U.S. patent application number 16/341536 was filed with the patent office on 2019-08-22 for methods for estimating modal bandwidth spectral dependence.
This patent application is currently assigned to Panduit Corp.. The applicant listed for this patent is Panduit Corp.. Invention is credited to Jose M. Castro, Yu Huang, Bulent Kose, Brett Lane, Asher S. Novick, Richard J. Pimpinella.
Application Number | 20190260470 16/341536 |
Document ID | / |
Family ID | 60162271 |
Filed Date | 2019-08-22 |
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United States Patent
Application |
20190260470 |
Kind Code |
A1 |
Castro; Jose M. ; et
al. |
August 22, 2019 |
Methods for Estimating Modal Bandwidth Spectral Dependence
Abstract
Methods for estimating the Effective Modal Bandwidth (EMB) of
laser optimized Multimode Fiber (MMF) at a specified wavelength,
.lamda.S, based on the measured EMB at a first reference
measurement wavelength, .lamda.M. In these methods the Differential
Mode Delay (DMD) of a MMF is measured and the Effective Modal
Bandwidth (EMB) is computed at a first measurement wavelength. By
extracting signal features such as centroids, peak power, pulse
widths, and skews, as described in this disclosure, the EMB can be
estimated at a second specified wavelength with different degrees
of accuracy. The first method estimates the EMB at the second
specified wavelength based on measurements at the reference
wavelength. The second method predicts if the EMB at the second
specified wavelength is equal or greater than a specified bandwidth
limit.
Inventors: |
Castro; Jose M.;
(Naperville, IL) ; Pimpinella; Richard J.;
(Frankfort, IL) ; Kose; Bulent; (Burr Ridge,
IL) ; Lane; Brett; (Hinsdale, IL) ; Huang;
Yu; (Orland Park, IL) ; Novick; Asher S.;
(Chicago, IL) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Panduit Corp. |
Tinley Park |
IL |
US |
|
|
Assignee: |
Panduit Corp.
Tinley Park
IL
|
Family ID: |
60162271 |
Appl. No.: |
16/341536 |
Filed: |
October 5, 2017 |
PCT Filed: |
October 5, 2017 |
PCT NO: |
PCT/US2017/055307 |
371 Date: |
April 12, 2019 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
62407695 |
Oct 13, 2016 |
|
|
|
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
H04B 10/0731 20130101;
H04B 10/2581 20130101 |
International
Class: |
H04B 10/073 20060101
H04B010/073; H04B 10/2581 20060101 H04B010/2581 |
Claims
1. A method for estimating modal bandwidth of multimode fibers at a
set of wavelengths, based on a DMD measurement performed at only
one wavelength .lamda..sub.M comprising performing a DMD
measurement at a first wavelength, extracting at least one signal
feature, the signal feature bring at least one of a centroid, peak
power, pulse width, and skew of the DMD measurement at the first
wavelength, and predicting an at least one signal feature for a
second wavelength based upon the at least one signal feature of the
first wavelength, and using the predicted at least one signal
feature of the second wavelength to estimate a modal bandwidth.
2. A method for estimating the centroids and peaks of multimode
fibers at a set of wavelengths, based on a DMD measurement
performed at only one wavelength .lamda..sub.M.
3. A method for estimating the DMD pulses energy position and width
of multimode fibers at a set of wavelengths, based on a DMD
measurement performed at only one wavelength .lamda..sub.M.
4. A method to extract features of DMD pulses that describe
spectral dependence of modal dispersion.
5. A method for enabling machine learning of multimode fiber by
identifying features and radial-offset regions that relates the EMB
at two wavelengths.
6. A method for predicting if EMB at an arbitrary wavelength,
.lamda..sub.S, is equal or greater than a specified bandwidth
threshold, EMB.sub.th, based on a DMD measurement at a different
wavelength, .lamda..sub.M.
7. A method according to 1 to reduce the testing time for fibers
designed to operate at more than one wavelength.
8. A method according to 2 to evaluate modal-chromatic dispersion
properties of a MMF at multiple wavelength based on measurements at
only one wavelength.
9. A method according to 3 to predict differential mode delay,
minimum effective modal bandwidth at more than one wavelength with
reduced testing time for fibers designed to operate at more than
one wavelength.
10. A method according to claim 1-4 to select MMFs with alpha
parameters lower than the alpha optimum function at a desired
spectral range.
11. A method according to claim 1-4 to select MMFs that produce
modal-chromatic dispersion compensation at a desired spectral
range.
12. A method according to claim 1-4 to select MMF that have desired
modal bandwidth at desired spectral range, i.e 840nm 980 nm.
13. A method according to claim 1-4 to sort production in order to
select standard compliant wideband fibers capable to operate in a
desired spectral range, i.e. 840 nm to 1000 nm, without the need to
measure the modal bandwidth at all the specified wavelengths.
14. A method according to claim 5-6 to sort production in order to
select standard compliant wideband fibers capable to operate in a
desired spectral range, i.e. 840 nm to 1000 nm, without the need to
measure the modal bandwidth at all the specified wavelengths.
15. A method according to claim 1-6 to reduce the number of modal
bandwidth measurements during manufacturing or quality test for
MMFs.
16. A method according to claim 1-6 to design MMF that complies
with modal bandwidth requirements at specific wavelengths based on
the extracted features such as centroid, width, peaks, skews.
Description
CROSS REFERENCES TO RELATED APPLICATIONS
[0001] This application claims priority to U.S. Provisional
Application No. 62/407,695, filed Oct. 13, 2016, the subject matter
of which is hereby incorporated by reference in its entirety.
BACKGROUND OF THE INVENTION
[0002] The present invention relates in general to the field of
optical fibers and more specifically, to multimode fibers (MMF)
designed for operation at multiple wavelengths. The present
invention also relates to the field of modeling, designing,
production, sorting and testing of MMFs. More specifically it
relates to the estimation of the MMF EMB at multiple
wavelengths.
[0003] The invention is also related to modal and chromatic
dispersion compensation in Vertical Cavity Surface Emitting Laser
(VCSEL) based MMF channels [1]. The methods described here can
provide an estimation of the skew in radial DMD pulse waveforms
(tilt) at different wavelengths which is critical in the field of
modal-chromatic dispersion compensation.
[0004] The need for higher bandwidth has been mainly driven by the
increasing demand for high-speed backbone data aggregation fueled
by video transmission, server applications, virtualization, and
other emerging data services. Cost, power consumption, and
reliability advantages have favored the predominance of short and
intermediate reach optical channels employing transmitters
utilizing VCSELs operating at 850 nm over MMF. MMF is currently
utilized in more than 85% of datacenter installations, and has a
larger core diameter than single-mode fiber (SMF), which reduces
connection losses, relaxes alignment tolerances, and reduces
connectorization cost.
[0005] Recently, new modulation technologies for VCSEL-MMF channels
such as PAM-4, and Short Wavelength Division Multiplexing (SWDM)
[SWDM alliance], has been proposed in order to increase the data
rates. Standards organizations, including the Institute of
Electrical and Electronics Engineers (IEEE) working group 802.3cd
and the T11 Technical Committee within the International Committee
for Information Technology Standards (INCITS) PI-7, are already
working on new applications for PAM-4 for optical serial rates over
50 Gb/s per wavelength.
[0006] The SWDM concept is similar to the Coarse Wavelength
Division Multiplexing (CWDM), already used for SMF channels
operating in the 1310 nm spectral region. SWDM requires the
specification of the minimum EMB at the wavelengths limits of the
operating spectrum (e.g. 850 nm and 953 nm).
[0007] The EMB is computed from DMD pulse measurements. The DMD
test method, specified within standards organizations [2],
describes a procedure for launching a temporally short and
spectrally narrow pulse (reference pulse) from a SMF into the core
of a MMF at several radial offsets [5]. After propagating through
the MMF under test, the pulses are received by a fast photodetector
which captures all the MMF core power. The EMB is estimated by the
Fourier domain deconvolution of the input pulse from a weighted sum
of the received signals for each radial offset launch. The set of
weight values utilized in the computation belong to a set of ten
representative VCSELs described elsewhere [2]. Due to the test
complexity, it is time consuming and the equipment required to
perform the test is expensive; EMB test requirements for multiple
wavelengths will significantly increase testing time and
consequently, increase fiber cost. A method to estimate the EMB
from measurements at a single wavelength would therefore, reduce
testing time and cost. The challenges to achieve such a method are
described below.
[0008] FIG. 1, shows a simulation of EMB vs wavelength 100 for a
MMF fiber compliant to the OM4 standard. In this figure, we show
the EMB 105 has a peak value at .lamda..sub.P 120. The labels 115
and 125 show the measured and predicted wavelengths, .lamda..sub.M
and .lamda..sub.S, respectively. The range 110 shows the spectral
window in which the fiber can maintain an EMB higher than a
specified value, i.e. 4700 MHzkm for OM4.
[0009] In principle, based on MMF theory, when all the physical
parameters of the fiber are known (i.e. dimensions, refractive
profile, dopant types and content), the EMB at .lamda..sub.S can be
predicted from the EMB value at .lamda..sub.M. In practice however,
variations in the refractive index design and dopant content during
the preform fabrication process produce changes in 100 which
prevent the estimation of the EMB at .lamda..sub.S. FIG. 2 shows
simulated MMFs with identical EMB at .lamda..sub.M 200, but
different EMB spectral dependence. Peaks 205, 210, 205 are
different and uncorrelated with 200. Moreover, since the spectral
windows 220, 225 and 230 are different, an estimation of the EMB at
.lamda..sub.S 240 is not possible.
[0010] Shown in FIG. 3. is the EMB at 850 nm and 953 nm for a large
number of simulated fibers, represented using rectangle markers 300
with random variations in their refractive index core. The
horizontal and vertical axes of this figure represents the EMB at
.lamda..sub.M=850 nm vs. EMB .lamda..sub.S=953 nm respectively. A
subset of these fibers that meet the TIA-492AAAD OM4 EMB
specification are represented by diamonds markers 305. This figure
shows the lack of correlation among EMBs at 850 nm and 953 nm. For
example, in 310, a measured fiber with EMB=6000 MHzkm at 850 nm can
have any value from 1500 to 3000 MHzkm at 953 nm. Conversely, 315
shows that a MMF with EMB=2000 MHzkm at 953 nm can have any value
from 200 to 15000 MHzkm at 850 nm. This simulation, which was
extended for a large range of wavelengths from 800 nm to 1100 nm,
clearly shows that there is no direct relationship between the
fiber's EMB at a specified wavelength, .lamda..sub.S, and the EMB
at a measured wavelength, .lamda..sub.M, when
.lamda..sub.S.noteq..lamda..sub.M.
[0011] A method that enables the prediction of the EMB at an
arbitrary wavelength based on measurements at another wavelength is
desirable to reduce testing time and cost of a MMF.
SUMMARY OF THE INVENTION
[0012] Methods for estimating the Effective Modal Bandwidth (EMB)
of laser optimized Multimode Fiber (MMF) at a specified wavelength,
.lamda..sub.S, based on the measured EMB at a first reference
measurement wavelength, .lamda..sub.M. In these methods the
Differential Mode Delay (DMD) of a MMF is measured and the
Effective Modal Bandwidth (EMB) is computed at a first measurement
wavelength. By extracting signal features such as centroids, peak
power, pulse widths, and skews, as described in this disclosure,
the EMB can be estimated at a second specified wavelength with
different degrees of accuracy. The first method estimates the EMB
at the second specified wavelength based on measurements at the
reference wavelength. The second method predicts if the EMB at the
second specified wavelength is equal or greater than a specified
bandwidth limit.
DETAILED DESCRIPTION OF THE INVENTION
[0013] The present invention discloses novel methods to estimate
the EMB of a MMF at a desired wavelength, from measurements
performed at another wavelength. The first method, Method 1, can be
used to predict the EMB at an arbitrary wavelength, .lamda..sub.S,
based on an EMB measurement at a different wavelength,
.lamda..sub.M. The second method can be used to evaluate if the EMB
at an arbitrary wavelength, .lamda..sub.S, is equal of greater than
a minimum specified threshold. Each method provides different
degree of complexity and accuracy.
[0014] These methods can be used for the design and manufacturing
processes of MMF that have a core and a cladding where the index of
refraction of the cladding is less than that of the core. The core
has a gradient index of refraction which varies from a peak value
at the center of the core to a minimum value at the cladding
interface following a predominant alpha-profile function to
minimize modal dispersion [JLT 2012]. Refractive index profiles for
two types of MMF are shown in FIGS. 4 and 5. In FIG. 4 a
traditional MMF refractive index profile is shown. The profile 400
does not present any abrupt discontinuity inside the core or inside
the cladding. The propagating mode groups of this fiber are shown
in 410. In FIG. 5 the refractive index profile 500 abruptly changes
in the cladding due to the refractive index trench 520 introduced
to provide lower bending loss. Labels 510 and 515 shows some of the
propagating and leaking mode groups respectively.
[0015] Waveguide theory for alpha-profile fibers has been well
developed [ref]. The theory can enable the modeling of fiber DMD
behavior over a broad range of wavelengths, when the profiles and
dopants concentrations are known. In practice however, due to
manufacturing variations the designed "optimum" refractive index
profile is distorted deterministically and randomly. Very small
alterations in 400 or 500, basically change the way the mode groups
410, 510 interact with the variations in refractive index, which
destroys or reduces the correlations among DMDs at different
wavelengths as it was showed in FIG. 3.
Method 1
[0016] This method, can be used to predict the EMB at an arbitrary
wavelength, .lamda..sub.S, based on an EMB measurement at a
different wavelength, .lamda..sub.M. The method was developed based
on the inventors' realization that in order to increase the
correlation among EMB measurements at .lamda..sub.M, and a second
wavelength, .lamda..sub.S, a new approach that fully utilizes the
information provided by the measured DMD waveforms is required. The
method proposed here uses the DMD pulse waveform information at
.lamda..sub.M, such as centroids, peak position, width, shapes,
energy per radial offset, and skews, to predict the EMB at a second
wavelength. Statistical and signal processing techniques disclosed
here, allow us to extract and utilize those parameters to distort
the DMD pulse waveforms acquired at .lamda..sub.M, to predict the
DMD pulse waveforms at .lamda..sub.S. This method which requires a
training of the algorithm, enables the prediction of EMBs at
different wavelengths from one measurement. FIGS. 6 and 7 show the
block diagrams for the training and estimation processes
respectively. For illustrative purposes, we use an example to
describe both methods.
Training for Method 1
[0017] In 600, the populations of TIA-492AAAD standards compliant
OM4 fibers from two suppliers (A and B), which use different
manufacturing processes are selected. It is understood that the
population used here is only an example and is not restricted to
any specific number of fiber suppliers. In 602, we select a subset
of 24 fibers from manufacturer A and 12 from manufacturer B for
training. In 604, the DMD of all fibers are measured at the first
measurement wavelength, .lamda..sub.M=850 nm, and the second
specified wavelength, .lamda..sub.S, which in this example is taken
to be 953 nm. These measurements are stored in the array y(r, t,
.lamda.) for analysis. FIGS. 8(a) and 8(b) show the DMD radial
pulses for three MMF from each population at 850 nm (dark trace)
and 953 nm (lighter trace). FIGS. 8(a) and 8(b) show that most of
the fibers have similar DMD pulses at low radial offset for both
wavelengths. For population A, the DMD pulse shapes are very
different at larger radial offset for the two wavelengths.
[0018] The EMBs computed from the measured DMD pulses for the A and
B populations at 850 nm and 953 nm are shown in FIG. 9. These
measurements agree with simulation results showed in FIG. 3, which
indicates that EMBs at different wavelengths are uncorrelated.
[0019] In step 606 of FIG. 6, the main features of the DMD pulses
at each wavelength are extracted. This process captures the main
characteristics required to describe the DMD pulses at each radial
offset and each wavelength for post-processing and analysis. As an
illustrative example, here we extract the centroid, mean power,
peak power value and position, and the root mean square (RMS)
width. The centroid feature is computed using,
C r , .lamda. = k t k y ( r , t k , .lamda. ) k y ( r , t k ,
.lamda. ) ( 1 ) ##EQU00001##
where r is the radial offset index that relates the position of the
single-mode launch fiber to the MMF core center axis during the DMD
measurement, t is the discrete length normalized temporal, k is the
time index. The variable t and k are related to the number of
temporal samples simulated or acquired from the oscilloscope during
DMD measurements at a given wavelength. The mean power is computed
by,
Ymean r , .lamda. = k y ( r , t k , .lamda. ) k t k ( 2 )
##EQU00002##
The peak power is computed using,
Ypeak.sub.r,.lamda.=max.sub.t(y(r,t,.lamda.)) (3)
where max.sub.t(.) is a function that finds the maximum of the DMD
pulses for each radial offset and for each wavelength. The peak
position is computed using.
P.sub.r,.lamda.=find_peak(y(r,t,.lamda.)) (4)
where, find_peak is a function that finds the maximum value of the
DMD pulses for each radial offset and for each wavelength. The RMS
width of the pulse for each radial offset is computed,
W r , .lamda. = k ( t k - C r , .lamda. ) 2 y ( r , t , .lamda. ) k
y ( r , t k , .lamda. ) - ( T REF ) 2 ( 5 ) ##EQU00003##
where T.sub.REF is the RMS width of the reference pulse used for
the measurement. The features extracted from DMD measurements at
.lamda..sub.M, are used to predict features at .lamda..sub.S, based
on the model described in equations (6-8).
C.sub.r,.lamda..sub.S=(1+I.sub.C(r))C.sub.r,.lamda..sub.M+F.sub.C(.lamda-
..sub.M,.lamda..sub.S)G.sub.C(r) (6)
where C.sub.r, .lamda..sub.S, and C.sub.t,.lamda..sub.M represent
the centroids per radial offset at .lamda..sub.M and .lamda..sub.S,
I.sub.C(.,.),F.sub.C(.,.),G.sub.C(.)is the set of polynomial
functions that describe the relationship between centroids at those
wavelengths.
P.sub.r,.lamda..sub.S=(1+I.sub.P(r))P.sub.r,.lamda..sub.M+F.sub.P(.lamda-
..sub.M,.lamda..sub.S)G.sub.P(r) (7)
where P.sub.r,.lamda..sub.S, and P.sub.r,.lamda..sub.M represent
the centroids per radial offset at .lamda..sub.M and .lamda..sub.S,
I.sub.P(.,.), F.sub.P(.,.),G.sub.P(.) is the set of polynomial
functions that describe the relationship between peak positions at
those wavelengths.
W.sub.r,.lamda..sub.S=(1+I.sub.W(r))W.sub.r,.lamda..sub.M+F.sub.W(.lamda-
..sub.M,.lamda..sub.S)G.sub.W(r) (8)
where W.sub.r,.lamda..sub.S, and W.sub.r,.lamda.M represent the
centroids per radial offset at .lamda..sub.M and .lamda..sub.S,
I.sub.W(.,.),F,.sub.W(.,.),G.sub.W(.) is the set of polynomial
functions that describe the relationship between widths at those
wavelengths.
[0020] The F(.,.) functions are solely dependent on the measured
and targeted wavelength. These functions accommodate for chromatic
effects in the refractive index and material. The G(.) functions
are solely dependent on radial offsets and accommodate for
relationships between the group velocity of DMD pulses at different
radial offset in the fiber core. The I(.) functions, dependent on
the radial offset, accommodates for mode transition due to the
change of wavelengths.
[0021] In step 608, the features extracted from the measured DMD
pulses at the two wavelengths are used to find the coefficients of
the polynomial functions described above (6-8). Standard curve
fitting techniques are applied as described in [3]. For the samples
used in this example, FIGS. 10(a) and (b), show the centroid
features for 850 nm and 953 nm for radial offsets from 1 to 24
microns for the two fiber populations A (red) and B (blue). FIGS.
11(a) and (b), show the peak positions for 850 nm and 953 nm for
radial offsets from 1 to 24 microns for the two fiber populations.
For these samples, F(850,953) was 16 ps/.mu.m/km for population A
and 13.3 ps/.mu.m/km for population B. The functions G.sub.C(.,.)
and G.sub.P(.,.) for a cubic polynomial curve fitting is shown in
FIGS. 12(a) and 12(b) for fiber populations A and B respectively.
Similarly, curves for the other features described above (1-5) are
obtained.
[0022] In 610 the correlations among the features, i.e. the ones
shown in FIGS. 1-12 are evaluated. If they are higher than a
determined threshold, e.g., 80%, the model is ready to use and the
process end in 615. If not, in 612 the signal to noise ratio (SNR)
of all DMD measurements are evaluated. If the noise of the
measurements is higher than a pre-determine threshold, the
measurements need to be repeated. If the SNR is high, but the
correlations are low, it is possible that the samples do not
represent the fiber population and a new set of samples will be
required.
Method 2: Estimation Method
[0023] After training, the method for the DMD mapping and
estimation, shown in FIG. 7, is ready to use. Here, we use the same
example to describe the processes. In 700 the fibers that require
EMB estimation are selected. In 702, the model described in (6-8)
and the wavelengths (in this case .lamda..sub.M=850 nm ,
.lamda..sub.S,=953nm) are selected. In 704, the DMD at
.lamda..sub.M is measured. In 706 the features are extracted from
the DMD pulse centroids at .lamda..sub.M using equations (1-5). In
708 the DMD pulses are estimated at .lamda..sub.S. Next, the model
described in equations (6-8) is used to estimate the features
C.sub.r,.lamda..sub.S, P.sub.r,.lamda..sub.S,W.sub.r,.lamda..sub.S,
Ymax.sub.r,.lamda..sub.S Ymean.sub.r,.lamda..sub.S at
.lamda..sub.S.
[0024] The parameter P.sub.r,.lamda..sub.S is used to reposition
each of the DMD pulses using,
Y.sub.P(r,t.sub.k,.lamda..sub.S)=y(r,t.sub.k-(P.sub.r,.lamda..sub.S-P.su-
b.r,.lamda..sub.M, .lamda..sub.M) (9)
[0025] where the y.sub.P(.,.,.) array represents the estimated DMD
pulses after the peak position correction.
[0026] The differences between the centroid and peak position are
computed at both wavelengths. The variation of these differences
are computed as shown,
.DELTA.=(C.sub.r,.lamda..sub.S-P.sub.r,.lamda..sub.S)-(C.sub.r,.lamda..s-
ub.M-P.sub.r,.lamda..sub.M) (10)
[0027] The parameter .DELTA. is used to estimate the new width and
skew of the DMD pulses at .lamda..sub.S. In the majority of cases,
when, .lamda..sub.S>.lamda..sub.M, the DMD pulse width tends to
increase. Conversely, when .lamda..sub.S<.lamda..sub.M, the
width tends to decrease. The changes in skew and width are
corrected using a linear filter as shown,
y W ( r , t k , .lamda. S ) = i = 0 Ntaps A i y p ( r , t k - Ki
.DELTA. , .lamda. S ) ( 11 ) ##EQU00004##
where y.sub.W(.,.,.) represents the estimated DMD after
equalization, i is the equalizer tap index, Ntaps the number of
taps, A.sub.i represents the tap coefficient, K is a scaling
factor.
[0028] For each fiber, the optimum values of Ntaps, A.sub.i, and K,
are found by numerically searching. The constraint conditions or
equations for this search are the estimated mean, peak, and the
values shown in table I.
TABLE-US-00001 TABLE I k y W ( r , t k , .lamda. S ) k t k .ltoreq.
Ymean r , .lamda. S ##EQU00005## max.sub.t (y.sub.W (r, t.sub.k,
.lamda..sub.S)) .ltoreq. Ypeak.sub.r,.lamda..sub.S k ( t k - C r ,
.lamda. ) 2 y W ( r , t k , .lamda. S ) k y W ( r , t k , .lamda. S
) .ltoreq. W r , .lamda. S ##EQU00006##
[0029] In 710, the algorithm evaluates if the conditions shown
above can be maintained below a pre-determined threshold, e.g., 60%
of the estimated constraint' values. If that is not achieved, in
712 the SNR of the DMD measurement is evaluated. Depending on this,
the DMD may need to be measured again 704. Otherwise, in 717 it is
indicated that the estimation failed. If the conditions compared in
710 are achieved, the algorithm provides the DMD corrected pulses
and the estimated EMB is obtained.
[0030] FIG. 13, shows the corrected DMD results for populations A
and B. In FIG. 14 the estimated and measured bandwidths at
.lamda..sub.S=953 nm are shown. The correlation for these results
is around 80%-90%.
Method 2
[0031] This method can be used to predict if the EMB at an
arbitrary second wavelength, .lamda..sub.S, is equal or greater
than a specified threshold, EMB.sub.th, based on a DMD measurement
at a different wavelength, .lamda..sub.M. As in the previous case
this method utilizes features of the DMD pulse waveforms at
.lamda..sub.M, such as centroids, peak position, width, shapes,
energy per radial offset, and skews. The average centroid for
positions R.sub.t.sub._.sub.start-R.sub.t.sub._.sub.end is defined
using,
C Top ( R T _ start , R T _ end ) = r = T T _ end R T _ end C r
.lamda. M R T _ end - R T _ start + 1 ( 12 ) ##EQU00007##
The average centroid for positions RB.sub.--start-RB.sub.--end is
defined using,
C Bottom ( R B _ start , R B _ end ) = r = R B _ end R B _ end C r
, .lamda. M R B _ end - R B _ start + 1 ( 13 ) ##EQU00008##
[0032] A function denominated, P-Shift is computed as
P-Shift(R.sub.T.sub._.sub.start,R.sub.T.sub._.sub.end,R.sub.B.sub._.sub.-
start,R.sub.B.sub._.sub.end)=C.sub.Top(R.sub.T.sub._.sub.start,R.sub.T.sub-
._.sub.end)-C.sub.Bottom(R.sub.B.sub.--start,R.sub.B.sub.--end)
(14)
[0033] The slopes using the peak pulse position for two or more
radial regions are computed as shown in equation below.
P - Slope_R k = 1 L r = R _ start k R _ end k ( P r .lamda. m - T k
) ( r - ( R_end k + R_start k ) / 2 ) r = R _ start k R _ end k ( r
- ( R_end k + R_start k ) / 2 ) 2 ( 15 ) ##EQU00009##
where k is the index that represent the selected radial offset
regions and
T k = 1 R_end k - R_start k + 1 r = R _ start k R _ end k P r
.lamda. m ( 16 ) ##EQU00010##
The widths for the same k regions that are computed using:
M - Width k = 1 L [ max r = R _ start k : R end k ( W ( r ) ) ] (
17 ) ##EQU00011##
[0034] It should be noted for features described in (15-17), the k
index can take values from 1 to N.sub.k where N.sub.k<25 r of
radial offsets, i.e. 25. In practice, as shown in the algorithm
training example described below, low values for Nk, i.e.
N.sub.k=2, are enough to provide estimations with low
uncertainty.
[0035] The training method, which is described below, utilize
machine learning techniques to find the radial-offset regions that
maximize the difference between parameters such as P_shift,
P_slopes and M_widths for two or more population of fibers. One
population of fiber will have EMB>EMB.sub.th at .lamda..sub.S
and other populations will not satisfy this constraint. After
training the estimation method simply evaluates if the extracted
features from MMF under test belong to the regions found during
training that satisfy the condition, EMB>EMB.sub.th at
.lamda..sub.S based on the DMD measurements at .lamda..sub.M.
Training for Method 2
[0036] The training process is identical to the one shown in FIG.
6, with exception of steps 606 and 608. We use the same example,
starting from 606 of FIG. 6, to illustrate the training method.
[0037] In step 606, the main features of the DMD pulses at
.lamda..sub.M, are extracted. Note the differences with the first
method which require the computation of the features at each
wavelength, .lamda..sub.M and .lamda..sub.S. The extracted features
are C.sub.r,.lamda..sub.M, P.sub.r, .lamda..sub.M and
W.sub.r,.lamda..sub.M (centroid, peak and width) using equations
(1-5).
[0038] In 608, the training is performed. The training is an
iterative process that has the goal to maximize a metric or a
series of metrics that represents the differences in features of
two groups of fibers. One group, Group 1 are composed by the MMFs
that have EMB>EMB.sub.th at .lamda..sub.S and the other group,
Group 2 by MMFs that have EMB<EMB.sub.th at .lamda..sub.S.
Initially, all the MMFs used for training are mapped in a space
defined by the P_shift, P_slopes and M_widths. The initial values
of the regions utilized in (12-17) which are
{R.sub.B.sub._.sub.start,R.sub.B.sub.--end},
{R.sub.T.sub._.sub.start,R.sub.T.sub._.sub.end},
{R_start.sub.k,R_end.sub.k} are set to random values.
[0039] In this example, the utilized metric is a function
implemented in C, Python, or Matlab, which computes p-norm
distances in the mentioned space, among the MMFs that belong to the
groups Group 1 and Group 2.
M ( R T _ start , R T _ end , R B _ start , R_start 1 , R_end 1 , ,
R_start N k , R_end N k ) = { ( P_Shift _Group1 - P_Shift _Group2 )
p + k = 1 N k A 1 , k ( P_Slopes _Group1 k - P_Slopes _Group2 k ) p
++ k = 1 N k A 2 , k ( M_Width _Group1 k - M_Width1 _Group2 k ) p }
1 / p , ( 18 ) ##EQU00012##
where A.sub.1,k, A.sub.2,k are weight parameters to quantify the
relative importance of each features and/or radial offset
regions.
[0040] In each iteration the coordinate axes are modified by
changing the values of {R.sub.B.sub._.sub.start,
R.sub.B.sub._.sub.end},{R.sub.T.sub._.sub.start,R.sub.T.sub._.sub.end},
and the set of k parameters {R_start.sub.k,R_end.sub.k}. In
addition, the norm parameter p and the weights, can be also
optimized in each iteration. During the optimization process, the
values can be changed at random, or in deterministic ways. For
example, using the random search algorithms or using gradient
methods. The features are recomputed using (12-17) for each new set
of regions. The MMFs are mapped in the new space and the utilized
metric, i.e. equation (18) is computed. The process continue until
the metric is maximized, or until an exhaustive search is
produced.
[0041] To illustrate how the algorithm improves the metric in each
iteration we use a set of 35 MMFs. For sake of simplicity we
utilize N.sub.k=2, A.sub.1,1-A.sub.1,2-1, and p=1 and the following
simplified version of the metric, (18)
M ( R T _ start , R T _ end , R B _ end , R_start 1 , R_start 2 ,
R_end 2 ) = { ( P_Shift _Group1 - P_Shift _Group2 ) p + k = 1 2 A 1
, k ( P_Slopes _Group1 k - P_Slopes _Group2 k ) } ( 19 )
##EQU00013##
[0042] FIG. 15 shows initial mapping of the population for one to
8000 iterations. In the figure. the square markers represent MMF
from Group 1 and the circle markers represents MMFs from Group 2.
It can be observed that for the initial iterations 1-5000, FIGS.
15(a), (b), (c), (d) and (e) it is not possible to differentiate
between both populations. After 7000 iterations the algorithm
capable of separate MMF from Group 1 and Group 2. The boundaries
between the groups, Group 1 and Group 2, in the plane shown in FIG.
15(i) can be established (see black trace). Based on this
classification the optimum radial offset that optimizes the feature
extraction from the DMD pulse waveforms was found. The values of
the found regions are: 2 to 10 micron radial offsets for the first
P-Slope (k=1), 12 to 23 microns for the second P-Slope (k=2). For
the P-shift calculation shown in (14), the optimum regions were 2
to 3 microns for C_Top and 18-24 microns for the C_Bottom
[0043] The training using the disclosed algorithm demonstrates that
the MMFs for Group 1 and Group 2 have distinctive features that can
be observed when the optimum set of radial regions to represent
them are selected. These results demonstrate a method to predict if
EMB>EMB.sub.th at .lamda..sub.S based on the DMD measurements at
.lamda..sub.M.
Estimation Method
[0044] During training the optimum radial-offset regions to extract
the features that optimally represent MMFs that have
EMB.sub.S>EMB.sub.th at .lamda..sub.S were found. In the
feature-space, see for example FIG. 15(i), the Groups of MMFs that
have the desired characteristics can be separated by a line or in
general by a polynomial that isolate two regions one for Group 1
and another for Group 2. For the estimation process the features of
a MMF are extracted from DMD measurements at .lamda..sub.M and
mapped in the feature-space. If the MMF belongs to the desired
regions that produce EMB>EMB.sub.th at .lamda..sub.S (see FIG.
17 the fiber is accepted. Otherwise the fiber is rejected.
[0045] Note that while this invention has been described in terms
of several embodiments, these embodiments are non-limiting
(regardless of whether they have been labeled as exemplary or not),
and there are alterations, permutations, and equivalents, which
fall within the scope of this invention. Additionally, the
described embodiments should not be interpreted as mutually
exclusive, and should instead be understood as potentially
combinable if such combinations are permissive. It should also be
noted that there are many alternative ways of implementing the
methods and apparatuses of the present invention. It is therefore
intended that claims that may follow be interpreted as including
all such alterations, permutations, and equivalents as fall within
the true spirit and scope of the present invention.
[0046] Also note that nothing in this disclosure should be
considered as limiting and all instances of the invention described
herein should be considered exemplary.
* * * * *