Note: Descriptions are shown in the official language in which they were submitted.
CA 02479081 2007-02-05
METHOD AND APPARATUS FOR PROVIDING POLARIZATION INSENSITIVE
SIGNAL PROCESSING FOR INTERFEROMETRIC SENSORS
CROSS-REFERENCE TO RELATED APPLICATIONS
[00011 This application contains subject matter that is related to the subject
matter
described in U.S. patent number 7,019,837 and U.S. patent number 7,088,878.
BACKGROUND OF THE INVENTION
Field of the Invention
[0002] The present invention relates to interferometric sensors and, more
particularly, the present invention relates to a method and apparatus for
providing
polarization-induced phase noise insensitive signal processing for
interferometric
sensors.
Description of the Related Art
[0003] When using interferometric sensors, the input light to the sensor is
split into
two paths (i.e., a reference path and a sensor path) and recombined. The
reference
path is a path from the transmitter to the receiver via a first path of the
sensor, while the
sensor path is the path from the transmitter to the receiver via a second path
of the
sensor. The path that experiences a length change due to a disturbance within
the
sensor, usually the longest path, forms the sensor path and the other path
forms the
reference path. The portions of fiber that are common to both the sensor path
and the
reference path define the lead fibers. The light beams that travel along the
two paths
are combined to form an interference signal that is altered by the magnitude
of the
disturbance. If the nominal path lengths are different, the interferometer is
said to be
unbalanced, and the imbalance is equal to the difference in time-delay
experienced by
the light propagating in the two paths. The change in length difference
between the two
paths is measured by extracting the phase of the interference between the
light that
has propagated the two paths. The visibility of the interference depends on
the state of
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polarization (SOP) of the two interfering light beams. The SOP of the two
interfering
light beams depends on the input polarization state into the interferometer as
well as
the retardance and the orientation of the polarization eigenstates of the two
paths of the
interferometer. Although the SOP of the light propagating in the reference and
sensor
paths may begin parallel, the propagation along the fibers may alter the SOP
of each
light beam such that the SOPs of the two interfering light beams may no longer
be
parallel. As the SOP of the interfering light beams approach orthogonality,
the visibility
worsens, and if SOPs are orthogonai, the visibility is zero and the
interference signal
can not be measured. This effect is known as polarization fading. The
interferometer
has two polarization eigenstates that represent the maximum and minimum phase
of
the interferometer. Depending on the input SOP, the measured interferometer
phase
can be any value between the phases of the two polarization eigenstates. Thus,
if the
sensor is birefringent, fluctuations in the SOP of the lead fiber will induce
phase noise.
[0004] In an application such as interferometric seismic sensor monitoring,
the lead
fiber from the interrogation unit to the sensor can be of substantial length
and sensitive
to environmental effects such as vibrations, bending and temperature. The
noise
performance of such sensor arrays may be limited by the polarization
fluctuations in the
lead fiber induced by environmental effects. See A. D. Kersey, M. J. Marrone,
and A.
Dandridge, "Observation Of Input-Polarization-Induced Phase Noise In
interferometric
Fiber-Optic Sensors", Optics Letters, 13(10):847-849, 1988.
[0005j Several methods have been proposed to eliminate the problem of
polarization fading in interferometric sensors while there are few methods
that eliminate
the phase noise that is induced by variations in the input polarization to the
sensor and
the retardance variations in the sensor. The polarization-induced phase noise
can be
eliminated using depolarized liight; however this method does not solve the
fading
problem. See A. D. Kersey, M. J. Marrone, and A. Dandridge, "Analysis Of Input-
Polarization Induced Phase Noise In lnterFerometric Fiber-Optic Sensors And
Its
Reduction Using Polarization Scrambling", IEEE Journal of Lightwave
Technology,
8(6):338-845, 1990.
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[00061 Several methods for reduction or elimination of the polarization fading
problem are known. One known method uses Faraday rotating mirrors, as
disclosed by
A.D. Kersey et ai. in "Polarisation Insensitive Fibre Optic Michelson
lnterferometer", El.
Lett., Vol. 27, pp 518-19, 1991. This method allows for a simple source and
detection
system, but it works only for a Michelson interferometer configuration.
Furthermore, the
Faraday rotating mirrors may be expensive, space consuming, and sensitive to
extreme
thermal, electromagnetic and other environmental conditions.
[0007] Another widely used method is to use a polarization diversity receiver
based
on three polarizers that are angularly spaced by 120', and the output with
best visibility
is selected. See N.J. Frigo et. al in "Technique For Elimination Of
Polarization Fading In
Interferometers", El. Lett. Vol 20, pp. 319-320, 1984.
[0008] Other known methods are based on active polarization control at the
input to
optimize the visibility of the ii?terference, as disclosed by A. D. Kersey et.
al. in
"Optimization And Stabilization Of Visibility In Interferometric Fiber-Optic
Sensors Using
Input-Polarization Control", J. of Lightwave Technol., Vol. 6, pp. 1599-1609,
1988.
When several sensors are multiplexed, this method requires input-polarization
control
of each multiplexed sensor, which makes it impractical for remote and
inaccessible
sensor arrays. Alternatively, one can optimize the visibility of the worst
sensor in the
array. See M. Tur et. al. in "Polarization-Induced Fading In Fiber-Optic
Sensor Arrays",
J. of Lightwave Technol., Vol. 13, pp. 1269-1276, 1995. A statistical
treatment shows,
the probability that the visibility is larger than 0.6 for all sensors in a 10-
element sensor
array is 80 %, however the visibility worsens as the number of sensors is
increased.
The visibility can also be optimized by the use of the polarizer combined with
active
polarization control at the output end, as disclosed by K. H. Wanser et. al.
in "Remote
Polarization Control For Fiber-Optic Interferometers", Opt. Lett., Vol. 12,
pp. 217-19,
1987. In both cases the polarization controller is continuously adjusted to
optimize the
fringe visibility. These techniques require relatively complex systems to
provide
feedback signals to the polarization controller. The polarization modulator
used for the
polarization control must be capable of modulating the SOP in three dimensions
on the
Poincare sphere.
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[0009] The only previously reported method that eliminates polarization
induced
fading and noise, is based on modulation of the SOP between two polarizations
with a
modulation frequency that is an odd multiple of one fourth of the free
spectral range
(FSR) of the sensor, and detection of four independent interference signals.
See E.
Ronnekleiv in "Elimination Of Polarization Fading", International patent
application
number WO 00/79335 (filed June 22, 2000). In systems that employ a continuous
wave
source such as wavelength division multiplexing (WDM), the minimum modulation
frequency of one fourth of the sensor FSR, gives a minimum detection bandwidth
equal
to the sensor FSR. In conventional CW interrogation, the minimum detection
bandwidth
is given by the information bandwidth of the interferometric signal. Thus, the
minimum
detection bandwidth required for this method is much larger than necessary for
CW
interrogation of interferometric sensors. In time division multiplexing(TDM)
two-pulse
interrogation, as disclosed in J.P. Darkin in "An Optical Sensing System", UK
patent
application number 2126820A (filed July 17, 1982), the four independent
interference
signals must appear within one sensor imbalance. Thus, the source polarization
must
be modulated with a modulation frequency that is at least 5/4 of the sensor
FSR, which
is the inverse of the sensor imbalance. The duration of the detected pulses is
at
maximum 1/5 of the duration of the detected pulses with conventional two-pulse
interrogation, and thus the detection bandwidth is at least five times higher.
For a
typical sensor imbalance of 5 m, the FSR is equal to 20 MHz, and the required
detection bandwidth must be at least 100 MHz. This high detection bandwidth
makes
this method impractical for TDM two-pulse interrogation.
[0010] Therefore, there is a need in the art for a method and apparatus that
eliminates the polarization-induced signal fading and provides polarization-
induced
phase noise insensitive signal processing for interferometric sensors.
SUMMARY OF THE INVENTION
[0011] The invention provides a method and apparatus that uses specific source
modulation and/or unique detectors to measure a response Jones matrix as a
measure
for the sensor Jones matrix, which describes the polarization dependent
response from
the sensor. The response Jones matrix describes the propagation through the
sensor
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path relative to the reference path and depends on the lead fiber
birefringence. The
difference and average of the phase of the two eigenvalues of the sensor Jones
matrix
can be used as a measure for differential birefringence phase and common mode
phase in the interferometer, respectively. Even though the response Jones
matrix and
the sensor Jones matrix may be different, the phase of the eigenvalues will be
equal for
the two matrices. Thus, these phase measurements are unaffected by lead fiber
birefringence.
[0012] In a first embodiment of the invention, a pulsed source for the
interferometric
sensor array is used. The SOP of the interrogation pulses is controlled
individually so
that two interfering pulses may originate from interrogation pulses that have
different
SOP such that at least four components of the detected signal can be separated
and
processed to extract a phase measurement from the response Jones matrix
without
error caused by polarization induced fading or noise caused by birefringence
fluctuations in the lead fibers.
[0013] In a second embodiment, the at least four signal components that are
required for a measurement of the response Jones matrix are separated by
continuous
or stepwise modulation of transmitter output SOP along a predefined path on
the
Poincare sphere through at least four polarization states that can be
represented by
four independent Stokes vectors and detection of at least four independent
signal
components of the generated output intensity modulation.
[0014] In a third embodiment, the source light is depolarized and a receiver
incorporates polarizers, where each of the polarizers transmits a different
SOP that
defines a set of eigenpolarization states. The eigenpolarization states can be
represented by at least four independent Stokes vectors, and the response
matrix is
found from the outputs of the polarizers. It follows from reciprocity that the
measurement provided by the third embodiment is equivalent to the measurement
provided by the second embodiment.
[0015] A fourth embodiment combines the modulation of the transmitter output
SOP
of the second embodiment with the polarization diversity receiver of the third
embodiment. The transmitter output SOP is modulated through a set of states
that
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includes at least three independent Stokes vectors and the polarizers within
the
polarization diversity receiver defines a set of eigenpolarizations that can
be
represented by two independent Stokes vectors. This may give six independent
signal
components from which the response matrix can be found.
[0016] A fifth embodiment is a reciprocal version of the fourth embodiment
where
the transmitter output SOP is modulated through a set of states that includes
at least
two independent Stokes vectors and the polarizers within the polarization
diversity
receiver defines a set of eigenpolarizations that can be represented by three
independent Stokes vectors.
[0017] These embodiments may be used with various modulation formats including
homodyne and heterodyne techniques and multiplexing techniques including time
division multiplexing (TDM), wavelength division multiplexing (WDM), frequency
division multiplexing (FDM) or combinations thereof.
BRIEF DESCRIPTION OF THE DRAWINGS
[0018] So that the manner in which the above recited features of the present
invention are attained and can be understood in detail, a more particular
description of
the invention, briefly summarized above, may be had by reference to the
embodiments
thereof which are illustrated in the appended drawings.
[0019] It is to be noted, however, that the appended drawings illustrate only
typical
embodiments of this invention and are therefore not to be considered limiting
of its
scope, for the invention may admit to other equally effective embodiments.
[0020] Figure 1 depicts a block diagram of a first embodiment of the present
invention;
[0021] Figure 2 depicts a timing diagram for the embodiment in Figure 1;
[0022] Figure 3 is a block diagram of a second embodiment of the present
invention;
[0023] Figure 4 is a block diagram of a third embodiment of the present
invention;
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[00241 Figure 5 is a further detaiied block diagram of a source used with the
third
embodiment;
[00251 Figure 6 is a block diagram of a test set up for testing the first
embodiment of
the invention;
[00261 Figures 7A, 7B and 7C depict graphs of the demodulated phase and
visibility
of each of four demodulated polarization channels for the test set up of
Figure 6; and
[0027] Figure 8 shows the simultaneously measured demodulated phase of all
four
time-division multiplexed sensors in the test set up of Figure 6.
DETAILED DESCRIPTION
[0028] Figure 1 depicts a first embodiment of the present invention
incorporated into
an optical interferometer sensor system 100. The optical interferometer sensor
system
100 comprises a transmitter 101, a receiver 107, an optical circulator 116, a
sensor
array 102, and a control and signal processing unit 122. The transmitter 101
comprises
a source 104, a Mach-Zender switch 103, a phase modulator 105 and a
polarization
modulator 106. The receiver 107 comprises a detector 118, a sample-and-hold
(S/H)
circuit 132 and an analog-to-digital (A/D) converter 134. The source 104 is a
light
source such as a laser. The light from the source 104 is pulsed by switch 103,
phase
modulated by phase modulator 105 and polarization modulated by the modulator
106 to
form polarization-induced phase noise insensitive interrogation pulses as
described
below. Preferably, the fibers that interconnect components within the
transmitter
should be polarization maintaining fibers so that the polarization into the
polarization
modulator 106 does not vary. T'he modulated light produced by the transmitter
101 is
coupled to the sensor array 102 through the circulator 116.
[00291 The sensor array 102 may comprise one or more Fabry-Perot (FP)
interferometers having a lead fiber optic cable 114, a reference reflector
108, at least
one length of fiber optic cable 112 and at least one sensor reflector 110. The
FP
interferometer sensor array 102 may contain multiple sensors that may be
positioned
along one or more parallel fibers that branch from the lead fiber 114. A
sensor is
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formed by a length of fiber between reflectors (e.g. fiber 112 between
reflectors 108
and 110). The reflectors 108 and 110 may be fiber Bragg gratings (FBG) that
are
formed along the fiber. Other forms of interferometers will function in the
context of the
present invention including Michelson interferometers, Mach-Zender (MZ)
interferometers, and the like. In each form of interferometer, the amplitude
of the
reflected interference signal at detector 118 varies according to the phase
difference
between the light that has propagated the sensor path (lead fiber 114, fiber
112 and
reflector 110) and the light that has propagated the reference path (in the FP
interferometer, the reference arm is lead fiber 114 and reference reflector
108). The
circulator 116 channels light that is reflected from the sensor array 102 to
the detector
118. It is also possible to use a directional coupler for this purpose. The
analog output
of the detector 118 is processed by the S/H circuit 132 and digitized by the
A/D
converter 134. The interference signal of combined light components from both
paths
is measured and changes in the pattern indicate a relative physical
disturbance of the
sensor.
[0030) The source 104, the switch 103, the phase modulator 105 and the
polarization modulator 106 are controlled by the control and signal processing
unit 122.
The control and signal processing unit 122 comprises a central processing unit
(CPU)
124, support circuits 126 and memory 128. The CPU 124 may be any processing
unit
that is capable of signal processing as well as controlling system
functionality.
Although a single CPU 124 is shown and discussed herein, those skilled in the
art will
realize that multiple processing units may be used wherein one processing unit
may be
used for controlling the components of the transmitter and another processor
may be
used for signal processing. The support circuits 126 comprise well known
circuits such
as cache, power supplies, timing circuitry, input/output circuits, and the
like. The
memory 128 may comprise one or more of random access memory, read only memory,
removable storage, disk drive storage, and the like. The memory 128 stores
signal
processing software that facilitates computing the sensor phase for the
reflected signals
from the sensor array 102.
[0031] One embodiment of the invention uses time division multiplexing (TDM)
to
form the interrogation signal by controlling the source 104, the switch 103,
the phase
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modulator 105 and the polarization modulator 106. In one version of TDM pulsed
interrogation of the interferometric sensors, two interrogation pulses are
generated
within each repetition period Tr. The second pulse propagating in the short
(reference)
path of the interferometer and the first pulse propagating in the long
(sensing) path of
the interferometer will overiap at the detector if the separation between the
end of the
first pulse and the start of thre second pulse is less than the sensor
imbalance.
Maximum overlap is achieved when the delay between the start of the first
pulse and
the start of the second pulse is equal to the sensor imbalance. The phase
modulator
105 induces a phase shift ~(n) between the two pulses of each pulse pair,
where n is a
number that increases by one for each repetition period Tr. The reflected
signals from
different sensors will arrive at different times due to the spatial
distribution of the
sensors. The repetition period is selected such that reflected signals from
all
multiplexed sensors are received within one period. The phase modulation a~(n)
between the interrogation pulses of each pulse pair results in one or a
plurality of sub-
carriers on the interference signal from which the amplitude and sensor phase
are
calculated. In this embodiment, the phase difference is iinear, i.e. ~(n)
=wnTr, where w
is the sub-carrier frequency, resulting in only one sub-carrier on the
interference signal.
In other modulation techniques, such as phase-generated carrier modulation,
~(n) is
not a linear function, which results in several sub-carriers on the
interference signal.
f0032, The response Jones matrix is found by switching of the source
polarization.
Let Eo(n)=LEo,,(n) Eoy(n)]T and E1(n)-[E1x(n) E1y(n)]T exp(-=J ~(n)) be
the.Jones vector
describing the state of polarization (SOP) of the first and the second
interrogation
pulse, respectively. The switch 103 forms the pulses of light, the phase
modulator 105
applies the phase modulation a~(n) to the second pulse, and the polarization
modulator
106 switches the polarization of each pulse. The second pulse propagating in
the short
(reference) path of the interferometer and the first pulse propagating in the
long
(sensing) path of the interferometer will interfere at the detector. The SOP
of the
pulses that have propagated in the reference path Er(n) and the sensing path
ES(n) are
given by,
E,{n) = BuBdE1(n) (1)
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Es(n) = BuRsBaEo(n) (2)
where Bd is the Jones matrix describing the down-lead fiber from the source to
the
sensor, B. is the Jones matrix describing the up-lead fiber from the sensor to
the
detector, and RS is the Jones matrix of the sensor. The response Jones matrix
is
defined as R=B aB u BõRSBd . The interference between Er(n) and ES(n) is given
by,
I(n) = 2RefEY(n)X Es(n)} = 2Re{ Ei (n) BdBuBURSBaEo(n)} (3)
= 2Re{E; (n) REo(n)} = 2Re{[RxxE;x (n)Eox(n) + RxyE;.X (n)Eoy(n) (4)
+ R.yxE,,, (n)Eox(n ) + RYyE *, (n)Eoy(n)J exp(jconTr) .1,
where t is the conjugate transpose matrix operation and Rxx, Rxy, Ry,, and Ryy
are the
four components of R. This equation shows. that the four components of R can
be found
when a modulation is applied to the source polarization so that the four
interference
terms RxxE;X(n)Eox(n) , RxyE;.~ (n)Eoy(n), RyXE,y (n)Eox(n) and RyyE;y
(n)Eoy(n) can be
extracted from four independent measurements provided that the interrogation
Jones
matrices Eo(n) and E1(n) are known.
(0033] The sensor phase ~s is defined as 0.5 times the phase of the
determinant of
Rs, which is equal to the phase of the geometrical mean of the two
eigenvalues. It can
be shown that Ldet RS= Zdet R:
Ldet R Ldet (B d B BuRSBd)
= L((det Bd)*(det B,,)*(det BU)(det Rs)(det Bd) ) (5)
= L(IdetBd 2'detBu12 detRs) =Ldetlgs
[00341 Thus, the measured components of R can be used to calculate the sensor
phase as ~5=0.5Ldet Rs=0.5.t!det R=0.5L(R,,,Ryy-RyRyx), and the measurement of
the
sensor phase ~S can be made independent of polarization fluctuations in the
lead fiber,
and if the sensor array does not have any component with polarization
dependent loss
(PDL), the fading factor defined as the magnitude of the complex number from
which
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the sensor phase is extracted divided by the maximum interference amplitude
for any
interrogation polarization, will be constant and equal to 1.
[0035] If the lead fiber to the sensor does not comprise polarization
dependent loss
(PDL), Bõ and Bd are described by real scalars multiplied by a unitary matrix.
One
property of unitary matrices is that the inverse and the conjugate transpose
of the
matrix are equal. Then B u Bõ =k2l, where I is the identity matrix, and k is a
real scalar.
Bd only rotates the coordinate system in which the matrix RS is measured. The
eigenvalues of a matrix are independent of the orientation of the coordinate
axes. Thus
the eigenvalues of R are equal to the eigenvalues R. Once the eigenvalues of a
sensor Jones matrix is found, both the common mode sensor phase and the
differential
birefringent phase between the eigenpolarization states of the sensor can be
calculated. In a polarimetric sensor, the measurand causes changes in the
phase
between the eigenpolarizations. Thus, the present invention allows for the use
of a
single sensor as both an interferometric sensor and a polarimetric sensor. The
sensor
can then measure two physical parameters simultaneously such as temperature
and
pressure.
[0036] In one embodiment of the present invention, the polarization modulator
106
switches the transmitter output SOP between the two orthogonal polarization
states x
and y. In a sequence of four consecutive pulse pairs, both pulses of the first
pulse pair
are x-polarized, the first pulse of the second pulse pair is x-polarized and
the second is
y-polarized, both pulses of the third pulse pair are y-polarized, and the
first pulse of the
fourth pulse pair is y-polarized and the second pulse is x-polarized.
Although, these
four pulse pairs have a specific order, those skilled in art should realize
that the order of
these four pulse pairs is arbitrary. All pulse pairs in the sequence of pulse
pairs that
have the same SOPs, defines a polarization channel. These four channels are
denoted
xx, xy, yy, and yx. In each of these polarization channels, only one of the
terms,
R,,E *x (n)Eo,(n) , R,yE 1 r(n)Eoy(n) RyXE,, (n)Eox(n) and RyyE; y(n)Eoy(n)
will be non-
zero.
[0037] Figure 2 depicts a timing diagram 200 of the optical power 202, phase
204
and polarization 206 of the two interrogation pulses. The source 104 outputs
one pulse
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pair per repetition period Tr, and the phase is modulated according to timing
diagram
204. The polarization modulator 106, such as an electro-optical modulator,
switches
the polarization of the pulses according to timing diagram 206. The timing
diagram
shows the polarization of the pulses in the repeated sequence xx, xy, yx and
yy as
arrows within each pulse, which represent the four polarization channels. With
the
interrogation field intensity normalized to 1, the interFerence intensity l(n)
of the
detected pulses as a response from the interferometer interrogated by the
pulse pairs
of the four polarization channels is given by,
Polarization channel xx: I~X(m)=2ReJR. e'" T 1 m= 4n (6)
Polarization channel xy: I, (m)=2 Re~R~Ye iw'nTr ~ an = 4n +1 (7)
Polarization channel yy: IYY (m)=2 Re{R,,ye''""T }, m= 4n + 2 (8)
Polarization channel yx: Iy,x (m)=2 Re~R Jxe''"nrr 1, m= 4n + 3, (9)
[0038] The sequence I.(m) represents a harmonic varying signal with a
frequency
given by the sub-carrier frequency c). For each sub-carrier period, the phase
and
amplitude of I.(m) are calculated relative to the generated sub-carrier. The
resulting
complex number equals the RXX component of the response Jones matrix. In
polarization channel xy, yy and yx the RXy, Ryv and RyX components are
measured,
respectively.
[0039] Figure 6 depicts an experimental setup 600 for interrogation of Fabry-
Perot
star-network 602 using TDM pulsed interrogation as discussed above. The setup
600
comprises a fiber laser 604, Mach-Zender switch 606, phase modulator 608, a
first
polarization controller 658, polarization modulator 610, automatic
polarization controller
616, erbium-doped fiber amplifier 620, detector 626 and an analog-to-digital
converter
628. The hardware was controlled by controller 630 and the detected signals
were
processed by signal processor 632. The star network 602 comprises three 50150
/
couplers 632, 634 and 636, sensors 638, 640, 642 and 644 (each comprising the
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reflectors and a length of cable), delay coils 646, 648 and 650, and fibers
652, 654 and
656.
[0040] The method for elimination of polarization-induced fading and phase
noise
was tested on the Fabry-Perot star-network 602 with four sensors 638, 640, 642
and
644. Two fiber Bragg gratings (FBGs) with - 30 % refiectivity were used as
reflectors
in each of sensor. The length of the sensor coils was 18 m. The sensor coils
were
wound on PZT-cylinders and placed in an acoustically sealed box. The three
50/50 %
telemetry couplers 632, 634 and 636 were used to supply signals to the sensors
638,
640, 642 and 644. The delay coils 646, 648 and 650 were used to ensure that
the
reflections from the second, third and fourth sensor were delayed by
approximately 1
s, 2 s and 3 s compared to the first sensor reflections, respectively.
[0041] A RIN and frequency stabilized DFB fiber laser (DFB-FL) was used as
source
604. The wavelength of the source was 1548 nm, corresponding to the center
wavelength of the FBGs. The TDM repetition period was Tr=5 s. Two 140 ns
optical
pulses were generated in each repetition period by the electro-optical Mach-
Zender
switch (SW) 606. The delay from the start of the first pulse to the start of
the second
pulse was 180 ns, thus equal to the sensor imbalance. The electro-optical
phase
modulator (PM) 608 was used to modulate the phase of the second pulse relative
to the
first pulse linearly from 0 to 27r within one sub-carrier period 27r/w=80 s.
The fiber from
the switch 606 to the phase modulator 608 was polarization maintaining to
ensure
polarization independent operation. The output from the modulator 608 was
further
guided via a polarization controller (PC1) 658 that transformed the input
polarization
into an electro-optical polarization modulator (POM) 610, so that equal
amounts of
optical power were coupled into the TE mode and the TM mode of the modulator
610.
The signal applied to the POM 610 was switched between two calibrated levels.
The
phase difference between the two modes changed according to the applied signal
level,
and the POM 610 produced two orthogonal polarization states. The polarization
of the
pulse pairs was modulated in a repeated sequence of the four polarization
channels, as
illustrated in Figure 2. With this modulation scheme, each of polarization
channels
consists of four pulse pairs per sub-carrier period.
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[0042] The sequence of reflected signals from the sensor array is detected by
the
photo detector 626, and the sequence is sampled by the analog-to-digital
converter
628. The digitized signal is processed by the signal processor 630. The signal
processor unit extracts the Jones matrix of each individual sensor and
calculates the
sensor phase as 0.5 times the phase of the determinant of the Jones matrix.
[0043] The automatic polarization controller 616 that squeezes the fiber
between
two PZT-elements, emulated polarization fluctuations in the lead fiber. The
polarization
controller was driven at a frequency of 75 Hz with approximately 27
differential phase
amplitude.
[0044] Figures 7A, 7B, and 7C show the demodulated phase and the fading factor
of
each of the four demodulated polarization channels of sensor 638. The figure
also
shows the sensor phase calculated as .5L det R and the combined fading factor
calculated as Idetig 1, which is equal to the geometrical mean of the
eigenvalue
amplitudes. Demodulation of each polarization channel is equivalent to two-
pulse
demodulation without any use of polarization handling techniques. The
demodulated
phase and fading factor og all polarization channels show strong dependence on
the
input polarization. If the lead fiber and the sensor array do not include any
polarizing
component, R can be written ke-'05U, where k is a proportionality constant, 0,
is the
sensor phase and U is an unitary matrix:
Im J~s U. Uxy r.1~,~ ~ CoS Oe Sin 61eJ~
R =ke ,IJ=ke =oce (10)
/~~
Uyx Uyy L- S1I1 C7e I13 CoS O --ia _]
Here, 0, a and P are arbitrary phases, Uyy is the complex conjugate of llxX,
and UyX is
the complex conjugate of -UX,,. The amplitude of the diagonal elements of U is
maximum when the off-diagonal elements are zero, and visa versa. This agrees
with
the measured behavior of R: The RXx and Ryy components have approximately the
same fading factor, while the variations in demodulated phase have opposite
signs.
The F2,;y and -RyX components show the same relationship as Rxx and Ryy.
[0045] Equation (10) shows that detected sensor response will never fade if
either of
the two components RXX and Ryy and either of the two components RXy and RyX
are
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CA 02479081 2004-08-25
measured. From the two components one may choose to always demodulate the
component with the best fading factor. This will produce a fading factor
between 0.5
and 1, thus the demodulated signal will never fade. However, the phases a and
R are
arbitrary, thus demodulation of the sensor response based on only two of the
response
Jones matrix components will not provide a phase readout that is insensitive
to
birefringence fluctuations in the lead fiber. This demonstrates that all four
components
of R must be measured to ensure polarization induced phase noise insensitive
interrogation.
[0046] Figure 7A shows that the combined fading factor of the demodulated
signals
calculated as IdetR I is between .98 and 1, while the peak-to-peak variation
in
demodulated sensor phase is only 32 mrad. Figure 7B shows the peak-to-peak
variations of the phase of the components RX,, R,y, Ryx and Ryy, where the R,,
and the
RyY component vary by 2.2 rad. Figure 7C shows a magnification of the
polarization
independent sensor phase ~detR I of Figure 7B. 7'hus, the proposed method has
reduced the sensitivity of the demodulated sensor phase to input polarization
fluctuation by at least 36 dB, and the variation in fading factor is reduced
to only 2%.
[0047] Figure 8 shows the simultaneously measured demodulated phase of all
four
time-division multiplexed sensors in the network when the input polarization
into the
array was modulated. AII the sensors show a variation in demodulated phase
less than
22 mrad. Thus, suppression of polarization-induced noise is achieved for all
sensors in
the network. When demoduiating every component of the Jones matrices of the
sensors individually (not shown in the figure), the maximum phase variation of
2.3 rad
was observed in RX, component of sensor 4.
[0048] in another version of the first embodiment, the four components of R
can be
separated in the frequency domain. With the Jones vectors of the two
interrogation
pulses given by Eo(n) = 11 e and E, (n) _ [e-'o'_"T, e-; "-n" ~ Equation (4)
becomes
I(n) = 2ReKejnT, + R~,~BI~'y.n7; -'r ~IX~Liu~ynT. -F- RyXQlroy.znT ~ (1 1 )
-15-
CA 02479081 2004-08-25
where wx,, w.vX, wyy and U)xy = wXX - cuyx+ wyy are four different sub-carrier
frequencies
that are chosen so that the four components are separable in the frequency
domain.
[0049] The first embodiment described above is based on having the SOPs of the
interrogation pulses controlled individually so that two interfering pulses
may originate
from interrogation pulses that have different SOP. This ernbodiment only works
for
pulsed interrogation systems. Figure 3 depicts a block diagram of the second
embodiment of the present invention. In this embodiment, the two interfering
beams
may originate from the same transmitter output SOP, and the modulation of the
transmitter output SOP can be made independent of the sensor imbalance. This
allows
for this method to be used in combination with both pulsed TDM and other
multiplexing
techniques that employs a CW (continuous wave) source such as frequency
division
multiplexing (FDM) and wavelength division multiplexing (WDM). In FDM, the
laser
frequency is swept over a range larger than the free spectral range of the
interferometers, and different electrical signal frequencies are generated at
the detector
corresponding to different delay difference of the two iriterfering signals.
One version of
FDM is imbalance division multiplexing (iDM), where different sensors have
different
imbalances. In WDM, the respolnse from each sensor appears at different
wavelengths.
[0050] The source 302 may be similar to source 104 in Figure 1, but may also
include the switch 103 and the phase modulator 105. The polarization modulator
106 of
Figure 1 is replaced by a pair of polarization modulators 304, and 3042 and a
pair of
phase controliers 306, and 3062. The source 302, the polarization modulators
3041 and
3042 and the phase controllers 3061 and 3062, define the transmitter 320. The
other
components of Figure 3 are substantially similar to the embodiment of Figure 1
and are
numbered as such, These polarization modulators modulate the differential
phase
between the two orthogonal modulation axes of the modulators. On the Poincare
sphere, the output SOP is represented by a point on a circle that is normal to
the
modulation axes and includes the input SOP.
[0051] In combination with TDM, this technique is similar to the one presented
with
respect to Figures 1 and 2 above; however, the polarization modulation is
equal for
both interrogation pulses, thus E1(n) = Eo(n)exp(-JA~(n)) = E(n) exp(-J ~(n)).
The SOP
of the transmitter output is described by a time-varying Jones vector E(t). In
FDM and
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CA 02479081 2004-08-25
C1IV-interrogated WDM, t is a continuous time-variable. For TDM t is modeled
as a
discrete variable t=nTr, so that E(t)= E(n)= E(nTr). The transmitter output
SOP can also
be described by a transmitted Stokes vector Sf (t) = [S~(t), S,(t), S 2(t), S
3(t)]. The
relation between the transmitted Stokes vector and the iones vector
E(t)=[EX(t) Ey(t)]T is
given by:
So (t) = EX (t)j 2 +,I Ey (t) 2
S; (t) = EX (t) z - Ey (t)j z ( 11)
Sz (t) = 2 Re(Ey (t)Ex (t))
S3 (t) = -j2Im(Ey (t)Ex (t))
Here, S o(t) describes the total optical po,wer, S (t) describes the
difference in optical
power between the vertical and horizontal polarized component, S 2(t)
describes the
difference in optical power between the linear 450 and linear -45 polarized
component,
and S J(t) describes the difference in optical power between left and right
circular
component.
[00521 In order to analyze the interference between the light beams that have
propagated in the reference path and the sensing path, an effective Stokes
vector is
defined:
sa ~ (t) = lEx (t)Ex (t - ,cs ) + .Ey (t)E3, (t - tis )~ .i~tt)
Sleff (t) = (Ex (t)EX (t - Ts Ey (t)Ey (t - -cs )VLW0
Szff(t) = (EY (t)Ex (t - -cs ) + EX (t)Ey (t - -C.r )~-jAot() (12)
Ssff(t) = -J(Ey (t)Ez (t - ~s ) - E~ (t)E~ (t - ~s ))e iA~(r)
The phase term A~(t) is the applied phase modulation of the source, which
generates
one or a plurality of sub-carrier on the interference sigrsal. In this
embodiment ~(t)=A,
where c) is the sub-carrier freguency of the interference signal. In other
embodiments,
A~(t) may not be a linear function of time. The term exp(-j ~(t)) in (12)
ensures that the
applied phase modulation is not included in the definition of the Stokes
vector. The
definition of the effective Stokes vector in (12) deviates from the definition
of the
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CA 02479081 2004-08-25
transmitted Stokes vector in (11) by the inclusion of the delay term C5. This
is to
compensate for the sensor imbalance. These two definitions become equal when
the
transmitter output SOP is modulated with a rate that is substantially smaller
than the
sensor FSR Urs, i.e., E(t) ~~E(t-zs)exp(-j ~(t)). In this case, all components
of the
effective Stokes vectors are real, while they may be complex in the general
case.
[0053] The Jones vector of the light that has propagated the reference path
and the
sensor path is given by Er(t)=BõBd E(t) and Es(t) 13õRS dE(t-Ts),
respectively, where 'CS
is the sensor imbalance. The response matrix is defined as R= B ~B ~BURS a. By
using
the relation between the effective Stokes vector and the Jones vector as given
in (12),
equation (4) can be written as:
I(t) = 2R.e{Et(t)BdBuBul2sB,E(t-,Ts)}= zR.e{El (t)RE(t-1;s)}
= 2 Re{[so (t)(Rzx + Ryy ) + ,~;ff(t)(R~. - Ryy ) + sz~ (r)(Ry + Rxy ) +
.~~'3ff(t)(Rtir - Rxy )3ej~O(t) },
(13)
[0054] A measurement of 1:he response Jones matrix R is performed by
continuous
or stepwise modulation of the polarization of the transmitter along a
predefined path on
the Poincare sphere through a set of polarization states that can be
represented by four
linearly independent effective Stokes vectors and detection of at least four
independent
signal components of the generated output intensity modulation.
[0055] A measurement of the response Jones matrix can be preformed by
modulating the transmitter output SOP through a set of polarization states
that can be
represented by four linearly independent transmitted Stokes vectors. However,
it is
possible to provide the set of four linearly independent effective Stokes
vectors by less
than four linearly independent transmitted Stokes vectors. If the modulation
is
performed at rate that is comparable to the sensor FSR, the two inferring
light beams
may originate from different transmitter output S P. This means that the
effective
Stokes vectors and the transrnitted Stokes vector may no longer be equal. As
an
example, in the first embodiment, the transmitter provides only two linearly
independent
transmitted Stokes vectors (the polarization states x and y), while the number
of linearly
independent effective Stokes vectors is four. Methods that provide the
response matrix
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CA 02479081 2004-08-25
with a set of less than four linearly independent transmitted Stokes vectors
requires a
modulation rate and sampling bandwidth that is in the range of the sensor FSR.
In
conventional CW interrogation, the minimum detection bandwidth is given by the
information bandwidth of the interferometric signal. Thus, the minimum
detection
bandwidth required by these methods is much larger than necessary for CW
interrogation of interferometric sensors. While if the transmitter provides
four linearly
independent transmitted Stokes vectors, the minimum detection bandwidth is
limited by
information bandwidth of the interferometric signal only.
[0056] In one embodiment, the two cascaded polarization modulators 304, and
3042 are not parallel or orthogonal and are modulated with different linear
rates. Let
the incident polarization into the modulators 304 be linear 45 , the first
moduiator is
oriented horizontally and modulated by w plt and the second modulator be
oriented
rotated 45 and modulated by o p2t . The signals to the modulators are
generated by
the pair of phase controllers 3061 and 3062. The transmitted Stokes vector at
the output
of the modulators 304 is real and given by,
F T
1 (COS((O pl + co p2 )t - COS(C) 2 0) pl )t)
st (t) - 2 c s(WPIt) (14)
2(sln(CA) pl + C') p2 )t - sin(CR7 p2 - U)pl )t)
The rates cJpl/2n and cop2/27c are chosen to be substantially smaller than the
sensor
FSR, so that the effective Stokes vector becomes equal to the transmitted
Stokes
vector. This polarization modulation of the source generates seven
polarization beat
components on the interference signal with frequencies with various offsets to
the sub-
carrier frequency o). This gives a total of seven frequencies
co -CJp2 -Wp19 (j)-(I)P19 C11+ (j)p2 -GJp1;(1), Ct;-(A7p2 +03p1, CO+C)p1 and
Cf)+(.o p2 +l1Jpl. Equation
(13) can be written,
w-~P2-Wpl (t)e j(tz~-wp2-wpl)t + Iw-mpl (t)ej(w-c~pl)t + Icu+wp2-Wpl (t)e
j(w+mp2-v)pl)t
I(t) = Re I
+P(t)e jot + 'Tm-cup2+wp1 ('t)e j(a)-cop2+wp1)t + Iw+(upl (t)e j(m+(Opl)t +
Jw+wp2+tup1 (t)e j(w+mp2+cop1)t
-~9-
CA 02479081 2004-08-25
where I,-cop2-wp1(t)'Icn-cupl(t)e Ico+cup2-mp1(t), Icu(t), lw-cup2+cop1(t),
Iw+wp1(t) and Iw+wp2+cop1(t) are the
signal phasors of the signal band centered at the frequency indicated by the
superscript. These signal components are given by,
~(U-(OPI ~~\ = TCO+CDnt (t) _ Z (R Sy - R
1'X ~
X ~-WCiz'~/P1 (G)~ = H ~+'Lw Z-cup1(0- 4 (Rxx ! Ryy _Rxy + R
yr I I ' (t) _ (Rxy + Ryx )
1w-'õZ+wp, (t) = jw+wPZ+wni (t) _ 4 (R.r~ - R, y + Rxy - Ryx ~
Note that the signal phasors are pair wise equal. From these four independent
signal
phasors, the components of R can be found.
[0057] In an alternative version of the second embodiment, the two
polarization
modulators 304 in Figure 3 can be used to set the source polarization states
in four
subsequent measurements to four linearly independent Stokes vectors
, k=1,..,4. As an example, if TDM is used, four subsequent
Sk =lS'o,S,k,S;,S3I
interrogation pulse pairs can have horizontal, vertical, 45 linear and right
circular
polarization states. These states represent four linearly independent Stokes
vectors,
and matrix R can be found using Equation (14). Although, this choice of
transmitter
output SOPs might be the preferred embodiment, any four polarization states
that can
be represented by four linear independent polarization states can be used.
This method
can also be applied to systems that do not employ TDM, such as WDM or FDM
systems or other systems that employ a continuous wave source. In this case
the
source polarization should be switched between the four polarization states at
a rate
that is at least 8 times the information bandwidth of the interferometric
signal.
[0058] It follows directly from the reciprocity principle that a system
comprising a
depolarized source and a polarized detector is equivalent to a system
comprising a
polarized source and an unpolarized detector if the down=-lead fiber replaces
the up-
lead fiber and visa versa.
[0059] Figure 4 depicts a third embodiment of the present invention. The third
embodiment 400 does not use polarization modulation, but rather has a
depolarized
source 402 that directly drives, through a circulator 116, the sensor array
102. A
polarization diversity receiver 404 that separates the reflected signal into a
plurality of
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CA 02479081 2004-08-25
polarization components processes the reflected signals from the sensor array
102.
The polarization diversity receiver 404 comprises a three-way optical splitter
406, a first
polarization beam splitter (PBS) 408, a second PBS 410, and a third PBS 412.
Each
PBS splits the incoming light into two orthogonal polarization components.
This gives a
total of six signal outputs that are numbered k=1 to 6. In addition, the
signal coupled
from the splitter 406 is processed by a polarization controller (PC) 414 prior
to entering
PBS 410. Similarly, a second polarization controller 416 controls the signal
that enters
the third PBS 412. An array of optical detectors 4181, 4182, 4183, 4184, 4185
and 4186
(collectively detector array 418) detects the intensity of each of the signal
outputs from
the polarization beam splitters 408, 410 and 412. The detectors 4181_6 that
are
sampled with sample and hold circuits 132 and digitized by A! converter 134.
[00601 The transmission frorn the input of optical splitter 406 to PBS-output
k is
described by the Jones matrix P''. The Jones vectors of the light that has
propagated
the reference path and the sensor path are given by Er(t)=PkBõBd E(t) and
ES(t)=PkBuRSBdE(t-TS), respectively. The measured interference between the
light
propagated along the reference path and the sensor path is given by,
Ik(t) = 2 Re f Ei (t)ES (t)j = 2 Re f Et (t)~3dB~ PkBõ ItsB d e' O(')E(t - zs
)I = 2 Re {Et (t)QkE(t - zs )ejo0(') }
= 2Rej(Q.',EX(t)EX(t-zs)+Qk, Ey(t)Ey(t-zs)+QyEy(t)Ey(t-zs)+QyEy(t)E(t-
zs))ejomW
1
= Re f [So (t)(Qk,, + Q yky) + SI (t)(Qz, - Qy) + sa (t)(Qy + Q'_ ) + Ss
(t)(Qy - Q )]e.i0(t)
1 (15)
where Qk=BdB' PkB~,RSBa. Assuming that there is no polarization dependent loss
in
the lead fiber; then, Bu=cuUu and Bd=cdlJd, where lJu and Ud are unitary
matrices and Cd
and cU are complex scalars. The matrix Qk can be written Qk= lJ d L9 u
PkRtJUlld, where
R= icd12B ~ RsBu. Note that the response matrix R is defined differently in
this
embodiment than in embodirnents I and 2. In this embodiment, R depends on the
propagation through the up-lead fiber, while in embodiments 1 and 2, R depends
on the
propagation through the down-lead fiber. However, the phase of the eigenvalues
of R
and RS are still equal.
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CA 02479081 2004-08-25
[0061] Since the source 402 is depolarized, the transmitter output SOP with
unity
output intensity, can be written S(t)=[1,0,0,0]. Thus, the measured
interference in (15) is
given by,
Ik (t) = Re { (Q ~ + Q,~Ywoxl (16)
The sum QkxX+Qkyy defines the trace of matrix Qk. It can be show that
Trace(Qk)
=Trace(PkR), thus the measurement of R is not affected by the transformation
UuUd of
Qk. The unitary matrix UuUd represents a rotation of the output SOP of the
depolarized
source 402. A depolarized source includes all SOPs, thus UõUd does not affect
the
source SOP. Without a polarizer, Trace(Q )=Trace(R), and the detected signal
would
be Ia (t) = Re ~ (Rxx + Ryy )ej4O(') I.
[0062] The output from polarizer k can be described as a projection of the
Stokes
vector of the incoming light to splitter 406 onto the eigenpolarization of the
transmission
from the splitter to the polarizer output given by the Stokes vector Sk =[1,
S; , S2 , S3 J. It
can be shown that (16) can be written,
lx (t) = Re { (Rxx+ RYY+ Si (R.~r - Ryy) +.S'z (Ryx + R~, ) + jSs (Ryx -
R,w))e.i,"(t) I k =1, 2, 3, ...
(17)
The similarity between equation (13) and equation (17) demonstrates the
reciprocity
principle which gives that a system comprising a depolarized source and a
polarized
detector is equivalent to a system comprising a polarized source and an
unpolarized
detector. At least four measurements of polarized outputs that can be
represented by
four linearly independent Stokes vectors are required in order to extract the
four
components of R. A polarization diversity receiver that can measure all
components of
the Stokes vector of the incoming light defines a Stokes analyzer, and any
type of
Stokes analyzer can be used for a measurement of R.
[0063] The polarization controllers (PC) 414 and 416 are used to adjust the
orientation of the input SOPs to the splitter 406 that are projected by the
PBS's 410 and
412. The SOP that is projected by the first PBS 408 is defined as
hor=izontai(H) and
vertical(V) SOPs, which is represented by Stokes vectors [1,1,0,0] and [1,-
1,0,0],
respectively. The polarization controller 414 is adjusted so that PBS 410
projects
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CA 02479081 2004-08-25
linear 45 degrees (P) and linear -45 degrees (Q) SOPs, which is represented by
Stokes vectors [1,0,1,0] and [1,0,-1,0], respectively. The polarization
controller 416 is
adjusted so that PBS 412 projects right circular(R) and left circular(L) SOPs,
which is
represented by Stokes vectors [1,0,0,1] and [1,0,0,-1 ], respectively.
[0064] In second version of the third embodiment three-way optical splitter
406 is
replaced by a four-way optical spiitter, and polarizers with output to only
one detector
each is used. The power in one of the outputs of the splitter is measured
without a
polarizer before the detector. This projection is represented by Stokes vector
[1,0,0,0].
The three other outputs may project the incoming light to splitter into
horizontal(H)
SOP, linear 45 degrees (P) SOP and right circular(R) SOP. However, using a
polarization diversity receiver not comprising poiarization splitters, half
the power will be
wasted on average compared to a polarization diversity receiver based on
polarization
splitters. Although these projections of the incoming light may be the
preferred
embodiments, any other projections can be used provided that four known and
linearly
independent Stokes vectors can represent the projections.
[0065] In a third version of the third embodiment, a time-varying Stokes
analyzer is
used. A time-varying Stokes analyzer comprises one or a plurality of
polarizers. These
polarizers may rotate so that a time-varying Stokes vector describes the
eigenpolarization of the polarizer. Alternatively, a time-varying Stokes
vector can be
generated by placing one or a plurality of polarization modulators 304 in
Figure 3 before
the polarizer. The combined set of the eigenpolarizations of all the
polarizers must
include at least four states that can be represented by four independent
Stokes vectors.
[0066] The method of the third embodiment works with all the multiplexing
techniques, (e.g., TDM, FDM and WDM), although the method used for generating
depolarized light for interrogation may be different for each type of
multiplexing. A
source is sufficiently depolarized if the cross-correlation between orthogonal
polarizations of the source does not contribute to the demodulated signal.
This can for
instance be achieved by letting the difference in optical frequency between
the
polarization modes of the source be outside frequency bands from which the
sensor
phase is calculated. Depolarization can be achieved using a source that
combines two
-23-
CA 02479081 2004-08-25
laser signals with orthogonal polarizations and different optical frequencies.
A source
can also be made depolarized by shifting the optical frequency of one of the
polarization modes by a frequency larger than the detection bandwidth using,
for
example, an acousto-optic moduiator (AOM), or by switching the source SOP
between
two orthogonal polarizations quickly.
[0067] Passive depolarization can be achieved using a depolarizing
interferometer
500 shown in Figure 5. The depolarizing interferometer 500 comprises two
polarization
beam splitters (PBSs) 502 and 504, a polarization controller 510 and two
lengths of
polarization maintaining fibers 506 and 508. The beam splitter 504 is
operating as a
beam combiner. The polarization controller 510 adjusts the SOP into PBS 502 so
that
outputs of the PBS have equai power. Each output of PBS 502 is connected to an
input
of PBS 504 using polarization maintaining (PM) fibers 506 and 508. The PM
fibers
ensure that the SOPs of the outputs of PBS 502 remain orthogonal at the inputs
of PBS
504. A depolarizing interferometer 500 utilizes the limited temporal coherence
of the
light to generate depolarized light. To every optical signal, it is associated
an
autocorrelation function, which describes the amount of suppression of an
interference
signal component on the demodulated signal as function of the difference in
delay
between the two interfering signals. The difference in delay of the light
propagating in
fiber 506 and 508 is such that the interference components with this delay
difference
are sufficiently suppressed in the demodulation process. This method can be
used in
TDM if the coherence length of the source is significantly less than the
length of the
interrogation pulses. In FDM, the laser source is swept, so that different
electrical signal
frequencies are generated at the detector corresponding to different delay
difference of
the two interfering signals. Thus, in FDM the source can be made depolarized
by
selecting a delay of the depolarizing interferometer such that the cross-
correlation
between orthogonal polarizations of the source does not appear on the
extracted
electrical signal frequencies.
[0068] A fourth embodiment of the invention combines embodiment two and three
by having both a polarized source and a polarized receiver. In this
embodiment, a
polarization diversity receiver with a multiple of detectors replaces the
detector 118 in
Figure 3. When a polarization beam splitter is used within a polarization
diversity
-24-
CA 02479081 2007-08-31
receiver, only one polarization modulator 304 is required. A single
polarization
modulator can modulate the transmitter output SOP through a set of states that
can be
represented by a maximum of three independent Stokes vectors. The combination
of a
polarization modulator and a polarization beam splitter with two detector
outputs may
provide three independent signal components at each detector, giving a total
of six
signal components from which the response Jones matrix can be found.
[0069] With a polarizer k described by the Jones matrix pk is placed before
the
detector, the Jones vector of the light that has propagated the reference path
and the
sensor path is given by Er(t)=PkBuBd E(t) and ES(t)=PkBuRSBdE(t-,rS),
respectively. The
measured interference between the light propagated the reference path and the
sensor
path is given by (15). Assuming that there is no polarization dependent loss
in the lead
fibers and that the propagation through the lead fibers can be described by
matrices on
a form as given in (10); then, Bu=cuU,, and BU=cd Ud, where cu and Cd are
complex
scalars, and U, and Ud are unitary matrices. This gives Qk=Pk'R, where Pk'=
U; U u PkUuUd and R= ~cu,2B ; RsBd. Thus, Pk describes the polarizer
transformed by the
matrix UuUd, which is arbitrary. This transformation can be described by two
real
parameters. Thus, the response matrix R and the transformation of the
polarizers can
be found from at least six independent signal components that appears if the
transmitter output SOP is modulated through a set of states that can be
represented by
at least three independent Stokes vectors and a set of eigenpolarizations of
the
polarization diversity receiver that can be represented by at least two
independent
Stokes vectors.
[0070] In a fifth embodiment, the response matrix R can be found if the
transmitter
output SOP is modulated through a set of states that can be represented by at
least
two independent Stokes vectors and set of eigenpolarizations of the
polarization
diversity receiver that can be represented by at least three independent
Stokes vectors.
This is the reciprocal version of the fourth embodiment, and this embodiment
will give
the same set of measured signal components as the fourth embodiment if the up-
lead
fiber replaces the down-lead fiber and visa versa.
-25-
CA 02479081 2004-08-25
[0071] In FDM systems, the laser can be swept over a range much larger than
the
free spectral range of the sensor, which gives a fringe signal with an
electrical
frequency at the detector that is proportional to the delay of the sensor. The
phase of
the fringe signal relative to the source frequency is a measure for the sensor
phase.
The frequency of the fringe signal provides a measurement of the delay of the
sensor.
See X. Wan et.al "Fiber-Bragg-Grating Pair Interfierometer Sensor with
Improved
Multiplexing Capacity and High Resolution", IEEE Photon. Tech. Letters, Vol
15, pp
742-744, 2003. When a FDM systern is combined with this invention, the
measurement
can be extended to include a common-mode phase response, a common-mode delay
response, differential birefringent phase and differential birefringent delay
that is
immune to fluctuations in iead fiber birefringence, where the differential
birefringent
delay is defined as the difference in transmission delay of the two
eigenpolarizations of
the sensor.
[0072] While foregoing is directed to specific embodiments of the present
invention,
other and further embodiments of the invention may be devised without
departing from
the basic scope thereof, and the scope thereof is determined by the claims
that follow.
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