtained with either one given setting of the wavelength
from tunable filter 16A and tunable filter 16B (FIG. 2K) and of the
A-SOPs by an A-SOP controller 12, as described in the Method of
Operation, constitutes an elementary data cell, i.e. one datum
consists of one power value. The data unit is one group of N
powers, two sets of N powers for the embodiment of FIG. 2K where
two powers are obtained substantially simultaneously from two
photodetectors 18A and 18B, both acquired with given approximately
same SOP as set by an A-SOP controller 12.
[0644] The powers are processed to obtain the DGD.sub.P(.nu.) value
of the SUT 60 and PMD value of the optical path using detected two
physically orthogonal (i.e. antipodal on the Poincare sphere)
polarization components from PBS 14 by rapid wavelength sweeping of
tunable filter means comprising tunable filters 16A and 16B (see
FIG. 2K), as will now be described. The labels x and y refer to the
probed light powers obtained from photodetectors 18A and 18B,
respectively.
1.17.2.2.1 Normalized Powers
[0645] The transmissions (normalized powers), labelled as T.sub.x
and T.sub.y, are computed for the embodiment of FIG. 2K for two
photodetectors 18A and 18B with a PBS 14 as follows either
T x ( k ) ( v ) = P x ( k ) ( v ) P x ( k ) ( v ) + P y ( k ) ( v )
SOP T y ( k ) ( v ) = P y ( k ) ( v ) P x ( k ) ( v ) + P y ( k ) (
v ) SOP or ( 7.45 a ) T x ( k ) ( v ) = P x ( k ) ( v ) u 0 P x ( k
) ( v ) SOP T y ( k ) ( v ) = P y ( k ) ( v ) u 0 P y ( k ) ( v )
SOP ( 7.45 b ) ##EQU00117##
where .sub.SOP is referred to average over all or many analyzer
SOPs (A-SOPs) at a given optical frequency .nu., and the reference
mean-value is u.sub.o=1/2. Equations (7.45a) and (7.45b) assume
that the measured overall total power, i.e. the sum of the two
polarization-diverse detectors, corresponding respectively to
orthogonal polarization components x and y, is stable throughout
the acquisition time.
[0646] Alternatively, the transmission values (normalized powers)
may be written as:
T x ( k ) ( v ) = P x ( k ) ( v ) P x ( k ) ( v ) + P y ( k ) ( v )
T y ( k ) ( v ) = P y ( k ) ( v ) P x ( k ) ( v ) + P y ( k ) ( v )
( 7.45 c ) ##EQU00118##
[0647] Consequently, the so-obtained transmission values
(normalized powers) advantageously exhibit little or negligible
dependence on possible instabilities in the transmitter light power
over the monitoring/measurement time.
[0648] It should be noted that above normalized power is computed
at each optical frequency (.nu.), i.e. from one wavelength to
others, for the entire optical frequency range. This is because
there may be different measured optical-power levels and
optical-noise (i.e. ASE) levels at different frequencies
(wavelengths), especially if the measurement is performed within a
narrow optical channel, e.g. a DWDM channel, so that their relative
variance may be different from one optical frequency to
another.
1.17.2.2.2 Signal Power Spectrum
[0649] In order to monitor a traffic signal (SUT) PMD penalty, one
must compute signal-only power as a function of frequency, i.e.
S(.nu.), and preferably S(.nu.) is calculated at each middle point
wavelength or frequency. For the embodiment of FIG. 2K, comprising
two tunable filters (16A, 16B), two photodetectors (18A, 18B) and
PBS 14, the transmitted signal power as a function of optical
frequency, .nu., is computed as follows
S ( v ) = P x ( k ) ( v ) - P y ( k ) ( v ) SOP or ( 7.46 a ) S ( v
) = ( P x ( k ) ( v ) - P y ( k ) ( v ) ) 2 SOP ( 7.46 b )
##EQU00119##
or, alternatively, a transmitted signal power may be calculated
maximum and minimum power measurement method, e.g. polarization
nulling, for a large number of A-SOPs as
S(.nu.)=max[P.sub.x.sup.k(.nu.),P.sub.y.sup.k(.nu.)].sub.SOP-min[P.sub.x-
.sup.k(.nu.),P.sub.y.sup.k(.nu.)].sub.SOP (7.47)
[0650] If the ASE power is negligible, for example when OSNR>20
dB, the S(.nu.) of the signal power at each wavelength and for any
A-SOP, may be calculated by the sum of the powers measured with the
two photodetectors PD.sub.x 18A and PD.sub.y 18B as
S(.nu.)=P.sub.x.sup.(k)(.nu.)+P.sub.y.sup.(k)(.nu.) (7.48)
[0651] Alternatively, an average over measured optical powers at
each wavelength for at least two A-SOPs may be expressed as
S(.nu.)=(P.sub.x.sup.(k)(.nu.)+P.sub.y.sup.(k)(.nu.).sub.SOP
(22a)S.sub.x(.nu.)=P.sub.x.sup.(k)(.nu.).sub.SOP (7.49b)
S.sub.y(.nu.)=P.sub.y.sup.(k)(.nu.).sub.SOP (7.49c)
where equations (7.49b) and (7.49c) can also be applied for the
embodiment of FIG. 2I where one tunable filter 16 and one
photodetector 18 with a linear polarizer 15 are used.
[0652] It should be appreciated that the calculated spectral power,
S(.nu.), in equations (7.46), (7.47), (7.48) and (7.49) may be
multiplied by any factor, but this factor should be the same for
any optical frequency within the optical-frequency range of
interest for further application of a computation of the
spectrally-weighted average DGD.sub.P for estimating a PMD penalty
of a SUT 60.
[0653] As well, the calculated S(.nu.) in above equations (7.46 to
7.49) should be at each middle point wavelength or frequency that
corresponds to a middle-point wavelength of computed DGD.sub.P.
1.17.2.2.3 Relative Variance
[0654] The relative variance arises principally from (un-polarized)
ASE from optical amplifiers, polarization noise, especially for
high-density DWDM networks, depolarization induced by nonlinear
effects (e.g. XPM). It may be computed at each optical frequency
as
.sigma..sub.r.sup.2(.nu.)=12[-1T.sub.x(.nu.)T.sub.y(.nu.).sub.SOP+1/4T.s-
ub.x(.nu.)+T.sub.y(.nu.).sub.SOP.sup.2] (7.50a)
or
.sigma..sub.r.sup.2(.nu.)=12.left
brkt-bot.-1T.sub.x(.nu.)T.sub.y(.nu.).sub.SOP+T(.nu.).sub.SOP.sup.2.right
brkt-bot. (7.50b)
where .sub.SOP refers to an average over all or many A-SOPs at each
given optical frequency .nu., and T(.nu.).sub.SOP refers to an
average over all or many output SOPs at each given optical
frequency, .nu., for these transmissions (normalized powers)
measured from two photodetectors 18A and 18B.
[0655] Advantageously, the above computed relative variance exhibit
negligible or minimal dependence on noise in the detected powers.
However, assuming negligible noise from the measured powers for
each of the two polarization-diverse detectors 18A, 18B
(corresponding to x and y, respectively), relative variance may be
obtained as
.sigma. r 2 ( v ) = 12 [ T x 2 ( v ) SOP + T y 2 ( v ) SOP - 2 T (
v ) SOP 2 2 ] ( 7.51 a ) .sigma. r 2 ( v ) = 12 T x 2 ( v ) SOP - T
x 2 ( v ) SOP 2 ( 7.51 b ) .sigma. r , y 2 ( v ) = 12 T y 2 ( v )
SOP - T y ( v ) SOP 2 ( 7.51 c ) ##EQU00120##
[0656] It should be noted that Equation (7.51b) or (7.51c) can be
applied to the embodiments of FIG. 2I where the PBS 14 is replaced
by a linear polarizer 15 and only one photodetector PD 18 is
employed.
[0657] Also note that after averaging over sufficient large number
of output SOPs (A-SOPs), relative variances being obtained from
equations (7.51a), (7.51b) and (7.51c) are equal, i.e.
.sigma..sub.r.sup.2(.nu.)=.sigma..sub.r,x.sup.2(.nu.)=.sigma..sub.r,y.sup-
.2(.nu.).
1.17.2.2.4 Equalization of Normalized Powers
[0658] The transmission values (or normalized powers) computed in
Section 2.1 have not undergone an "equalization" procedure, i.e.
they may be affected by ASE and any signal-depolarizing effects,
e.g. depolarization induced by inter-channel XPM, etc., therefore
they may not be equalized between 0 and 1. However, to compute the
DGD.sub.P of the SUT 60 and therefrom the PMD of the optical link
24 as used in equations (24a) and (24b) below, the measured
transmission values (or normalized powers) must be equalized so as
to be uniformly distributed between 0 and 1 if the A-SOPs are
themselves substantially uniformly distributed on the Poincare
sphere. This equalization procedure applied to the normalized
powers thus effectively acts to remove any `depolarization` effects
on the polarized signal-under-test (SUT) 60. These equalized
transmission values (or equalized normalized powers) are then can
be directly used to calculate the mean-square difference for the
DGD.sub.P and PMD computations.
[0659] The equalized transmissions (or equalized normalized
powers), labelled as T.sub.e,x and T.sub.e,y, are computed for the
implementation of FIG. 2K for two photodetectors 18A and 18B with a
PBS 14 as follows
T e , x ( k ) ( v ) = T x ( k ) ( v ) .sigma. r ( v ) - 1 2 ( 1
.sigma. r ( v ) - 1 ) T e , y ( k ) ( v ) = T y ( k ) ( v ) .sigma.
r ( v ) - 1 2 ( 1 .sigma. r ( v ) - 1 ) ( 7.52 a ) ##EQU00121##
where .sigma..sub.r(.nu.) can be obtained from equations
(7.50).
[0660] Under the assumption of negligible noise contribution in the
power detected by the polarization-diverse detectors, the equalized
transmission values (or equalized normalized powers) may also be
expressed as
T e , x ( k ) ( v ) = T x ( k ) ( v ) .sigma. r , x ( v ) - 1 2 ( 1
.sigma. r , x ( v ) - 1 ) T e , y ( k ) ( v ) = T y ( k ) ( v )
.sigma. r , y ( v ) - 1 2 ( 1 .sigma. r , y ( v ) - 1 ) ( 7.52 b )
##EQU00122##
where .sigma..sub.r,x(.nu.) and .sigma..sub.r,y(.nu.) can be
obtained from equations (7.51).
[0661] Note that equation (20b) can be applied to the
implementation of FIG. 2I in which the PBS 14 is replaced by a
linear polarizer (P) 15 and only one photodetector 18 is used.
[0662] It should be noted that the equalization of the transmission
values (or normalized powers) needs to be performed at each optical
frequency, since relative variance is in general not constant for
different optical frequencies (wavelengths), especially for example
for a narrow SUT bandwidth in the in-service DWDM network with a
high ASE from optical amplifiers. However, if there is no
difference for relative variance against optical frequency
(wavelength), an averaged relative variance may be calculated.
1.17.2.2.5 Mean-Square Differences
[0663] The calculation of mean-square differences using equalized
transmissions (or equalized normalized powers), T.sub.e,x and
T.sub.e,y, from two photodetectors 18A and 18B with a PBS 14 for
the embodiments of FIG. 2K, can be expressed as
.DELTA. T e 2 ( v ) SOP = - 1 ( T e , x ( k ) ( v + 1 2 .delta. v )
- T e , x ( k ) ( v - 1 2 .delta. v ) ) ( T e , y ( k ) ( v + 1 2
.delta. v ) - T e , y ( k ) ( v - 1 2 .delta. v ) ) SOP = - 1 K k (
( T e , x ( k ) ( v + 1 2 .delta. v ) - T e , x ( k ) ( v - 1 2
.delta. v ) ) ( T e , y ( k ) ( v + 1 2 .delta. v ) - T e , y ( k )
( v - 1 2 .delta. v ) ) ) ( 7.53 ) ##EQU00123##
where K is total output SOPs (A-SOPs).
[0664] As shown in equation (7.53), by using equalized
transmissions (or equalized normalized powers), T.sub.e,x and
T.sub.e,y, to compute the mean-square difference for the PBS-based
implementation of FIG. 2K with two photodetectors, the noise
averages to zero instead of being `rectified`, because the noise
superimposed on a measured power by one detector is not correlated
with the noise superimposed on the measured power by a different
detector. That is achieved by acquiring data with different
detectors x and y (18A and 18B).
[0665] Equalized transmission values (or equalized normalized
powers) obtained from one photodetector connected either after one
of two ports of a PBS or after a linear polarizer, for example for
implementation in FIG. 2I where only one photodetector PD 18 (e.g.
that corresponding to x or y in equations (7.54a) or (7.54b),
respectively) is employed, can also be used to calculate
mean-square difference as,
.DELTA. T e 2 ( v ) SOP = ( T e , x ( k ) ( v + 1 2 .delta. v ) - T
e , x ( k ) ( v - 1 2 .delta. v ) ) 2 SOP = - 1 K k ( ( T e , x ( k
) ( v + 1 2 .delta. v ) - T e , x ( k ) ( v - 1 2 .delta. v ) ) 2 )
( 7.54 a ) .DELTA. T e 2 ( v ) SOP = ( T e , y ( k ) ( v + 1 2
.delta. v ) - T e , y ( k ) ( v - 1 2 .delta. v ) ) 2 SOP = - 1 K k
( ( T e , y ( k ) ( v + 1 2 .delta. v ) - T e , y ( k ) ( v - 1 2
.delta. v ) ) 2 ) ( 7.54 b ) ##EQU00124##
where K is total A-SOPs. Equations (7.54a) and (7.54b) are under an
assumption of negligible noise for the measured powers for the
photodetector PD (18) of FIG. 2I or each individual detectors of
PD.sub.x or PD.sub.y (18A and 18B) in FIG. 2I.
[0666] Note that an angle .phi. is related to launched polarization
of a SUT 60, i.e. a signal polarization dependent parameter, that
is usually kept constant during an acquisition time, however, if
.phi. is varied in an acquisition time period, an averaged value of
rms or mean difference (as well of DGD.sub.P and PMD) over varied
angle .phi. may be obtained.
[0667] Note that .sub.SOP in above equations refer to only
averaging over the SOP at a given midpoint frequency
(.nu..sub.i,mid) (or midpoint wavelength, .lamda..sub.i,mid), i.e.,
only changing the A-SOP from one group of powers to another.
1.17.2.2.6 Computation of the DGD.sub.P Value of SUT Using
Mean-Square Differences of Equalized Transmissions
[0668] The DGD.sub.P(.nu.), .tau..sub.PB(.nu.), is computed
according to the arcsine formula from calculated mean-square
differences using equalized transmissions (or equalized normalized
powers) for the embodiments of FIG. 2K with PBS 14 and two
photodetectors 18A and 18B as,
.tau. PB ( v ) = 1 .pi..delta. v arcsin ( 3 .DELTA. T e 2 ( v ) SOP
) ( 7.55 a ) ##EQU00125##
where .sub.SOP refers to average over the A-SOPs only,
.delta..nu.=.nu..sub.i+n-.nu..sub.i, an optical frequency
difference between two closely-spaced optical frequencies,
.nu..sub.i and .nu..sub.i+n, is used for computing DGD.sub.P.
[0669] It should be appreciated that the arcsine formula, in above
equations, is not the only possible one. This formula provides a
result that is unbiased even if a relatively large
optical-frequency step is used, e.g. such that
DGD.sub.P.delta..nu..about.0.20, thereby maximizing the
signal-to-noise ratio and therefore the dynamic range of the
instrument. Although applicable to any step size, if one were not
concerned with maximizing the dynamic range, one could select a
small step, in which case the following simpler differential
formula is valid:
.tau. PB ( v ) = 1 .pi..delta. v 3 .DELTA. T e 2 ( v ) SOP ( 7.55 b
) ##EQU00126##
[0670] This is not to infer that this formula is better or
particularly advantageous, but merely that it may conveniently be
used if the optical-frequency step is much smaller, i.e.,
satisfying the condition DGD.sub.P.delta..nu.<0.01-0.05.
[0671] It should also be noted that above equations are applicable
whether or not the SUT exhibits any significant ASE (typically from
optical amplifiers, and leading to signal-to-noise ratio as low as
.about.3 dB) or any depolarization effects etc. This insensitivity
to ASE is a consequence of the equalization of the transmission
values (or normalized powers) that has been performed in an earlier
step (in Section 2.4).
[0672] In order to estimate the PMD-induced penalty, an average
DGD.sub.P value over SUT bandwidth with the spectral power
weighting can be expressed as:
.tau. _ PB SUT = .intg. v S ( v ) .tau. PB ( v ) v .intg. v S ( v )
v ( 7.56 a ) ##EQU00127##
where the DGD.sub.P is obtained from equation (7.55a) or (7.55b)
and preferably a SUT bandwidth for such average may be defined to
fall within the spectral range for which the level of the SUT
spectral profile is greater than a specified number (e.g. -3 to -20
dB) with respect to the spectral peak value.
[0673] The light power spectral weighting factor, S(.nu.), can be
obtained from equations (19-22). Again, the average can be
performed over any pre-defined SUT bandwidth, for example, from 3
dB to 10-20 dB bandwidth may be chosen.
[0674] Alternatively, if S(.nu.) is set to equal to any constant
value (e.g. 1) in equations (25a) above, a mean DGD.sub.P value
over a specified wavelength range, e.g. of a SUT bandwidth, is
obtained as:
.tau..sub.PB.sub.SUT=.tau..sub.PB(.nu.).sub..nu. (7.56b)
or, alternatively, a rms DGD.sub.P value may be used, which is
expressed as:
.tau. _ PB SUT = .tau. PB 2 ( v ) v ( 7.56 c ) ##EQU00128##
where .sub..nu. indicates an average performed over a specified
wavelength range within the SUT bandwidth, e.g. -3 to -10 dB down
with respect to the spectral peak power. 1.17.2.2.7 Computation of
the PMD Penalty of a SUT from an Average DGD.sub.P Value Over a
Signal Bandwidth
[0675] Based on the above-computed average DGD.sub.P value over a
specified wavelength range, e.g. of a SUT bandwidth, in equation
(7.56a), (7.56b) or (7.56c), an PMD-induced impairment of a SUT due
to pulse broadening from a relative time delay of two orthogonally
polarization components during transmission passing through an
optical path (lightpath) of a DWDM network may be written as a PMD
penalty, .eta., as:
.eta. = A ( .tau. _ PB SUT 2 B ) 2 ( 7.57 ) ##EQU00129##
where .eta., is expressed in dB, which is assumed small, and B is
the bit (or symbol interval), and A may be a predetermined
parameter, for example, that depends on modulation format, pulse
shape, network characteristics (e.g. optical noise, optical filter,
etc.), and receiver characteristics (e.g. electrical filter,
electrical noise, etc.).
[0676] It should be appreciated that the above equation (26) is not
the only possible one and it may be expressed as any other formula,
for example, a PMD-induced system penalty, .eta.(.phi.), may be
further expressed as:
.eta. = A 1 ( .tau. _ PB SUT 2 B ) 2 + A 2 ( .tau. _ PB SUT 2 B ) 4
( 7.57 ' ) ##EQU00130##
where a PMD power penalty, .eta.(.phi.), is expressed in dB, B is a
bit period, and A.sub.1 and A.sub.2 may be predetermined
parameters, for example, that may be extracted from measurements or
simulations.
[0677] It should be appreciated that above said predetermined
parameters A, A.sub.1 and A.sub.2 in equations (7.57) and (7.57')
may be extracted from either or both of the measured values (e.g.
calibration, reference, etc.) and or simulations.
[0678] It should be appreciated that a PMD penalty in equation
(26') may include higher-order PMD (e.g. second-order, etc.)
induced penalty while a PMD penalty expressed in equation (26) or
(6) may mainly include a first-order PMD penalty for the SUT. For
example an `equivalent` DGD.sub.P, .tau..sub.PB,1st+2nd.sub.SUT,
that may replace an average DGD.sub.P, .tau..sub.PB.sub.SUT, in
equation (26) or (26') may be expressed as:
.tau. _ PB , 1 st + 2 nd SUT = .intg. v S ( v ) .tau. PB ( v ) v
.intg. v S ( v ) v + .chi. B .intg. v S ( v ) .tau. PB ( v ) v v
.intg. v S ( v ) v ( 7.56 a ' ) ##EQU00131##
where .chi. is a constant. 1.17.2.2.8 Computation of the Lightpath
DGD or Link PMD Value from a Single Channel SUT DGD.sub.P
Measurement
[0679] Based on above-computed DGD.sub.P at each wavelength in
equation (7.55a) or (7.55b) and if there may be environmental
fluctuations, e.g. causing variation of the SOP of the SUT,
variation of the PSP axes of a lightpath of a DWDM network, and/or
DGD variation, lightpath PMD in a DWDM network may also be roughly
estimated by averaging DGD.sub.P over some or all of these
fluctuations, e.g. over time or signal SOP fluctuations, etc.,
and/or over wavelength of a SUT bandwidth as,
PMD = 3 2 .tau. PB 2 ( v ) ( t , v ) ( 7.58 ) ##EQU00132##
respectively, where .tau.(.nu.) is DGD at each wavelength, and
.sub.(t,.nu.) indicates an average over time (t), and/or signal
light polarization fluctuation, and/or optical frequency over the
SUT bandwidth.
[0680] Thus, PMD of an optical path may be roughly estimated from
the DGD.sub.P measured on only a single SUT if the measurement time
extends over a sufficiently long period, e.g. many hours to several
days, and, in some cases, many months. However, such "single-SUT"
PMD estimations generally have greater uncertainty than
measurements taken concurrently over multiple, widely-spaced SUTs.
A rough guide to the reliability of PMD estimation using multiple
measurements with a single-SUT may be gleaned from the degree to
which the measured DGD.sub.P values adhere to a Rayleigh
distribution [6] of measured PBs from a long time.
1.17.2.2.9 Computation of the PMD Value of a Link from DGD.sub.P
Measurements of Multiple SUTs
[0681] Based on above-computed DGD.sub.P at each wavelength in
equation (7.55a) or (7.55b) and if there may be a large number of
SUTs, e.g. 2-40, a lightpath PMD in a DWDM network may also be
measured or estimated by averaging DGD.sub.P over all (or some) of
wavelengths corresponding to the number of SUTs, as:
PMD = 3 2 .tau. PB 2 ( v ) v or ( 7.59 a ) PMD = 1 .pi..delta. v
arcsin ( 9 2 .DELTA. T e 2 ( v ) SOP ; v ) ( 7.59 b )
##EQU00133##
where the equation (28a) is averaged measured DGD.sub.P over these
wavelengths for a large number of SUT bandwidths, and equation
(28b) is an average from measured normalized power differences over
both SOP (i.e. A-SOP) and optical frequency (wavelength).
[0682] It should be appreciated that the arcsine formula, in
equation (7.59), is not the only possible one. This formula permits
a substantially unbiased result to be obtained even if using a
relatively large step, such that PMD.delta..nu..about.0.15-0.20.
However, for the case where a small step is selected, the following
simpler differential formula is valid:
PMD = 1 .pi..delta. v 9 2 .DELTA. T e 2 ( v ) SOP ; v ( 7.59 c )
##EQU00134##
[0683] This is not to infer that this formula is better or
particularly advantageous, but merely that it may conveniently be
used if the step is much smaller, i.e., satisfying the condition
PMD.delta..nu.<0.01-0.05. It should be noted that measured PMD
accuracy can be further improved if an average is performed both
over time and over varied SOPs of the launched signals are applied
to equations (7.59a), (7.59b) and (7.59c), as described in
commonly-owned United States patent publication number
US2010/0073637A1 (Cyr et al.) supra, wherein a test source is
employed. However, when the launched input light is a data-carrying
signal from a network Tx, it is not generally feasible to vary or
control its SOP.
[0684] For the case where the tunable filters have a relatively
large bandwidth (i.e. RBW) and a high-PMD is under test, a further
RBW `correction factor` may be applied in equations in order to
extract a PMD value of the lightpath. Thus, although optional, data
"post-processing" step may correct for any bias on the measured PMD
introduced by the instrumental RBW by multiplying an appropriate
correction factor with an appropriate formulas or relationships
that can be computed either analytically or numerically.
1.17.2.2.10 Computation of an Average of the Second-Order DGD.sub.P
for Improving Link PMD Measurement Accuracy
[0685] Based on above computed DGD.sub.P (i.e. a first-order
DGD.sub.P, .tau..sub.PB(.nu.)) at each wavelength in equations
(7.55a) or (7.55b), it may also be possible to compute a
second-order DGD.sub.P that may be written as:
.tau. PB , .omega. ( v ) = 1 2 .pi. .tau. PB ( v ) v ( 7.60 )
##EQU00135##
where .tau..sub.PB,.omega.(.nu.) is a calculated second-order
DGD.sub.P.
[0686] If there are a multiplicity of SUTs, e.g. 2-40, the link PMD
in a DWDM network may also be estimated from an average over some
or all of the so-obtained second-order DGD.sub.P values (e.g.
.tau..sub.PB,.omega.(.nu.) in equation (7.60)) according to a
predefined function. For example, it may be expressed as:
P M D = C 0 .tau. PB , .omega. 2 ( v ) ( 7.61 a ) ##EQU00136##
where C.sub.0 is a constant that may be obtained theoretically, or
from simulation or experiment.
[0687] Advantageously, the optical-link PMD may be computed
directly from second-order normalized power (i.e. transmission),
.DELTA.(.DELTA.T.sub.e(.nu.,.phi.)), for example, for a small
frequency step it may be written as following differential formula
as:
PMD = C 1 .delta. v 4 ( .DELTA. ( .DELTA. T e ( v ) ) ) 2 ( 7.61 b
) ##EQU00137##
where C.sub.1 is a constant that may be obtained theoretically, or
from simulation or experiment.
[0688] It should be appreciated other equations than equation
(7.61a) and (7.61b)) may be used for computing PMD from either
second-order DGD.sub.P or second-order normalized power difference.
For instance, alternative equations may be expressed as any other
formula by using second-order DGD.sub.P, or second-order normalized
power difference, or any other similar second-order parameter, for
example, an absolute value of a second-order normalized power (i.e.
transmission), |.DELTA.(.DELTA.T.sub.e(.nu.,.phi.))|, may be used
with different formula.
[0689] It should further be appreciated that any normalized power
described in the present invention may be used in the above formula
(i.e. equation (7.61b) to compute PMD and, in the case that the
SUTs may be depolarized, it may be necessary to compensate for this
depolarization by including relative variance, i.e.
.sigma..sub.r.sup.2(.nu.), in the computations.
[0690] Furthermore, an accurate PMD measurement of an optical link
in a network may be estimated from an average of both estimated PMD
values from first- and second-order DGD.sub.P measurements or from
first- and second-order normalized power difference as a predefined
function. In this way, a PMD measurement uncertainty [10] may be
reduced or decreased.
[0691] It should be noted that for the aforedescribed embodiment in
FIG. 2K, for which the A-SOP controller 12 is operable as be a
two-state polarization switch such that the successively generated
pair of A-SOPs are orthogonal on the Poincare sphere (e.g. 0
degrees linear, 45 degrees linear), then a third normalized power,
T.sub.3,x(.nu.), related to the third Stokes component may be
calculated based on the first two measured normalized powers,
T.sub.1,x(.nu.), and T.sub.2,x(.nu.), related to their Stokes
components corresponding to orthogonal analyzer A-SOPs under an
assumption of negligible or known depolarized lights as:
T.sub.3,x(.nu.)=1/2(1.+-. {square root over
(1-(2T.sub.1,x(.nu.)-1).sup.2-(2T.sub.2,x(.nu.)-1).sup.2)})
(7.62)
a. where
T 1 , x ( v ) = P 1 , x ( v ) P 1 , x ( v ) + P 1 , y ( v ) , T 2 ,
x ( v ) = P 2 , x ( v ) P 2 , x ( v ) + P 2 , y ( v ) ,
##EQU00138##
and P.sub.1,x(.nu.), P.sub.1,y(.nu.), P.sub.2,x(.nu.), and
P.sub.2,y(.nu.) are measured powers after a PBS for two switchable
A-SOPs, respectively, by assuming to have negligible depolarized
lights or such depolarized lights being subtracted from such
measured powers. Therefore, a third normalized power difference
between two closely-spaced optical frequencies is ready to be
computed for further calculating DGD.sub.P, PMD, etc. using above
described equations, e.g. Eqs (7.55), (7.58), (5.59), etc.
[0692] We point also out here that other methods may also be
possible, for example to obtain a third normalized power difference
from a predefined function of first two normalized powers and their
differences.
1.18 Data Processing and Computation
Single-Ended Overall PMD Measurement
1.18.1 Single-Ended Overall PMD
The Data Structure
[0693] Each backreflected light power from the localized reflection
(such as a Fresnel reflection) at the distal end of FUT 18,
obtained with any given setting of the wavelength and of the
(I-SOP, A-SOP) couples, as described in the Method of Operation for
the single-ended overall PMD measurement, constitutes the
elementary data cell, i.e. one datum consists of one power value.
The next data unit is one group of four powers (i.e. four data
cells), two sets of four backreflected powers for the
implementations of FIG. 3C and FIG. 3G where two backreflected
powers are obtained simultaneously from photodetectors 22B and 22C,
all obtained with a given (I-SOP.sub.k, A-SOP.sub.k) as set by
I/A-SOP controller 14. The two sets of four powers forming group k
preferably are obtained in the following sequence (time flowing
from left to right):
TABLE-US-00002 ##STR00002##
where the labels x and y refer to the power obtained simultaneously
(or at slightly different times from photodetectors 22B and 22C,
respectively, .lamda..sub.U.sup.(k)-.lamda..sub.L.sup.(k) is equal
to the step .delta..lamda., the midpoint wavelength is defined as
.lamda..sub.k=(.lamda..sub.U.sup.(k)+.lamda..sub.L.sup.(k))/2, and
the double prime indicates the repeated power measurements.
[0694] Finally, the overall data stored in the data file after
acquisition is depicted as a matrix in Equation (6.63) below, to
which we will refer in all that follows. The matrix comprises K
groups each of four powers of backreflected light (two sets of four
when two photodetectors are used):
TABLE-US-00003 ##STR00003##
1.18.2 Single-Ended Overall PMD
Auto-Calibration of the Relative Gain
[0695] For the preferred implementation of FIG. 2 using a
polarization beam splitter (PBS), as shown in FIG. 3F, it is
necessary to perform the below-described calibration procedure of
the relative gain of the two detectors 22B and 22C before
proceeding with any further computation. (A very similar procedure
is also performed for an implementation of Embodiment (3), the
"single-ended cumulative PMD" measurement embodiment described in a
subsequent section hereinbelow.)
[0696] The calibration principle is predicated upon the fact that,
when an I/A-SOP scrambler 14 is used to generate a sufficiently
large number of SOPs so as to substantially cover the Poincare
Sphere, the average power of the backreflected light from the
distal end (or other positions) of the FUT 18 will exit from the
two ports of the PBS with a 2:1 ratio, the higher power
corresponding to the port to which detector 22B is connected and
the lower power corresponding to the port to which detector 22C is
connected. Hence, any observed deviation from this 2:1 ratio for
the observed detector powers can be quantified and taken into
account, as follows.
[0697] After data acquisition is completed, K groups of four
backreflected light powers obtained from both photodetectors have
been stored, i.e., a total number of J=4K powers (data) from
detector 22B and also J=4K traces from detector 22C, as depicted in
matrix (53). The j.sup.th powers (j=0, 1 . . . (J-1)) from 22B and
22C are referred to below as Px.sub.j and Py.sub.j, respectively.
If the overall losses in the two arms of the PBS were identical and
the gains of both photodetectors and associated electronics were
also equal, the ratio of the powers Py and Px after averaging both
populations over all J occurrences would be
< Px > < Py > .ident. j Px j j Py j = 2
##EQU00139##
[0698] In practice, the ratio obtained from the average of the
measured powers does not equal 2 because of different losses in the
arms of the PBS and different "effective" gains of the
photodetectors, which includes the photodiode responsivity as well
as the overall gains of the following electronics, amplifiers and
sampling circuitry. (Note that it is not necessary to determine the
individual gains separately.) Therefore, before proceeding with the
rest of the computations, all the J powers obtained from
photodetector 22C, i.e. all the Py.sub.j, are multiplied as
follows:
Py j .ident. g RoundTrip Py j ##EQU00140## where ##EQU00140.2## g
RoundTrip = 1 2 < Px > < Py > = j Px j j Py j
##EQU00140.3##
[0699] In practice, for center wavelengths that are relatively
closely-spaced (e.g. <20 nm), the relative wavelength dependence
of the optical components, detectors, etc. may be neglected and
this calibration process need only be carried out once per
single-ended PMD measurement sequence. Otherwise, this calibration
may need to be carried out at every center wavelength, thereby
increasing the overall measurement time of the measurement
sequence.
[0700] As a result of the calibration, i.e. after all Py powers
(data) have been multiplied by the measured relative gain as
described above, the data processor 34 can compute the normalized
backreflected light powers. More precisely, the normalized powers
in the case of the implementation of FIG. 3F (or FIG. 3G) using a
PBS are obtained by dividing the sampled and averaged signal Px
from detector 22B, or the signal Py from detector 22C, or (and
preferably) the difference (Px-Py)/2 or (Py-Px)/2, as will be
described in more detail in the next section, or any weighted
difference (1+w).sup.-1(Px-wPy), where w is a weighting factor, by
the sum (Px+Py) of the sampled and averaged signals from both of
the detectors 22B and 22C, which sum represents the total power
impinging on the PBS, i.e., without selection of a particular
polarization component.
[0701] It should be noted that other calibration may also be
possible. For example, a potential alternative calibration
technique is to use an internal reference with fiber couplers
(splitters) or internal reflector to send a predefined amount
(percentage) of light power from launched OTDR light to two
different detectors.
[0702] The preferred computational approach for determining the
normalized powers of the preferred embodiments will now be
described in detail.
1.18.3 Single-Ended Overall PMD
Computation
[0703] The powers are processed to obtain the DGD or PMD values, as
will now be described. It should be note that, in all that follows,
the symbols refer to the matrix "Data" in Equation (7.63). The
labels x and y refer to the backreflected light powers obtained
from photodetectors 22B and 22C, respectively.
1.18.3.1 The Normalized Powers
[0704] The normalized powers (i.e. transmissions), labelled
hereinafter as T, are computed differently according to the
implementation.
(i) For the implementation of FIG. 3F (two photodetectors with a
PBS), the normalized power is computed in the same manner as a
normalization procedure for the previously-described "two-ended"
implementation of FIG. 1F (two photodetectors with a PBS). Note
that the different Py powers are presumed to have been already
pre-multiplied by the measured relative gain, g.sub.RoundTrip, from
single-ended measurement, as indicated in the description of the
auto calibration procedure, before they are used in this
normalization procedure. (ii) For the implementation of FIG. 3D
(two photodetectors with a coupler), the normalized power is
computed in the same manner as the normalization procedure for the
implementation of FIG. 1D (two photodetectors with a coupler) for
the two-ended PMD measurement previously described hereinabove,
except that a different reference mean-value u.sub.o=2/3 is used
for the single-ended measurement case. Here, the auto-calibration
procedure is not required, i.e. the above mentioned
pre-multiplication of the powers Py by the measured relative gain
may be skipped. (iii) For the implementation of FIG. 3B (single
photodetector), again the normalized power is computed in the same
manner as a normalization procedure for the implementation of FIG.
1B (single photodetector) for the two-ended PMD measurement as
already described in the previous related section and a reference
mean value of u.sub.o=2/3 for single-ended measurement must also be
used in this normalization procedure.
[0705] Here we assume that light powers being launched into FUT at
.lamda..sub.U.sup.(k) and .lamda..sub.L.sup.(k) are nearly the
same.
[0706] It should be noted that, in the equations above,
.sub.SOP;.nu. can refer to averaging over either the I-SOPs, the
A-SOPs, or the midpoint optical frequency (wavelength), ideally
over all three, i.e., changing both the (I-SOP, A-SOP) couple and
wavelength from one group of powers to the next. All of these
relationships are fundamentally valid in all cases even if only
polarization scrambling is applied, giving the correct value of the
DGD at one particular midpoint wavelength. Then, scanning the
midpoint wavelength only serves the purpose of averaging DGD over
wavelength as per the definition of the statistical PMD value. On
the contrary, as discussed earlier, averaging only over wavelength
while keeping the (I-SOP, A-SOP) couple unchanged requires that
assumptions about the FUT be met, and also requires a large value
of the product PMD.DELTA..nu.. The same remarks apply for the
equations presented hereinafter.
1.18.3.2 Mean-Square Differences
[0707] The calculation here differs from the simple mean-square
found in Eqs. (1) (3) (12) and (13) which, for greater clarity, did
not take into account the noise. Instead, the product of the
repeated differences between normalized traces at .lamda..sub.U and
.lamda..sub.L is averaged as follows,
.DELTA. T 2 ( v ) SOP ; v = ( T U - T L ) ( T U '' - T L '' ) SOP ;
v = 1 K k ( T U ( k ) - T L ( k ) ) ( T U '' ( k ) - T L '' ( k ) )
( 7.53 ' ) ##EQU00141##
[0708] Note the equation (7.53') is the same as equation (7.53). In
conventional mathematical terms, equation (7.53') may be referred
to as the second-order joint moment of the repeated differences.
Doing so, the noise averages to zero instead of being "rectified",
because the noise superimposed on a given trace is not correlated
with the noise superimposed on the corresponding repeated trace.
That is the first motivation for sampling repeated traces.
1.18.3.3 Computation of the PMD Value
[0709] The PMD then is directly computed according to the arcsine
formula as,
PMD = .alpha. rt 1 .pi..delta. v arcsin ( .alpha. ds .DELTA. T 2 (
v ) SOP ; v ) ( 7.64 ) ##EQU00142##
where a roundtrip factor
.alpha. rt = 3 8 . ##EQU00143##
A theoretical constant
.alpha. ds = 15 4 ##EQU00144##
is valid for the cases where a common (same) state of polarization
controller (scrambler) is used to control both input and output
light SOPs, such as for FIGS. 2, 2C-G.
[0710] It should be appreciated that the arcsine formula, in Eq.
(7.64), is not the only possible one. The purpose of using this
formula is to obtain a result that is unbiased even if using a
relatively large step, such that PMD.delta..nu..about.0.15, without
introducing a significant error; this in order to maximize the
signal-to-noise ratio and therefore the dynamic range of the
instrument. If one were not concerned with maximizing the dynamic
range, or keeping the overall measurement time reasonable, one
might select a much smaller step, and use the simpler differential
formula that follows,
PMD = .alpha. rt .alpha. ds .pi..delta. v .DELTA. T 2 ( v ) SOP ; v
( 7.64 a ) ##EQU00145##
[0711] This is not to infer that this formula is better or
particularly advantageous, but merely that it may conveniently be
used if the step is much smaller, i.e., satisfying the condition
PMD.delta..nu.<0.01.
[0712] It should be noted that a forward PMD calculated from
equations (7.64) and (7.64a) is a PMD or rms DGD of FUT.
[0713] It should also be noted that roundtrip rms DGD or roundtrip
mean DGD can also obtained from a root-mean-square for
DGD.sub.RoundTrip(.nu.) or mean for DGD.sub.RoundTrip(.nu.) at many
different wavelengths for a given wavelength range and
DGD.sub.RoundTrip(.nu.) at each given wavelength can be computed
the arcsine formula as either,
DGD RoundTrip ( v ) = 1 .pi..delta. v arcsin ( .alpha. ds .DELTA. T
2 ( v ) SOP ) . ( 7.65 ) ##EQU00146##
or use the simpler differential formula that follows,
DGD RoundTrip ( v ) = .alpha. ds .pi..delta. v .DELTA. T 2 ( v )
SOP . ( 7.65 a ) ##EQU00147##
where normalized power (T) is obtained from each give
wavelength.
[0714] A rms DGD and mean DGD (forward) can also be obtained by
simply multiplying a roundtrip factor of {square root over (3/8)}
and 2/.pi. on rms DGD.sub.RoundTrip and mean DGD.sub.RoundTrip,
respectively, where a rms DGD.sub.RoundTrip or mean
DGD.sub.RoundTrip can be obtained from measured
DGD.sub.RoundTrip(.nu.) for many different midpoint wavelengths by
root-mean square or mean DGD.sub.RoundTrip(.nu.) from equations
(7.65) or (7.65a) over a prescribed wavelength range, e.g.
rms D G D RoundTrip = D G D RoundTrip 2 ( v ) v ##EQU00148## and
##EQU00148.2## mean D G D RoundTrip = D G D RoundTrip ( v ) v ,
##EQU00148.3##
[0715] It should also noted that above computation equations for
extracting DGD and PMD using normalized power (usually a normalized
power is ranged between 0 to 1) may be replaced by other methods.
For example, only a relative power may be computed from the
measured powers, then a "normalization factor" may be employed in
the equations (54) and (55) to cancel this factor that is
multiplied on mean-square difference, so as to obtain correct a DGD
or PMD value.
[0716] It should be noted that the above equations for calculating
the DGD or PMD include a factor representing a theoretical
constant
.alpha. ds = 15 4 . ##EQU00149##
This theoretical constant value is valid for the cases where the
same common state of polarization controller (scrambler) is used
for controlling both input and output SOPs, such as for FIGS.
3B-3G. However, when two separate independent input- and
analyzer-SOP controllers (scramblers) are used in conjunction with
a polarizer or PBS located just before the detector, for example as
shown in FIG. 2, a different theoretical constant, i.e.
.alpha. ds = 9 2 , ##EQU00150##
must be used. (Note that this theoretical constant is the same as
that employed with the two-ended PMD measurement equations
described in the corresponding section hereinbefore).
[0717] For the case where the tunable pulsed light source has a
relatively big linewidth and a high PMD fiber is under test, a
linewidth "correction factor" may need to be applied in Eq. (7.64,
7.64a) in order to extract an accurate PMD value from the FUT.
[0718] It should also be noted that repeated powers may be obtained
from two or more measurements at different times using the same
detectors, or from measurements using different detectors, e.g.
where the light power is split by a coupler, and the power is
detected by the different detectors contemporaneously.
1.19 Data Processing and Computation
Single-Ended Cumulative PMD Measurement
1.19.1 Single-Ended Cumulative PMD
The Data Structure
[0719] Each OTDR trace, obtained with one given setting of the
wavelength and of the (I-SOP, A-SOP) couple, as described in the
Method of Operation for the single-ended cumulative PMD measurement
(also called as single-ended POTDR based cumulative PMD
measurement), constitutes the elementary data cell. One trace
consists of N power values corresponding to N values z.sub.n of the
distance z, with n=0 . . . (N-1).
[0720] The next larger data unit is one group of four traces, two
sets of four traces for the implementations of FIG. 4 and FIG. 4B
where two traces are obtained simultaneously from photodetectors
22B and 22C (or sequentially in the case where an optical switch is
used with one detector), all obtained with a given (I-SOP, A-SOP)
couple as set by I/O-SOP controller 14. The two sets of four traces
forming group k preferably have been obtained in the following
sequence (time flowing from left to right), where the labels x and
y refer to the traces obtained simultaneously from photodetectors
22B and 22C, respectively,
.lamda..sub.U.sup.(k)-.lamda..sub.L.sup.(k) is equal to the step
.delta..lamda., the midpoint wavelength is defined as
.lamda..sub.k=(.lamda..sub.U.sup.(k)+.lamda..sub.L.sup.(k))/2, and
the double prime indicates the repeated traces:
TABLE-US-00004 ##STR00004##
[0721] Finally, the overall data stored in the data file after
acquisition is depicted as a matrix in Eq. (56) below, to which we
will refer in all that follows. The matrix comprises K groups each
of four OTDR traces (two sets of four when two photodetectors are
used), each trace consisting of N points corresponding to N values
of distance z.sub.n, where n=0 . . . (N-1):
TABLE-US-00005 ##STR00005##
The data structure of equation (7.66) is similar to that of
equation (7.63), but data in equation (7.66) correspond to OTDR
traces as function of distance z instead of powers reflected from
the distal end of FUT.
1.19.2 Single-Ended Cumulative PMD
Auto Calibration of the Relative Gain
[0722] For the preferred implementation of FIG. 4, it is necessary
to perform a calibration procedure very similar to that described
hereinabove in the context of Embodiment (3): "single-ended overall
PMD" measurement. The calibration principle is predicated upon the
fact that, when an I/A-SOP scrambler 14 is used to generate a
sufficiently large number of SOPs so as to substantially cover the
Poincare Sphere, the average power of the backreflected light
originating from any position along the FUT 18 will exit from the
two ports of the PBS with a 2:1 ratio, the higher power
corresponding to the port to which detector 22B is connected and
the lower power corresponding to the port to which detector 22C is
connected. Hence, any observed deviation from this 2:1 ratio for
the observed detector powers can be quantified and taken into
account, as follows.
[0723] After data acquisition is completed, K groups of four OTDR
traces obtained from both photodetectors have been stored, i.e., a
total number of J=4K traces from detector 26A and also J=4K traces
from detector 22B, as depicted in matrix (56). The j.sup.th traces
(j=0, 1, . . . , (J-1)) from 22C and 22B are referred to below as
Px(z).sub.j and Py(z).sub.j, respectively. If the overall losses in
the two arms of the PBS were identical and the gains of both
photodetectors and associated electronics were also equal, the
ratio of the traces Py and Px after averaging both populations over
all J occurrences and over all the N values of z would be
< Px > < Py > .ident. j n Px ( n ) j j n Py ( n ) j = 2
##EQU00151##
[0724] In practice, the ratio obtained from the average of the
measured traces does not equal 2 because of different losses in the
arms of the PBS and different "effective" gains of the
photodetectors, which includes the photodiode responsivity as well
as the overall gains of the following electronics, amplifiers and
sampling circuitry. (Note that it is not necessary to determine the
individual gains separately.) Therefore, before proceeding with the
rest of the computations, all the J traces obtained from
photodetector 22C, i.e. all the Py(z).sub.j, are multiplied as
follows:
Py ( ) j .ident. g RoundTripC Py ( n ) j ##EQU00152## where
##EQU00152.2## g RoundTripC = 1 2 < Px > < Py > = j n
Px ( n ) j j n Py ( n ) j ##EQU00152.3##
[0725] In practice, for midpoint wavelengths that are relatively
closely-spaced (e.g. <20 nm), the relative wavelength dependence
of the components, detectors, etc. is usually negligible and this
calibration process need only be carried out once per POTDR
measurement sequence. Otherwise, this calibration may need to be
carried out at every midpoint wavelength, thereby increasing the
overall measurement time.
[0726] As a result of the calibration, i.e. after all Py traces
have been multiplied by the measured relative gain as described
above, the data processor 34 can compute the normalized OTDR
traces. More precisely, the normalized traces in the case of the
implementation of FIG. 1 are obtained by dividing either the
sampled signal Px from detector 22B, or signal Py from detector
22C, preferably the difference between the sampled signals from
detectors 22B and 22C, (Px-Py)/2 or (Py-Px)/2, as will be described
in more details in the next section, or any weighted difference
(1+w).sup.-1(Px-wPy), by the sum (Px+Py) of the sampled signals
from both of the detectors 22B and 22C which represents the total
backreflected power impinging on the PBS, i.e., without selection
of a particular polarization component.
[0727] The preferred computations giving the normalized OTDR traces
for all preferred implementations will now be described in
detail.
1.19.3 Single-Ended Cumulative PMD
The Point-Bby-Point Computation
[0728] The OTDR traces are processed to obtain the cumulative PMD
as will now be described. It should be noted that the computation
of PMD.sub.n at each point z.sub.n along the FUT 18 is performed
independently of any other point n. Each is deduced from averages
over at least one of I-SOP, A-SOP and wavelength, preferably over
all. Thus, in the computations described below it is inappropriate
to use the index n; it must simply be understood that the
calculation is repeated in the same way for each point n, or, in
other words, effectively at each distance z.sub.n. In all that
follows, the symbols refer to the matrix "Data" in Eq. (56). It
should also be emphasized that the labels x and y refer to the
traces obtained from photodetectors 22B and 22C, respectively.
1.19.3.1 The Normalized Traces
[0729] The normalized traces, labelled hereinafter as T(z), are
computed differently according to the implementation.
(i) For the implementation of FIG. 4 (two photodetectors with a
PBS), the normalized OTDR trace is computed as follows, either
T L ( k ) = P x L ( k ) P x L ( k ) + P y L ( k ) T L '' ( k ) = P
x L '' ( k ) P x L '' ( k ) + P y L '' ( k ) T U ( k ) = P x U ( k
) P x U ( k ) + P y U ( k ) T U '' ( k ) = P x U '' ( k ) P x U ''
( k ) + P y U '' ( k ) or T L ( k ) = 1 2 P x L ( k ) - P y L ( k )
P x L ( k ) + P y L ( k ) T L '' ( k ) = 1 2 P x L '' ( k ) - P y L
'' ( k ) P x L '' ( k ) + P y L '' ( k ) T U ( k ) = 1 2 P x U ( k
) - P y U ( k ) P x U ( k ) + P y U ( k ) T U '' ( k ) = 1 2 P x U
'' ( k ) - P y U '' ( k ) P x U '' ( k ) + P y U '' ( k ) ( 7.76 a
) ##EQU00153##
where it should be appreciated that the different Py traces have
been pre-multiplied by the measured relative gain,
g.sub.RoundTripC, as indicated in the description of the auto
calibration procedure, before they are used in Eq. (7.67a). (ii)
For the implementation of FIG. 4B (two photodetectors with a
coupler), the ratio of trace Px over trace Py is first computed
as,
R L ( k ) = P x L ( k ) P y L ( k ) R L '' ( k ) = P x L '' ( k ) P
y L '' ( k ) R U ( k ) = P x U ( k ) P y U ( k ) R U '' ( k ) = P x
U '' ( k ) P y U '' ( k ) ( 7.67 b ) ##EQU00154##
and then the above ratio is normalized with respect to its average
over the K groups as,
T L ( k ) = u o R L ( k ) R SOP ; v T L '' ( k ) = u o R L '' ( k )
R SOP ; v T U ( k ) = u o R U ( k ) R SOP ; v T U '' ( k ) = u o R
U '' ( k ) R SOP ; v ( 7.67 c ) ##EQU00155##
where the reference mean-value is u.sub.o=2/3 by assuming measured
power for an input SOP aligned with an analyzer axis, and the
average ratio R is defined as,
R SOP ; v = 1 4 K k ( R L ( k ) + R L '' ( k ) + R U ( k ) + R U ''
( k ) ) , ( 7.67 d ) ##EQU00156##
[0730] Here, the auto calibration procedure is not required, i.e.
the above-mentioned pre-multiplication of the traces Py by the
measured relative gain may be skipped.
(iii) For the implementation of FIG. 4A (single photodetector), the
only available traces are the Px traces (obtained here from
photodetector 22). The normalized trace is obtained as in (5c) but
without computing the ratio of trace x over trace y first, i.e.
T L ( k ) = u o P L ( k ) P SOP ; v T L '' ( k ) = u o P L '' ( k )
P SOP ; v T U ( k ) = u o P U ( k ) P SOP ; v T U '' ( k ) = u o P
U '' ( k ) P SOP ; v ( 7.67 e ) ##EQU00157##
where the average trace is defined as,
P SOP ; v = 1 4 K k ( P L ( k ) + P L '' ( k ) + P U ( k ) + P U ''
( k ) ) ( 7.67 f ) ##EQU00158##
[0731] All of these relationships are fundamentally valid in all
cases even if only I/A-SOP scrambling is applied, giving an
estimation of the DGD at one particular midpoint wavelength. If
these measurements are then repeated for a multiplicity of
wavelengths across a prescribed wavelength range, the average DGD
value so obtained then represents definition of the PMD. On the
other hand, as discussed earlier, averaging only over wavelength
while keeping the I/A-SOP unchanged requires that assumptions about
the FUT be met, and also requires a large value of the product
PMD.DELTA..nu.. The same remarks apply for the equations presented
hereinafter.
[0732] It should be also noted that Equations (7.67d) and (7.67f)
assume that there is negligible wavelength dependence on coupling
ratio and detected powers, respectively.
1.19.3.2 Relative Variance
[0733] The relative variance, as in equation (7.67b), is computed
here as the average of the four available estimates, i.e.,
.sigma. r '2 = ( 1 .sigma. 10 ) 2 [ var ( T L ) + var ( T U ) 2 ] (
7.68 ) ##EQU00159##
where the reference variance is .sigma..sub.10.sup.2= 4/45, and the
function "var" is defined as,
var(T.sub.L)=.left
brkt-bot.T.sub.LT.sub.L''.sub.SOP;.nu.-T.sub.L.sub.SOP;.nu..sup.2.right
brkt-bot.
var(T.sub.U)=.left
brkt-bot.T.sub.UT.sub.U''.sub.SOP;.nu.-T.sub.U.sub.SOP;.nu..sup.2.right
brkt-bot..
1.19.3.3 Mean-Square Differences
[0734] The calculation here differs from the simple mean-square
found in Eq. (3a) which, for greater clarity, did not take into
account the noise. Instead, the product of the repeated differences
between normalized traces at .lamda..sub.U and .lamda..sub.L is
averaged as follows,
.DELTA. T 2 ( v ) SOP ; v = ( T U - T L ) ( T U '' - T L '' ) SOP ;
v = 1 K k ( T U ( k ) - T L ( k ) ) ( T U '' ( k ) - T L '' ( k ) )
( 7.69 ) ##EQU00160##
[0735] In conventional mathematical terms, Eq. (7.69) may be
referred to as the second-order joint moment of the repeated
differences. Doing so, the noise averages to zero instead of being
"rectified", because the noise superimposed on a given trace is not
correlated with the noise superimposed on the corresponding
repeated trace. That is the first motivation for sampling repeated
traces.
1.19.3.4 Noise Variance
[0736] The second motivation for sampling repeated traces, which
are substantially identical in the absence of noise, for each
setting of center wavelength .lamda. and SOP, is the ability to
obtain an accurate estimate of the noise variance. That is because
the relative variance, as computed in Eq. (7.68), includes both the
variance of the hypothetical noiseless trace and the variance of
the noise. However, if the noise variance is known, it can be
subtracted since the variance of the sum of two independent random
variables is equal to the sum of the variances. But thanks to the
repeated traces, the noise variance can be estimated independently
as follows:
.sigma. noise 2 = ( 1 .sigma. 10 ) 2 ( T L - T L '' ) ( T U - T U
'' ) SOP ; v ( 7.70 ) ##EQU00161##
[0737] The noise variance (Eq. 7.70) is then subtracted from the
first estimate of the relative variance (Eq. 7.68) in the
computation of the final relative variance as follows,
.sigma..sub.r.sup.2=.sigma.'.sub.r.sup.2-.sigma..sub.noise.sup.2
(7.71)
1.19.3.5 Computation of the Cumulative PMD
[0738] The cumulative PMD then is computed according to the arcsine
formula as,
PMD ( z ) = .alpha. rt 1 .pi. .delta. v arc sin ( .alpha. ds
.DELTA. T 2 ( v , z ) SOP ; v .sigma. r 2 ( z ) ) ( 7.72 )
##EQU00162##
where a roundtrip factor
.alpha. rt = 3 8 . ##EQU00163##
A theoretical constant
.alpha. ds = 15 4 ##EQU00164##
is valid for the cases where a common state of polarization
controller (scrambler) is used to control the SOP of both light
input to and output from the FUT, such as depicted in FIGS. 3, 3A
and 3B.
[0739] It should be appreciated that the arcsine formula, (7.72),
is not the only possible one. The purpose of using this formula is
to obtain a result that is unbiased even if using a relatively
large step, such that PMD.delta..nu..about.0.15, without
introducing a significant error; this in order to maximize the
signal-to-noise ratio and therefore the dynamic range of the
instrument. If one were not concerned with maximizing the dynamic
range, or keeping the overall measurement time reasonable, one
might select a much smaller step, and use the simpler differential
formula that follows,
PMD ( z ) = .alpha. rt .alpha. ds 1 .pi. .delta. v .DELTA. T 2 ( v
, z ) SOP ; v .sigma. r 2 ( z ) ( 7.73 ) ##EQU00165##
[0740] This is not to infer that this formula is better or
particularly advantageous, but merely that it may conveniently be
used if the step is much smaller, i.e., satisfying the condition
PMD.delta..nu.<0.01. The cumulative PMD curve as a function of z
is obtained by repeating the computation above, from equations
(7.67) to equation (7.72), at each point n corresponding to
distance z.sub.n.
[0741] It should be noted that the above equations employ the
theoretical constant
.alpha. ds = 15 4 ##EQU00166##
(see Equation 6.11a), which applies when a common (I/A-SOP)
polarization controller for the light launched into and the
backreflected light received from the FUT, such as for the
implementations shown in FIGS. 3, 3A and 3B. However, when separate
I-SOP and A-SOP polarization controllers (scramblers) are used with
a polarizer or if the PBS is located just before the detector, for
example as shown in FIG. 4C, then the theoretical constant
corresponding to "uncorrelated" polarization scrambling must be
used, i.e.
.alpha. ds = 9 2 ##EQU00167##
(see Equation 6.11b).
[0742] It should also be noted that the above computation equations
(7.72) and (7.73) for extracting cumulative PMD using a normalized
OTDR trace may be replaced by using a relative OTDR trace that is
proportional to a normalized OTDR trace.
[0743] It should be noted that a forward PMD calculated from
equations (7.72) and (7.73) is PMD (according to the rms DGD
definition) of FUT.
[0744] It should further be emphasized that the cumulative PMD may
also be obtained by averaging over (either rms or mean roundtrip
DGDs at different optical frequencies, e.g.
rms D G D RoundTrip ( z ) = D G D RoundTrip 2 ( z , v ) v
##EQU00168##
and mean DGD.sub.RoundTrip(z)=DGD.sub.RoundTrip(z,.nu.).sub..nu.
where a rms DGD.sub.RoundTrip(z) or mean DGD.sub.RoundTrip(z) can
be obtained from measured DGD.sub.RoundTrip(z,.nu.) for many
different midpoint wavelengths by root-mean square or mean
DGD.sub.RoundTrip(z,.nu.) (see below) over a prescribed wavelength
range. The measured and calculated roundtrip DGDs at different
optical frequencies is
DGD Round Trip ( z , v ) = .alpha. ds .pi. .delta. v .DELTA. T 2 (
z , v ) .sigma. r 2 ( z , v ) ##EQU00169##
where
.sigma. r 2 ( z , v ) = ( 1 .sigma. 10 ) 2 [ T ( z , v ) T '' ( z ,
v ) SOP , v - T ( z , v ) SOP , v 2 ] . ##EQU00170##
[0745] The rms DGD(z) and mean (forward) DGD(z) can also be
obtained by simply multiplying rms DGD.sub.RoundTrip(z) and mean
DGD.sub.RoundTrip(z), by a roundtrip factor of {square root over
(3/8)} and 2/.pi., respectively.
[0746] As shown in the equations (42) and (43), if the PMD
calculation involves the use of the relative variance,
.sigma..sub.r.sup.2(z,.nu.), of the normalized power (T), then it
is not necessary that the power be normalized to lie between 0 and
1. In other words, some steps of above normalization procedure for
obtaining normalized powers may be skipped. The relative power
P.sub.R(z,.nu.) and relative variance .sigma..sub.R.sup.2(z,.nu.)
computed from relative suffice to compute the cumulative PMD with
equations similar to equations (42) and (43).
[0747] It should also be noted that repeated powers may be obtained
from two or more measurements at different times using the same
detectors, or from measurements using different detectors, e.g.,
where the light power is split by a coupler and the power detected
contemporaneously using two detectors.
1.19.4 Optional Application of a Linewidth Correction Factor
[0748] If the effective spectral linewidth of the pulsed laser
source is large, it may be desirable to perform an additional,
although optional, data "post-processing" step to take into account
the dependence of the measured cumulative PMD on the linewidth of
the laser. Thus, one may multiply the N above-measured cumulative
PMD values at z.sub.n, PMD.sub.n, by an appropriate
linewidth-dependent correction factor. One expression of such a
correction factor, suitable when the laser lineshape is
approximately Gaussian, is:
.alpha. LW n = 1 1 - ( PMD n PMD sat ) 2 ( 7.74 ) ##EQU00171##
where PMD.sub.sat is the saturation cumulative PMD value, i.e., the
limiting value towards which the measured cumulative PMD tends as
the actual cumulative PMD grows toward infinity, if no linewidth
correction factor is applied. It is given by:
PMD sat = 1 4 .pi. 1 .sigma. v L ( 7.75 ) ##EQU00172##
where .sigma..sub.yL is the rms-width of the laser spectrum. (Note:
for a Gaussian lineshape, the full-width at half-maximum is related
to the rms-width by .DELTA..nu..sub.L= {square root over
(8ln(2))}.sigma..sub..nu.L.)
[0749] The last, optional, step comprises the computation of the N
values of the correction factor according to Equation (7.75), and
then the obtaining of the corrected PMD values, PMD'.sub.n, via
multiplication of the PMD values measured before correction by the
correction factor, i.e.
PMD'.sub.n=.alpha..sub.LW.sub.nPMD.sub.n (7.76)
[0750] For example, if no correction factor is applied, Eqs. (44)
and (45) indicate that the maximum cumulative PMD value
corresponding to a bias of, say, -10%, is
PMD.sub.max=0.0817.DELTA..nu..sub.L.sup.-1. For this example, a
full-width at half-maximum .DELTA..nu..sub.L=2 GHz gives
PMD.sub.sat.about.94 ps and PMD.sub.max.about.41 ps. If the
measured value happens to be equal to this pre-determined maximum
value of 41 ps then the actual PMD is in fact approximately 45 ps,
i.e., the measured value suffers a bias of -10%, as stated. Such a
residual bias level may be acceptable in many field
applications.
[0751] However, under these same physical circumstances, if the
correction factor .alpha..sub.LW=1.11 is applied according to Eq.
(7.76), one obtains the actual cumulative PMD' of 45 ps. In
practice, the uncertainty on the correction factor itself will grow
if the correction factor becomes very large, i.e., when the
directly measured (i.e., uncorrected) cumulative PMD is too close
to PMD.sub.sat, since any small error in the directly-measured PMD
value or in the laser linewidth (or uncertainties as to the
effective laser lineshape) can make the correction factor very
unreliable, as can be appreciated from Equation (44). However, the
uncertainty remains small if the maximum allowable value of the
correction factor is limited to a predetermined value, which then
determines the maximum PMD that can be measured when the correction
factor is applied. Doing so, not only is PMD.sub.max larger than it
would be without the correction, but more importantly, in contrast
with the case where no correction is applied, there is no
systematic bias when the actual PMD is equal to PMD.sub.max, but
rather only a small additional, zero-mean uncertainty. Using the
previous example, and setting the correction factor to a reasonable
maximum value of 1.25, i.e., still close to unity, the maximum
value of the actual PMD that can be measured, without bias, is
PMD.sub.max.about.70 ps, compared to 41 ps with a bias of -10% if
no linewidth correction factor is used.
[0752] Obviously, whenever the product PMD.DELTA..nu..sub.L is much
smaller than unity, the application of such a correction factor is
superfluous.
[0753] It should be appreciated that Equation (7.75) applies for
the case of a nearly Gaussian-shaped laser spectrum, and is given
by way of example. Other formulas or relationships can be computed
either analytically or numerically for any particular laser
lineshape that deviates substantially from a Gaussian lineshape.
The Gaussian lineshape is a special, though practically relevant,
case for which the correction factor can be expressed as a simple
analytical formula, whereas such simple analytical formulas cannot
be found for arbitrary laser lineshapes.
2. Optical Source Means Appropriate for Implementations of
Embodiments of this Invention
2.1 Tunable Laser Source Suitable for Two-Ended Pmd Measurement
[0754] Examples of tunable laser sources capable of successively
and repetitively generating coherent light at two or more closely
spaced wavelengths are detailed in FIGS. 7 and 7A and accompanying
description of commonly-owned United States patent publication
number application US2010/0073667 (Cyr et al), supra. FIG. 7A
therein shows schematically such a tunable modulated light source
(used in 12A in FIGS. 1(B-H)), designed to emit three
closely-spaced wavelength, in rapid sequence, where an optical
chopper (reference number 130 therein) enables switches between the
closely-spaced wavelengths. Tuning of the "midpoint" wavelength may
be carried out by means of a rotatable diffraction grating, for
instance.
[0755] Other kinds of tunable modulatable light source could be
used. For example, it is envisaged that an external phase modulator
could be used to generate optical sidebands on the output of an
external cavity laser (ECL), distributed Bragg reflector laser
(DBR), or distributed feedback laser (DFB).
[0756] A person skilled in this art will be aware of other
alternatives for this tunable modulatable coherent source.
[0757] The spectral linewidth of suitable tunable modulated
coherent sources in the various above-described implementations
might range from less than 1 GHz to about 4 GHz. It may be
advantageous for this linewidth to be known, at least
approximately, in order to facilitate application of the linewidth
correction factor as described hereinbefore.
2.2 Tunable Moderately Broadband Optical Source for Two-Ended Pmd
Measurement
[0758] A type of broadband source 12B, a tunable moderately
broadband light source 12B', that is well suited for many
implementation of Embodiment (1) of this invention is depicted
schematically in FIG. 1L. This source could be advantageously used
in the exemplary implementations of Figs. I, J, and K, for
two-ended measurement of the DGD within one or more narrow DWDM
channels lying within a prescribed spectral range (e.g. such as the
telecom C and/or L bands).
[0759] The tunable moderately broadband light source 12B' comprises
a broadband light source 252, which could be an a substantially
un-polarized light source such as an amplified spontaneous emission
(ASE) source, or a partially or substantially polarized source such
as a superluminescent diode (SLED) or light emitting diode
(LED).
[0760] The broadband light source 252 is filtered by an optical
bandpass filter 254 to provide moderately broadband CW light, e.g.
sufficient to encompass most or all of the bandwidth corresponding
to a DWDM channel, for instance. For example, appropriate bandwidth
(FWHM) values of the optical bandpass filter 254 may be from
0.5-2.0 nm, but should not be considered to be limited to this
range. The optical bandpass filter 254 is preferably a tunable
optical bandpass filter, whose center bandpass wavelength can be
tuned or adjusted over a much wider wavelength range than the
spectral extent of the filter bandpass. It is often desirable to
amplify the filtered light, for instance to a power level of about
0 dBm that would make it compatible with power levels expected in
active optical networks, especially if the broadband light source
252 is a low-power (and hence low-cost) SLED or LED, for instance.
To this end, the filtered moderately broadband light, e.g. usually
a CW light source, then passes through an optional semiconductor
optical amplifier (SOA) 256 where it is amplified. If the resulting
light exiting the SOA 256 is not highly or sufficiently polarized,
it may be transformed into a nearly 100% degree of polarization
(DOP) using an optional polarizer 258 (possibly using a
polarization controller--not shown--disposed between the SOA 256
and polarizer 258 to maximize the exiting output power. However, if
the output light from the SOA is well polarized, the polarizer 258
may not be required.
[0761] It is envisaged that this tunable moderately tunable light
source 12B' could be easily modified to render it appropriate as a
source for in-channel relative group delay (i.e. chromatic
dispersion) measurements, using a variant of the well known "phase
shift" method, as described in commonly-owned patent Babin et al,
U.S. Pat. No. 6,429,929. To this end, the gain of the SOA 256 could
be modulated by a sinusoidal RF modulation 260. A typical
modulation frequency may be in the range from 100 MHz to 2 GHz. (It
should be emphasized that such an rf modulation is not required for
the two-ended PMD or DGD measurement embodiments specified
herein.)
[0762] If the light emitted by the broadband light source 252 such
as a SLED exhibits a high DOP (e.g. >90%), and the optical
bandpass filter 254 and SOA 256 are also polarization-dependent
components, then it is preferable to employ PMF (polarization
maintaining fiber) to interconnect these components.
(Alternatively, as already described hereinabove,
factory-adjustable polarization controllers may be placed between
each component to ensure optimal polarization alignment.)
[0763] It should be noted for the two-ended chromatic dispersion
measurement, the light exiting the tunable moderately-broadband
light source 12B' needs to have a DOP close to 0%. This may be
achieved by using I-SOP controller 14A to "temporally scramble" the
polarized light at a very rapid rate (i.e. much faster than the
electronic bandwidth of the sampling circuitry in the
analog-and-digital processing unit 40). However, such temporal
scrambling would not be necessary for chromatic dispersion
measurement if the light emitted by SOA 256 is un-polarized, for
example if a polarization-insensitive SOA were "seeded" with
moderately-broadband-filtered light (via optical bandpass filter
254). It should be also noted that the different design for the
broadband source 12B/12B' for the two-ended PMD and DGD measurement
is also possible, for example a (wavelength tunable or fixed)
filtered moderately broadband optical light source may be amplified
by an erbium doped optical amplifier (EDFA) rather than a SOA.
However, advantageously if a SOA is used it can not only amplify
the input light power but it can also act as a fast optical light
modulator because of its fast response time so that this filtered
moderately broadband optical light source can be used for both the
PMD and DGD measurement and the chromatic dispersion measurement in
which a phase-shift dispersion measurement method may be used.
3. Tunable OTDR for Single-Ended PMD Measurements
[0764] As mentioned hereinbefore, it is desirable to use many
midpoint wavelengths .lamda..sub.mid as well as many I-SOPs and
A-SOPs. Consequently, it is desirable for the tunable OTDR to be
tunable over a large range of wavelengths. Suitable tunable OTDRs,
that are tunable over a range of several hundred nanometers, are
known to those skilled in this art and so are not described in
detail herein.
[0765] A tunable pulsed laser source 12 that is particularly well
suited for the single-ended PMD measurements embodiments is
disclosed in commonly-owned United States patent H. Chen et al,
U.S. Pat. No. 7,957,436, filed Jul. 18, 2007, the contents of which
are incorporated herein by reference.
[0766] It should be appreciated that other kinds of tunable pulsed
light source could be used instead of that described hereinbefore.
For example, FIG. 10A is an alternative design of that described in
aforementioned H. Chen et al, where no delay line is used. The
low-cost design in FIG. 10A can effectively generate a long pulse
from 275 ns to 20 .mu.s, however, it may not suitable to produce an
OTDR pulse of less than 275 ns.
[0767] Tunable pulsed laser source 12 of FIG. 10A comprises a SOA
202, a TBF 204 and a beamsplitting coupler 207 connected in a ring
topology by PMF to form a fiber ring laser cavity. The coupler 207
extracts a portion, typically 25-50%, of the light from the cavity
as an output. A control unit 30 is coupled to the SOA 202 and the
TBF 204 by lines 220 and 222, respectively, whereby it supplies the
bias current on the SOA 202 and adjusts the wavelength of the TBF
104. The control unit 30 controls the SOA 202 by way of line 220,
turning its bias current on and off to cause it to generate light
pulses.
[0768] A further example of a suitable tunable pulsed light source,
where an acousto-optic modulator is used to pulse the light from a
continuous-wave tunable laser, is disclosed by Rossaro et al. (J.
Select. Topics Quantum Electronics, Vol. 7, pp 475-483 (2001)),
specifically in FIG. 3 thereof.
[0769] FIG. 10B illustrates schematically another suitable
alternative tunable pulsed light source comprising a continuous
wave (CW) widely-tunable linewidth-controllable light source 212''
in combination with an independent SOA 230'' which serves only as
an amplifying modulator. The CW light source comprises a broadband
semiconductor optical gain medium 232'', typically an optical
semiconductor optical amplifier (SOA), and a tunable bandpass
filter (TBF) 234'', controlled by the control unit 30 (FIG. 2). The
minimum small optical signal gain of >3-5 dB can be close to 200
nm (e.g. from 1250-1440 nm or 1440-1640 nm). This minimum
small-signal gain is required to compensate the cavity loss so as
to achieve laser oscillation.
[0770] The continuously tunable TBF is typically a grating based
bandpass filter with a bandwidth of 30 to 80 pm (FWHM), which is
used to tune the laser wavelength accurately and also to confine
the light (photons) in this small TBF bandwidth so as to give an
accurately laser wavelength with a narrow linewidth. The "other
components" identified in FIG. 10B by reference number 136'' will
include an output coupler (typically 25/75 coupler where the 25%
coupling ratio is the output port, but a 50/50 coupler could
alternatively be employed in order to extract more output power)
and an optical isolator (which might be integrated into the optical
gain medium, such as at the input of the SOA).
[0771] If a PMF cavity is used, no additional components are
required. But if the cavity is based on SMF-28 fiber, for instance,
one or two polarization controllers likely will be required to
adjust the SOP of the light circulating within the laser
cavity.
[0772] Use of the SOA 230'' as an external modulator yields several
advantages: one is a high light extinction (ON/OFF) ratio of about
50-60 dB, and a second is to amplify the input light to 10-20 dBm
with a relative input power (of 0-6 dBm). (Note that the output
power intensity is dependent on the operating wavelength). It is
also worth noting that the device of FIG. 10B will not produce a
very narrow linewidth laser. The laser linewidth strongly depends
on the TBF bandpass width. Typically, the tunable pulsed light
source of FIG. 6 can be designed to emit at any wavelength over a
nearly 200-nm spectral range (for example, from 1250-1440 nm or
1440-1640 nm) by proper choice of SOAs (such as SOAs centered at
1350 nm and 1530 nm, respectively having 3-dB gain bandwidth
extending beyond 70 nm and maximum gain >22 dB).
[0773] It should also be noted that the device of FIG. 10B will not
yield a very narrow linewidth laser. The laser linewidth strongly
depends on the TBF bandpass width. Typically, laser linewidth is
about 4 to 15 GHz (for TBF bandwidth of 30-80 pm). However, a wide
laser linewidth (bandwidth) is advantageous for any OTDR
application (including POTDR) for reducing coherence noise on the
OTDR traces.
[0774] The spectral linewidth of the tunable pulsed laser sources
in the various above-described embodiments may range from less than
1 GHz to more than 15 GHz. It may be advantageous for this
linewidth to be known, at least approximately, in order to
facilitate application of the linewidth correction factor as
described hereinbefore. It may also be very advantageous for the
laser linewidth to be adjustable in a known controlled manner, at
least over some range, so as to circumvent or significantly
mitigate the above mentioned limitation regarding maximum
measurable PMD. If such an ability to adjust the laser linewidth is
available, one may select a larger linewidth where a small PMD
value is to be measured, and select a smaller linewidth where a
large PMD value is to be measured. Optimally, the laser linewidth
would always be set as equal to approximately one half of the
selected step .delta..nu..
[0775] A person skilled in this art will be aware of other
alternatives to these tunable light sources.
Scrambling
[0776] The term "pseudo-random-scrambling" as used herein is to
emphasize that no deterministic relationship between one SOP and
the next is needed or assumed by the computation. That is not to
say, however, that the physical SOP controller 24 must be truly
random as such. It may also follow, for example, that the SOPs
define a uniform grid of points on the Poincare Sphere, with equal
angles between the Stokes vectors.
Uniformly-Distributed
[0777] A "pseudo-random" SOP means that each of the three
components (s1, s2, s3) of the Stokes vector that represents that
SOP on the Poincare Sphere is a random variable uniformly
distributed between -1 and 1, and that any one of the three
components is uncorrelated with the two others (average of the
product=0). Nonetheless, whether the SOPs are on a grid or form a
random set, the points on the Sphere must be
uniformly-distributed.
[0778] However, if a grid is used instead of a random set, the
calculation or processing must not assume a deterministic
relationship between one SOP and the next. Otherwise, if the FUT 16
moves, as may occur in real telecommunications links, such
deterministic relationships between traces obtained with a
deterministic grid will be lost.
Advantages of Embodiments of the Present Invention
(1) Two-Ended PMD Measurement
[0779] The FUT 18 stability requirements are relaxed with the
pseudo-random-scrambling approach in comparison with most other
prior art techniques because no deterministic relationships have to
be assumed between powers obtained with different SOPs and/or
wavelengths. Consequently, the measurement may be tolerant to
FUT-induced SOP changes on timescales as small as 10 ms or even
smaller, depending upon the particular embodiment; The measurement
result is reliable for any optical-fiber type; Certain embodiments
readily permit the measurement of DGD at one given wavelength, and,
when repeated at different wavelengths, permit the determination of
DGD as function of wavelength and, hence, to further obtain mean
DGD or rms DGD; Permit the measurement of very high DGD or overall
PMD values (e.g. 50 to 100 ps) of the FUT if light of relatively
high coherence (e.g. linewidth of less than 1-2 GHz) is detected,
while the use of random scrambling also enables measurement of
small PMD values (e.g. less than 0.1 ps) to good accuracy; The
dynamic range of this approach can be very high (typically 30 dB to
over 60 dB for overall acquisition times ranging from approximately
30 minutes to a few minutes); Permit measurement of a FUT
comprising in-line optical amplifiers, for example erbium doped
fiber amplifiers (EDFAs) or Raman fiber amplifiers, since reliable
measurements can be taken even in the presence of significant ASE
light arising from these optical amplifiers; and Most embodiments
require minimal two-way communications between the two ends of the
FUT.
(3) Single-Ended Overall PMD Measurement
[0780] FUT 18 stability requirement via the
pseudo-random-scrambling approach is relaxed with respect to most
other prior-art techniques because no deterministic relationships
have to be assumed between powers obtained with different SOPs
and/or wavelengths. The method thereby can relax the FUT stability
requirement even for instabilities occurring over a very short time
period, for example 0.2 to 0.4 seconds, depending upon the
particular implementation and the choice of light source and/or
tunable filter means; The measurement result is reliable for any
optical-fiber type; They permit all measurement equipment to be
located at only one end of the FUT, They permit the use of very
long pulses, e.g. about 1 to 20 .mu.s or more, provided that the
OTDR can distinguish the localized refection at the distal end from
other reflections, leading to a significantly high dynamic range,
an overall short acquisition time, and a reduction of interference
or coherence noise. For example, the total acquisition time may
range from less than 2 minutes to over 5 minutes for a dynamic
range exceeding 25 dB; Permit the measurement of very high overall
PMD values (e.g. 50 ps or more) from the FUT if the tunable pulsed
laser has an appropriately narrow linewidth (e.g. of 1-2 GHz or
less), while maintaining the capability to satisfactorily measure a
small PMD (e.g. less than 0.1 ps); The single-ended overall PMD
measurement method uses an OTDR-based technique that can
distinguish the Rayleigh backscattering from the localized
reflection at the distal end of fiber, so that one does not need to
take into account the Rayleigh backscattering or other reflections,
such as from connectors between fiber sections, thereby improving
the reliability of the PMD measurement; Embodiments of this
single-ended PMD measurement method disclosed here further may
measure PMD from a test instrument to any strong localized
reflection along the fiber, well separated from other localized
reflections, for example from any connector or splice of along FUT,
if its backreflected light power is high enough to be adequately
detected.
(4) Single-Ended Cumulative PMD Measurement
[0781] Relaxes the FUT 18 stability requirement via the
pseudo-random-scrambling approach because no deterministic
relationships have to be assumed between traces obtained with
different SOPs and/or wavelengths. Moreover, this advantageous
relaxing of the FUT 18 stability requirement is obtained whether it
is actually performed via I/A-SOP scrambling (the preferred
method), or, in the case of an "ideal" FUT (as defined previously),
by relying only on the "natural" scrambling of the input PSPs of
the optical link that occur randomly and uniformly as a function of
wavelength and fiber length; Permit the use of optical pulses
having a spatial extent greater than the beat length of the FUT,
leading to:
[0782] (i) significantly increased dynamic range, for example from
10 dB to over 20 dB for overall acquisition times ranging from less
than 10 minutes to over 30 minutes for a typical pulse length of
100 or 200 ns;
(ii) reduction of OTDR coherence noise that may be superimposed on
the traces; (iii) increased maximum measurable PMD for a given
laser spectral linewidth; Cumulative PMD is measured directly, in
contrast to previously-known POTDRs of the first type discussed
herein, so no assumed specific birefringence model is needed, in
particular, they are especially suitable for measuring cumulative
PMD of spun fibers, They produce quantitative results; and The
measurement result from this invention is a consequence of the
random scrambling approach which leads notably to a simple
relationship, Equation (62), that is valid for any FUT 18 and any
pulse length according to theory, and of the associated signal
processing. Embodiments of the invention can measure PMD over a
range extending from a few hundredths of picoseconds to over 50
picoseconds and can be used to locate high PMD fiber sections with
excellent spatial resolution. For two-ended measurement, the said
polarization-and-analyzer means may be connected to the optical
path at or adjacent the distal end of the optical path.
[0783] In embodiments for measurement of DGD at a specified
wavelength, for example, for narrow DWDM channel measurement, each
said group may comprise wavelength pairs having substantially the
same said prescribed midpoint wavelength, and the said at least one
polarization-related optical path characteristic is the
differential group delay (DGD) at the said midpoint wavelength.
[0784] The said measured power parameter may be the computed
normalized power T(.nu.), and said predetermined function can be
expressed, for small optical-frequency differences (.delta..nu.),
according to the following differential formula:
DGD ( v ) = .alpha. ds .pi..delta. v .DELTA. T 2 ( v ) SOP
##EQU00173##
where the constant
.alpha. ds = 9 2 , ##EQU00174##
and .nu. is the optical frequency corresponding to the said
midpoint wavelength and .DELTA.T(.nu.) is normalized power
difference obtained for a particular I-SOP and A-SOP couple. FIG. 9
shows how PMD determination may be carried out using measurement
instruments suitable for partial-DGD measurement of a plurality of
SUTs at any (non-filtered) monitoring point along a link. For the
case of a filtered monitoring port (e.g. an optical DeMux port),
DGD of the respective SUT may be measured/monitored;
INDUSTRIAL APPLICABILITY
[0785] Although embodiments of the invention have been described
and illustrated in detail, it is to be clearly understood that the
same are by way of illustration and example only and not to be
taken by way of the limitation, the scope of the present invention
being limited only by the appended claims.
[0786] Polarization mode dispersion is a major cause of impairment
in modern fiber-optic networks, and hence measurements enabling its
characterization, in all of its manifestations (e.g. fiber PMD,
channel or lightpath DGD, and partial-DGD) are of great important
to telecom network operators. Armed with such information, remedial
action might be undertaken, for instance to replace particular
problematic sections of an optical link, or identify the cause of
otherwise unexplained intermittent error bursts in a DWDM channel.
In addition, such information might be used by the operator to
indicate that the particular already field-deployed optical link is
not suitable to be "upgraded" to carry higher-bandwidth optical
signals.
[0787] Preferred embodiments of this invention are directed towards
practical implementations of such measurements and diagnostics in
the field, and include: [0788] Non-intrusive PMD measurement of an
"in-service" optical fiber link of an optical network using a test
source launched into "dark" DWDM channels; [0789] Non-intrusive PMD
measurement of an "in-service" optical fiber link of an optical
network using the polarized light from multiple data-carrying DWDM
signals propagating therein; [0790] Measurement of DGD of a DWDM
channel in order to ensure that it is capable of carrying
high-bandwidth traffic; [0791] Measurement of the partial-DGD, and
hence the degree of pulse spreading (or equivalently, "PMD
penalty") of a real data-carrying signal in a DWDM channel; [0792]
Rapid characterization, from a single-end, of overall PMD over long
distances of an optical fiber via a cost-effective variant of
field-portable OTDR-based instrumentation; Detailed
characterization of cumulative PMD along an optical fiber, normally
already having been identified as having excessive PMD, in order to
identify the or those segments of the long fiber responsible for
most of the overall PMD, and thereby enable a link to be markedly
improved for a cost much less than replacing the entire length of
fiber.
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