U.S. patent application number 10/520819 was filed with the patent office on 2008-01-10 for polarization diversity detection without a polarizing beam splitter.
Invention is credited to Mark E. Froggatt, Brian J.. Soller, Matthew S. Wolfe.
Application Number | 20080007718 10/520819 |
Document ID | / |
Family ID | 30115699 |
Filed Date | 2008-01-10 |
United States Patent
Application |
20080007718 |
Kind Code |
A9 |
Froggatt; Mark E. ; et
al. |
January 10, 2008 |
Polarization diversity detection without a polarizing beam
splitter
Abstract
A fiber optic measurement device including an optical frequency
domain reflectometer (10) performs polarization diversity detection
without using a polarizing beam splitter.
Inventors: |
Froggatt; Mark E.;
(Blacksburg, VA) ; Soller; Brian J..; (Blacksburg,
VA) ; Wolfe; Matthew S.; (Christiansburg,
VA) |
Correspondence
Address: |
NIXON & VANDERHYE, PC
901 NORTH GLEBE ROAD, 11TH FLOOR
ARLINGTON
VA
22203
US
|
Prior
Publication: |
|
Document Identifier |
Publication Date |
|
US 20060164627 A1 |
July 27, 2006 |
|
|
Family ID: |
30115699 |
Appl. No.: |
10/520819 |
Filed: |
July 8, 2003 |
PCT Filed: |
July 8, 2003 |
PCT NO: |
PCT/US03/21336 |
371 Date: |
July 26, 2005 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60394260 |
Jul 9, 2002 |
|
|
|
Current U.S.
Class: |
356/73.1 |
Current CPC
Class: |
G01M 11/3181 20130101;
G01M 11/337 20130101; G01M 11/3172 20130101; G01M 11/331
20130101 |
Class at
Publication: |
356/073.1 |
International
Class: |
G01N 21/00 20060101
G01N021/00 |
Claims
1. A fiber optic measurement device comprising an optical frequency
domain reflectometer (OFDR) configured to employ polarization
diversity detection without using a polarizing beam splitter.
2. The fiber optic measurement device according to claim 1, further
comprising: a first coupler for receiving a first optical signal
from a device or system under test and generating first and second
coupler outputs, and a second coupler for receiving a second
optical signal from a reference source and generating third and
fourth coupler outputs.
3. The fiber optic measurement device according to claim 2, further
comprising: a polarization controller (PC) for changing a
polarization state of the third coupler output and generating a PC
output; a third coupler for receiving the first coupler output and
the PC output and generating a first combined output; and a fourth
coupler for receiving the second coupler output and the fourth
coupler output and generating a second combined output.
4. The fiber optic measurement device according to claim 3, further
comprising: a first detector for detecting a first power of the
first combined output in a first projection plane, and a second
detector for detecting a second power of the second combined output
in a second projection plane.
5. The fiber optic measurement device according to claim 4, further
comprising: processing circuitry for processing interference terms
of the first and second powers in the first and second projection
planes to determine one or more characteristics of the first
optical signal.
6. The fiber optic measurement device according to claim 5, wherein
the fiber optic measurement device accounts for polarization of the
first optical signal without using a polarizing beam splitter.
7. The fiber optic measurement device according to claim 5, further
comprising: a second polarization controller for changing a
polarization of the first optical signal before being received in
the first optical coupler, wherein the first and second
polarization controllers are adjustable for calibrating the fiber
optic measurement device, wherein for multiple different settings
of the second polarization controller resulting in multiple
corresponding vector measurements at the first and second
detectors, the processing circuitry is configured to calculate a
vector calibration matrix using the vector measurements.
8. The fiber optic measurement device according to claim 7, wherein
the processing circuitry is configured to correct detected vector
measurements using the vector calibration matrix such that the
corrected vector measurements result in a vector representation of
the first optical signal in an orthonormal basis.
9. An optical frequency domain reflectometer (OFDR) configured to
employ polarization diversity detection comprising: a first coupler
for receiving a first optical signal from a device or system under
test and generating first and second coupler outputs; a second
coupler for receiving a second optical signal from a reference
source and generating third and fourth coupler outputs; a
polarization controller (PC) for changing a polarization state of
the third coupler output and generating a PC output; a third
coupler for receiving the first coupler output and the PC output
and generating a first combined output; a fourth coupler for
receiving the second coupler output and the fourth coupler output
and generating a second combined output; a first detector for
detecting a first power of the first combined output in a first
projection plane; a second detector for detecting a second power of
the second combined output in a second projection plane; and
processing circuitry for processing interference terms of the first
and second powers in the first and second projection planes to
determine one or more characteristics of the first optical
signal.
10. The OFDR according to claim 9, wherein the OFDR accounts for
polarization of the first optical signal without using a polarizing
beam splitter.
11. The OFDR according to claim 9, further comprising: a second
polarization controller for changing a polarization of the first
optical signal before being received in the first optical coupler,
wherein the first and second polarization controllers are
adjustable for calibrating the fiber optic measurement device, and
wherein for multiple different settings of the second polarization
controller resulting in multiple corresponding vector measurements
at the first and second detectors, the processing circuitry is
configured to calculate a vector calibration matrix using the
vector measurements.
12. The OFDR according to claim 11, wherein the processing
circuitry is configured to correct detected vector measurements
using the vector calibration matrix such that the corrected vector
measurements result in a vector representation of the first optical
signal in an orthonormal basis.
13. A method comprising detecting one or more parameters of an
optical signal using polarization diversity detection without using
a polarizing beam splitter.
14. The method according to claim 13, further comprising: receiving
at a first coupler a first optical signal from a device or system
under test and generating first and second coupler outputs, and
receiving at a second coupler a second optical signal from a
reference source and generating third and fourth coupler
outputs.
15. The method according to claim 14, further comprising: changing
in a first polarization controller a polarization state of the
third coupler output and generating a changed third coupler output;
receiving at a third coupler the first coupler output and the
changed third coupler output and generating a first combined
output; and receiving at a fourth coupler the second coupler output
and the fourth coupler output and generating a second combined
output.
16. The method according to claim 15, further comprising: detecting
a first power of the first combined output in a first projection
plane, and detecting a second power of the second combined output
in a second projection plane.
17. The method according to claim 16, further comprising:
processing interference terms of the first and second powers in the
first and second projection planes to determine one or more
characteristics of the first optical signal.
18. The method according to claim 17, further comprising: changing
in a second polarization controller a polarization of the first
optical signal before being received in the first optical coupler;
for multiple different settings of the second polarization
controller, generating multiple corresponding detected vector
measurements; calculating a vector calibration matrix using the
vector measurements.
19. The method according to claim 18, further comprising:
correcting detected vector measurements using the vector
calibration matrix such that the corrected vector measurements
result in a vector representation of the first optical signal in an
ortho-normal basis.
Description
CLAIM OF BENEFIT OF PROVISIONAL PATENT APPLICATION
[0001] Priority is claimed from U.S. Provisional Patent Application
No. 60/394,260, filed on Jul. 9, 2002. The contents of this
provisional application are incorporated by reference.
RELATED APPLICATIONS
[0002] This application is related to commonly-assigned PCT
Application No. ______, entitled "Heterodyne Optical Spectrum
Analyzer," filed on Jul. 8, 2003, and to commonly-assigned, U.S.
patent application Ser. No. 10/005,819, entitled "Apparatus and
Method for the Complete Characterization of Optical Devices
Including Loss, Birefringence, and Dispersion Effects," filed on
Dec. 14, 2001.
FIELD OF THE INVENTION
[0003] The present invention relates to optical measurements, and
more particularly, to a device and method for performing
polarization diversity detection.
BACKGROUND AND SUMMARY OF THE INVENTION
[0004] Mixing between a reference signal and a data signal is often
necessary to extract information about an optical device. A probe
signal and a reference signal originating from the same source are
typically mixed, resulting in fringes that can be detected and used
to asses information about the device being probed. In
interferometric sensing, a reference signal is mixed with a signal
whose phase and/or amplitude is modified by a parameter to be
measured.
[0005] The mixing produces an interference signal, and the
amplitude of the interference signal depends on how efficiently the
two optical signals mix. When the two signals have the same
polarization state, the mixing efficiency is 100%. When the two
signals have orthogonal polarization states, no mixing occurs--0%
efficiency. Between these two limits, only the portion of the
signals whose polarization states resolve onto a single
polarization axis actually mix. The reduced, mixed-signal amplitude
results from an unmixed component in an orthogonal polarization
state. This inefficiency is usually referred to as polarization
induced fringe fading.
[0006] Polarization diversity detection overcomes polarization
induced fading. One commonly known interferometric scheme that can
suffer from polarization fading is Optical Frequency Domain
Reflectometry (OFDR). OFDR injects a highly monochromatic beam of
light into the optical system or device to be tested. The frequency
of that light is varied slowly with a time-linear sweep, and the
optical signal back-scattered from the optical system is detected
by coherently mixing the back-scattered signal with the reference
input signal. The beat frequency component of the mixed signal,
(corresponding to an interference signal), is measured to determine
a position of the back-scattering (reflection) point in the optical
system/fiber. The interference signal amplitude also determines a
back-scattering factor and an attenuation factor for the reflected
light.
[0007] U.S. Pat. Nos. 6,376,830 and 5,789,521 provide further
details regarding OFDR measurement and are incorporated herein by
reference. Reference may also be made to commonly-assigned, U.S.
patent application Ser. No. 10/005,819, entitled "Apparatus and
Method for the Complete Characterization of Optical Devices
Including Loss, Birefringence, and Dispersion Effects," filed on
Dec. 14, 2001.
[0008] A single mode optical fiber supports two degenerate
polarization modes. This degeneracy causes field energy to be
transferred between the modes as they propagate down the fiber.
This phenomenon causes the polarization fading in fiber-optic
interferometers. FIG. 1 shows schematically a Mach-Zender
interferometer. The arrows denote electric field (E) vector
components. Polarization fading occurs whenever E.sub.1 and E.sub.2
are not co-linear, i.e., E.sub.1 E.sub.2=| E.sub.1.parallel.
E.sub.2|cos .theta., .theta..noteq.0. The power measured at the
detector is proportional to the square of the absolute value of
(E.sub.1+E.sub.2). The interference terms of this relationship are
proportional to E.sub.1E.sub.2*+E.sub.2E.sub.1*, where * denotes a
complex conjugate. When a first coupler C1 splits the input field
E.sub.in, there is a chance that the split fields E.sub.1 and
E.sub.2 in the respective interferometer arms evolve into
orthogonal polarizations. As described above, in that situation, no
interference fringes will be detected, and there is complete
polarization fading or 0% mixing efficiency.
[0009] A worst case scenario in which the fields interfering on the
detector, E.sub.1 and E.sub.2, are orthogonal is shown in FIG. 2.
More formally, in some orthogonal basis, the fields can be written
E1=(a, 0)exp(i.omega..tau.) and E.sub.2=(0, d), where .tau. is the
propagation time difference between the two interferometer arms
(.tau.=n.sub.eL/c, where n.sub.e is the effective (modal) index of
the fiber. The basis of a vector set includes two vectors in two
dimensions or three vectors in three dimensions that are used to
represent all other possible vectors. Knowing the basis of a vector
set is essentially the same as knowing the coordinate system for a
point in space. For example, a location may be described as being
at 32 degrees North and 25 degrees West. The coordinate system is
the set of latitude and longitude lines on the Earth, and the
particular location is understood. The basis set is a pair of
vectors, each one degree (60 nautical miles) long, with one vector
pointed to the North and one vector pointed to the West.
[0010] Now in the S-P basis set, shown in FIG. 2 as orthogonal, the
fields can be written as E.sub.1=(a', b')exp(i.omega..tau.) and
E.sub.2=(c', d') so E.sub.1E.sub.2=0, but E.sub.1+E.sub.2=(a' exp
(i.omega..tau.)+c', b' exp (i .omega..tau.)+d'). Polarization
diversity detection detects the s and p components (or projections
onto the s and p axes) of E.sub.1+E.sub.2 separately using two S
and P detectors. The power at each detector is proportional to the
modulus squared of the components of the total field:
P.sub.S.varies.|a' exp(i.omega..tau.)+c'|.sup.2 (1)
P.sub.P.varies.|b' exp(i.omega..tau.)+d'|.sup.2 (2) These diversity
power signals exhibit fringes even though the total field, i.e.,
the sum of two orthogonal fields, does not.
[0011] Polarization diversity detection may be implemented using a
polarizing beam splitter (PBS) as show in FIG. 3. If the field at
the PBS is E.sub.bS and is given by E.sub.bs=(A, B) in the basis
set of the polarizing beam splitter, then the measured powers at
the S and P detectors are P.sub.S.varies.|A|.sup.2 and
P.sub.p.varies.|B|.sup.2. When the PBS splits the field into
different components, the crystalline structure of the PBS imposes
an orthonormal basis onto which the incident field is projected.
That orthonormal basis is needed to extract information contained
in the E.sub.1 and E.sub.2 amplitudes.
[0012] But there are drawbacks with using polarizing beam
splitters. First, they are bulky and expensive. Second, polarizing
beam splitters add stray reflections to the detected signals.
Third, if the polarizing beam splitter is designed to operate in a
particular wavelength, e.g., 1500 nm, it cannot be easily and
inexpensively altered to operate at a non-standard wavelength, such
as 800 nm, at least as compared to a standard optical coupler. For
these and other reasons, it is an object of the present invention
to perform polarization diversity detection without a polarizing
beam splitter.
[0013] The present invention performs polarization diversity
detection without using a polarizing beam splitter. Field vectors
from one interferometer arm are used as the basis upon which to
project a field vector from the other interferometer arm.
Polarization diversity detection is performed using only standard
optical couplers, e.g., 50-50 couplers. A polarization beam
splitter is not needed.
[0014] A first coupler receives a first optical signal from a
device or system under test and generates first and second coupler
outputs. A second coupler receives a second optical signal from a
reference source and generates third and fourth coupler outputs. A
first polarization controller (PC) changes the polarization state
of the third coupler output and generates a PC output. A third
coupler generates a first combined output from the first coupler
output and the PC output. A fourth coupler generates a second
combined output from the second coupler output and the fourth
coupler output. A first detector detects a first power of the first
combined output in a first projection plane, and a second detector
detects a second power of the second combined output in a second
projection plane. A processor processes interference terms in the
first and second powers in the first and second projection planes
to determine one or more characteristics of the first optical
signal.
[0015] A second polarization controller changes the polarization of
the first optical signal before it is received in the first optical
coupler. The first and second polarization controllers are adjusted
to calibrate the fiber optic measurement device. Different second
polarization controller settings result in multiple corresponding
vector measurements at the first and second detectors. The
processor calculates a vector calibration matrix using these vector
measurements. The processor corrects subsequent detected vector
measurements using the vector calibration matrix. The corrected
vector measurements ensure that the vector representation of the
first optical signal are in an ortho-normal basis set.
[0016] The OFDR components can be constructed simply using optical
fiber, and if desired, from the same type of standard low-loss
fiber. Matching the type of fiber throughout the optical network
results in very low losses with essentially zero scattering events
in the network. As a result, the OFDR produces very clean time
domain measurements (only reflection events from the device under
test appear).
[0017] Another advantage of fiber-based OFDR construction is
significant cost reduction and increased reliability and
flexibility. A polarization controller can be implemented simply as
a single loop of fiber that is moved to achieve a certain
polarization state at the output. Once the loop is positioned, it
need not be moved again. Couplers are constructed by melting two
optical fibers together. In order to manufacture couplers for
operation at widely different wavelengths, (e.g., 615 nm and 1550
nm), coupler manufacturers need only purchase fiber (an inexpensive
commodity) designed for that wavelength and melt two sections
together using the same process for all wavelengths. No re-tooling
or significant changes to the process are required. As a result,
couplers are readily available at all wavelengths at a reasonable
price in contrast to polarization beam splitters and other
bulk-optic based optical components.
[0018] Other features, aspects, and advantages of the present
invention will become apparent from the following detailed
description, taken in conjunction with the accompanying drawings,
illustrated by way of example the principles of the invention. Like
reference symbols refer to like elements throughout.
BRIEF DESCRIPTION OF THE DRAWINGS
[0019] FIG. 1 illustrates a Mach-Zender interferometer;
[0020] FIG. 2 illustrates orthogonal measurement field vectors
E.sub.1 and E.sub.2 and two basis vectors S and P;
[0021] FIG. 3 illustrates a Mach-Zender interferometer with a
polarization beam splitter;
[0022] FIG. 4 illustrates in function block format an optical
frequency domain reflectometer (OFDR) for polarization diversity
detection without a polarization beam splitter;
[0023] FIG. 5 illustrates a different configuration of the OFDR
shown in FIG. 4;
[0024] FIG. 6 illustrates in further detail the detectors shown in
FIGS. 4 and 5;
[0025] FIG. 7 illustrates in further detail the data acquisition
block in FIGS. 4 and 5;
[0026] FIG. 8 is a vector diagram showing the measurement field
vector E.sub.1 and reference field vector E.sub.2 each being
projected and summed on each of the basis axes S and P in
accordance with projections implemented by a polarization beam
splitter;
[0027] FIG. 9 is a similar vector diagram for the all coupler OFDR
implementations found in FIGS. 4 and 5; and
[0028] FIG. 10 is a vector projector diagram showing E.sub.1
projected onto virtual reference fields E'.sub.S and E'.sub.P.
DETAILED DESCRIPTION OF THE INVENTION
[0029] The following description, for purposes of explanation not
limitation, sets forth specific details, such as particular
components, electronic circuitry, techniques, etc. in order to
provide an understanding of the present invention. But it will be
apparent to one skilled in the art that the present invention may
be practiced in other embodiments that depart from these specific
details. In other instances, detailed descriptions of well-known
methods, devices, and techniques, etc. are omitted so as not to
obscure the description with unnecessary detail. Individual
function blocks are shown in the figures. Those skilled in the art
will appreciate that functions may be implemented using discrete
components or multi-function hardware. Processing functions may be
implemented using a programmed microprocessor or general-purpose
computer, using an application specific integrated circuit (ASIC),
and/or using one or more digital signal processors (DSPs).
[0030] A first, non-limiting, example OFDR embodiment that does not
employ a polarizing beam splitter is described in conjunction with
FIG. 4. An OFDR 10 includes a tunable laser 12 for generating an
electric field at a particular frequency (controlled by the
frequency sweep signal from processor 32) provided to a standard
optical coupler 14. Any such coupler may be employed, and one
non-limiting example is Gould part number 23-40355-33-01201
manufactured by Gould Fiber Optics Division of Gould Electronics of
Baltimore, Md. Coupler 14 splits the input field E.sub.IN into two
electric field signals E.sub.1 and E.sub.2. E.sub.1 is provided
through optical coupler 36 and connector 38 to a device or system
under test (DUT) 40. A back-scattered signal E.sub.1 to be measured
as a function of its reflection point along the fiber is provided
through coupler 36 to a first coupler 16.
[0031] The reference signal E.sub.2 is provided to a second coupler
22. A polarization state of a first output of coupler 22 is changed
in polarization controller 24. The output of polarization
controller 24 is the reference signal E.sub.2 in a first reference
plane denoted "S" so that this reference signal is referred to as
E.sub.S. The second output of coupler 22 corresponds to the
reference signal in another reference plane labeled "P" so that
this signal is denoted E.sub.P. The first output of coupler 16 is
E.sub.X and equals M.sub.13E.sub.1 as described below. The second
output of coupler 16 is E.sub.Y and equals M.sub.14E.sub.1.
[0032] The couplers 18 and 26 output the signals E.sub.X+E.sub.S
and E.sub.Y+E.sub.P, respectively, which are detected by respective
detectors 20 and 28. The output of S-detector 20 is a power
P.sub.S, and the output of P-detector 28 is a power P.sub.P. Both
powers are provided to a data acquisition unit 30 which provides
digital information to processor 32. The processor 32 processes the
information and generates the desired electric field output signal
E.sub.OUT which is then provided to a display 34 to display one or
more parameters of E.sub.OUT. Such parameters may include amplitude
and phase of the scattered light and the particular location at
which the reflection occurs. Processor 32 sweeps the tunable laser
12 through a particular sweep range specified by a starting
wavelength and a finishing wavelength, e.g., 1540 nm-1580 nm.
[0033] FIG. 5 illustrates another example embodiment with a
slightly different configuration in which the device under test 40
is coupled directly to the output of the coupler 14. Both
embodiments employ a polarization controller 42 used in calibrating
the OFDR 10 as will be later described.
[0034] The detectors 20 and 28 are illustrated in further detail in
FIG. 6. Any suitable detector may be employed, and one non-limiting
example is a ThorLabs PDA 400 optical detector manufactured by
ThorLabs of Newton, N.J. Each detector includes a photodetector 42
and an amplifier 44 coupled to a low-pass filter 46. The data
acquisition block 30 includes an analog-to-digital conversion block
48 coupled to a buffer 50. The filtered output from the detector is
converted into a digital format by the digital-to-analog conversion
means 48, and the digital signal is stored in the buffer 50 before
being processed by the data processor 32.
[0035] The vector diagram in FIG. 8 shows projected fields on the S
and P power detector reference planes. The reference fields S and P
are assumed orthogonal--a reasonable assumption if a PBS is used.
The S component or projection of the measured field E.sub.1 is
denoted E.sub.X on the horizontal axis, and the P component or
projection of the measured field E.sub.1 is denoted E.sub.Y along
the vertical axis. The reference field E.sub.2 is also projected
onto the S and P axes. The sum of E.sub.X and E.sub.S is detected
on the S detector 20, and the sum of the projections E.sub.P and
E.sub.Y is detected on the P detector 28.
[0036] But when the two fields E.sub.1 and E.sub.2 are detected by
the coupler pair 16 and 22, the S and P axes cannot be assumed to
be orthogonal or even the same length. Although the interference
takes place at two separate detectors between signals traveling
significantly different paths, that interference can be represented
as the projection of the original signal of interest E1 onto two
non-parallel vectors. To account for the non-orthonormal basis,
E.sub.1 is altered by two transforming matrices M.sub.13 and
M.sub.14 prior to being projected onto the reference fields E.sub.S
and E.sub.P as shown in FIG. 9. So long as the two transforming
matrixes M.sub.13 and M.sub.14 do not vary with time, this is an
acceptable transformation.
[0037] Rather than the projection of E.sub.1 onto the S and P axes,
FIG. 9 shows the projection of E.sub.X onto E.sub.S and the
projection of E.sub.Y onto E.sub.P. Even though the transforming
matrices M.sub.13 and M.sub.14 are unknown, the reference fields
E.sub.S and E.sub.P may still be transformed in a precise way that
allows the detected fields as projections of E.sub.1 onto some set
of vectors. This is illustrated in FIG. 10 in which E.sub.1 is
projected onto two non-parallel vectors E'.sub.S=M.sup.-1.sub.13
E.sub.S and E'.sub.P=M.sup.-1.sub.14 E.sub.S. As will be
demonstrated below, E.sub.1 can be recovered from these projections
shown in FIG. 10 using a linear mathematical transformation.
[0038] The propagation of a field in an optical fiber from one
location to another through any linear section of the system (e.g.,
optical fiber, optical component, etc.) can be represented by a
complex 2.times.2 matrix. This matrix will account for all effects
of the linear section including loss, polarization rotation, and
polarization-dependent loss. Let the propagation from coupler i to
coupler j (i, j=1,2,3,4) be represented by the matrix M.sub.ij. We
therefore have E.sub.x=M.sub.13 E.sub.1 and E.sub.y=M.sub.14
E.sub.1. The interference terms measured at the S- and P-detectors
20 and 28 are proportional to P.sub.s.varies. E.sub.x s*+ E.sub.x*
s=M.sub.13 E.sub.1 s*+(M.sub.13 E.sub.1)* s, (3) P.sub.p.varies.
E.sub.y p*+ E*.sub.y p=M.sub.14 E.sub.1 p*+(M.sub.14 E.sub.1)* p.
(4)
[0039] As described, without a polarizing beam splitter, the
vectors S and P no longer form an orthonormnal basis. But knowledge
of the amplitude and relative angle between the vectors S and P
allows the reconstruction of E.sub.1 in an orthogonal basis.
[0040] From Eqs. (3) and (4), it is seen that the detector power
measurements of P.sub.s and P.sub.p project the vectors
M.sub.13E.sub.1 and M.sub.14E.sub.1 into the S-P basis. The fact
that the basis-vectors S and P are arbitrary allows use of the
identity, x(M y)= y(M.sup.t x), where x and y are arbitrary
vectors, M is an arbitrary matrix, and M.sup.t is the transpose of
matrix M, to write the following: (M.sub.13 E.sub.1) s=
E.sub.1(M.sub.13.sup.t s*)= E.sub.1 s' (5) (M.sub.14 E.sub.1) p=
E.sub.1(M.sub.14.sup.t p*)= E.sub.1 p' (6)
[0041] The vectors s' and p' act as the basis vectors onto which
E.sub.1 is projected. Knowledge of the amplitudes of and relative
angle between s' and p' allows the projection of E.sub.1 onto an
orthogonal basis set. What is required is a process by which this
correcting matrix can be quickly and efficiently found to transform
the measurements into an ortho-normal basis set.
[0042] Power measurements at the S and P detectors yield
information about the vector field E= E.sub.x+ E.sub.y in the S-P
basis set. Those measurements are of the form
P.sub.s=|E.sub.x|.sup.2+|s|.sup.2+2E.sub.xs cos .phi..sub.x (7)
P.sub.p=|E.sub.y|.sup.2+|p|.sup.2+2E.sub.yp cos .phi..sub.y (8)
[0043] Omitting dc components, we can form the vector, v=(2E.sub.xs
cos .phi..sub.x,2E.sub.yp cos .phi..sub.y)=(E.sub.s, E.sub.p). But
again E.sub.s and E.sub.p are not orthogonal. To remedy this, a
calibration matrix, M, is determined. When it is multiplied by v,
the product gives a new vector E that represents the field E.sub.1
in a calibrated, orthogonal basis.
[0044] The calibration begins by adjusting the polarization
controllers PC.sub.1 and PC.sub.2 (41 and 24). With the reference
laser 12 in the continuous sweep mode, PC.sub.1 is adjusted so that
the fringes observed on the P-detector 28 are maximized. When this
is accomplished, the fringes on the S-detector 20 are minimized by
adjusting PC.sub.1. When this is accomplished, PC.sub.1 is adjusted
so the fringe levels on the S- and P-detectors are approximately
equal (to within .+-.10%).
[0045] Once the polarization controllers PC.sub.1 and PC.sub.2 are
adjusted, the OFDR can be calibrated by taking measurements of
v=(2E.sub.xs cos .phi..sub.x,2E.sub.yp cos .phi..sub.y) for four
distinct but random settings of PC.sub.1. The following represent
these measurements: v 1 = ( E s 1 E p 1 ) , v 2 = ( E s 2 E p 2 ) ,
v 3 = ( E s 3 E p 3 ) , v 4 = ( E s 4 E p 4 ) . ( 9 ) ##EQU1##
[0046] With the above definitions, the following matrix can be
formed [ p g q h ] = [ v 1 v 2 ] - 1 .function. [ v 3 v 4 ] ( 10 )
##EQU2## where [x y] is a matrix with columns formed by the
elements of the vectors x and y. Using the following set of
definitions: A = 1 - p 2 - q 2 ##EQU3## B = 1 - g 2 - h 2
##EQU3.2## C = 2 .times. .times. Re .times. p * .times. q
##EQU3.3## D = - 2 .times. .times. Im .times. p * .times. q
##EQU3.4## E = 2 .times. .times. Re .times. g * .times. h
##EQU3.5## F = - 2 .times. .times. Im .times. g * .times. h
##EQU3.6## ( x y ) = ( C D E F ) - 1 .times. ( A B ) ##EQU3.7##
.alpha. = x + I .times. .times. y ##EQU3.8## .beta. = 1 - .alpha. 2
##EQU3.9## M ^ = ( 1 .alpha. 0 .beta. ) .function. [ v 1 v 2 ] - 1
##EQU3.10## the vector-calibration matrix is given by M ^ = ( 1
.alpha. 0 .beta. ) .function. [ v 1 v 2 ] - 1 ##EQU4## Any
measurement vector v.sub.m=(2E.sub.mxs cos .phi..sub.mx,2E.sub.myp
cos .phi..sub.my) can be corrected by performing the following
multiplication E={circumflex over (M)} v.sub.m where, after the
above multiplication, E is guaranteed to be in some orthonormal
basis.
[0047] Although the above-description is directed to the two
polarization modes of standard optical fiber, optical fiber can
support a variety of different modes. To handle that mode variety,
one coupler and one detector would be added for each new mode
present in the fiber. "Mode Controllers" corresponding to fiber
loops (like the polarization controller loops) would also be used
in each reference path. Calibration would be carried out using
analogous linear algebra operations. The absence of stray
reflections as described above means that the invention is
particularly effective at measuring the very low scatter levels
that come from the non-homogeneities in the optical fiber core.
Optical-fiber, scatter-level measurements can be used to measure
losses within an optical network independently of the manner of
connection to the network.
[0048] While the invention has been described in connection with
practical and preferred embodiments, the invention is not limited
to the disclosed embodiments. On the contrary, the invention covers
various modifications and equivalent arrangements included within
the scope of the appended claims.
* * * * *