Reduction of crosstalk in inline sensor arrays using inverse
scattering
Ole Henrik Waagaard, Erlend Rnnekleiv, Stig Forbord and Dag Thingb
Optoplan AS, P.b. 1963, NO-7448 Trondheim, Norway
ABSTRACT
Suppression of crosstalk in an FBG-based serially multiplexed interferometric sensor array is demonstrated by
employing the layer peeling inverse scattering algorithm. A polarization resolved impulse response (array reection Jones matrix versus time) is measured using dual pulse heterodyne interrogation with varying combinations
of polarization states in the interrogating pulse pair, and used as input to the layer peeling algorithm. < 40
dB crosstalk is achieved with > 97 % condence in a sensor array with 5 % FBG reectivity. This is a 15-20 dB
improvement compared to interrogation without inverse scattering.
Keywords: Interferometric sensors, time division multiplexing, inverse scattering
1. INTRODUCTION
Optical ber interferometric sensors are attractive for several applications due to their potential for high sensitivities, large dynamic range and immunity to electromagnetic interference. One application where such sensors
is expected to gain signicant market shares in the near future is as seismic sensors for the o-shore oil and gas
industry. This includes ocean bottom cables (OBCs) for lifetime monitoring of production elds and downhole
seismic sensors. In these applications each interferometers may comprise several meters of ber wound onto
actuators that that expand and contract in response to pressure (hydrophones) or acceleration (accelerometers).
An OBC system may include thousands of sensors, and eective multiplexing techniques are required to
address several sensors on the same ber for a cost-eective system. An attractive way to achieve high channel
count multiplexing is a combination of time division (TDM) and wavelength division multiplexing (WDM).
The WDM/TDM multiplexing scheme can be used with multiple sensor array topologies. 1 These include the
ladder topology,2 and the in-line Michelson topology. 3 The disadvantages of these multiplexing schemes are the
extensive use of couplers and optical add-drop multiplexers to achieve WDM. These components may reduce the
reliability of the sensor array.
In this article, we evaluate a sensor array consisting of sensor groups with N inline TDM Fabry-Perot sensors
formed between N + 1 equally spaced ber Bragg gratings (FBG). 4 WDM is enabled by letting FBGs in dierent
sensor groups reect dierent wavelengths. In the 4C OBC application, a sensor station may consist of three
accelerometer and one hydrophone. We also include a reference sensor to suppress cable noise, thus giving a
total of ve sensor coils per group. 5 The advantage of this scheme is that FBGs are used as wavelength-selective
reectors, such that the sensor array may entirely consist of optical bers, which improves reliability. A potential
disadvantage with this conguration is the crosstalk that is caused by multiple reections within the sensor group.
Control
unit
Signal
processing
D
ADC
CIF
Sensor coils on PZTs
3
4
5
2
EDFA
1
SW
POL
MOD
DFB−FL
PHASE
MOD
FBGs
0 1 2 3 4 5 6 7 8
Reflected pulse train
Figure 1. Experimental setup. DFB-FL, distributed feedback ber laser; SW, Mach-Zehnder optical switch; CIF, compensating interferometer; PHASE MOD, electrooptic phase modulator; POL MOD, electrooptic polarization modulator;
EDFA, erbium doped amplier; ADC, analog to digital converter; PZT, piezo cylinders.
Contact: ole.henrik.waagaard@optoplan.com, Telephone: +47 73870527
19th International Conference on Optical Fibre Sensors, edited by David Sampson, Stephen Collins, Kyunghwan Oh,
Ryozo Yamauchi, Proc. of SPIE Vol. 7004, 70044Z, (2008) 0277-786X/08/$18 doi: 10.1117/12.786176
Proc. of SPIE Vol. 7004 70044Z-1
In this paper we demonstrate a demodulation scheme that can eliminate this crosstalk. The sensor array is
interrogated using a polarization-resolved two-pulse heterodyne technique, and the received interference signal
is processed using a polarization-resolved layer-peeling inverse scattering algorithm
6 to obtain a measure for the
sensor phase without crosstalk from other sensors.
2. THEORY
Φ1
ρ0
Φ2
ρ1
Sensor 1
ρ2
Sensor 2
Φ3
Φ4
ρ3
Sensor 3
Φ5
ρ4
ρ5
Sensor 4
Sensor 5
Signal path a
Signal path b
Signal path c
Signal path d
Signal path e
Figure 2. A sensor group consisting of 6 reectors and 5 sensors.
Figure 2 shows a ber-optic Fabry-Perot in-line sensor group consisting of 6 equally spaced FBGs reecting
N
j = 0 ; 1; : : : ; N
the same wavelength, and the
= 5 sensors are the ber sections between a pair of subsequent FBGs. The
Jones matrix
describes the reection from FBG
j ,
matrix describing the single-pass propagation through sensor
j , while j , j = 1; 2; : : : ; N is the Jones
j , and includes information about the sensor phase.
Several groups can be multiplexed in the same ber in the wavelength domain by ensuring that the FBGs of each
sensor group reect dierent wavelengths. The signal path
a
of a pulse that is reected from the fourth reector
( 3 ) is illustrated in the gure. The transmission delay of this path is 3 s , where s is the dual pass sensor delay.
The phase of this pulse relative to a pulse reected from the third reector comprises the information about the
third sensor which we want to demodulate. Also shown are signal paths
b,c,d
and
e
for other output pulses that
have a time-delay equal to 3 s . These pulses have been reected more than once within the sensor group (multiple
reections), and lead to crosstalk from the preceding sensors to the detected interference signal from the third
sensor. The number of multiple reection that has a time-delay equal to
ks increases quadratically with k, and
7 Without compensation of
7
these multiple reection, very low reectivity is required to achieve an acceptable crosstalk level. Kersey et.al
the amplitude of the multiple reections are proportional to the FBG reectivity.
showed a crosstalk level of
dB crosstalk,
26 dB in a sensor array with 4 sensors and 5
0:1% gratings are required.
1% reectors.
To achieve
<
40
Such low reectivities would give a limited system range and/or
reduced signal-to-noise ratio.
Figure 1 shows an experimental setup for interrogating ve sensor coils wound onto PZT-rings. The sensor
array is interrogated using two-pulse heterodyne interrogation, where two interrogation pulses are generated
T .4 The time delay between the two pulses is equal to the dual pass sensor
s and is generated by producing one pulse with an electrooptic Mach-Zehnder switch and clone this pulse
within each TDM repetition period
delay
with a compensating interferometer (CIF). The phase dierence between the two pulses is modulated with a
electrooptic phase modulator to form a sub-carrier on the detected interference signal.
Each FBG reects a
portion of the interrogation pulses, resulting in a pulse train that is detected and sampled by the ADC.
The visibility and phase of the interference depends upon the state of polarization (SOP) of the two interfering
light signals. The layer-peeling algorithm can only remove the crosstalk due to multiple reections when this
visibility is known.
To solve this, we propose a polarization-resolved interrogation technique to measure the
full Jones matrix of the sensor. We use an electrooptic polarization modulator to switch the polarization of the
x and y such that the sensor array is interrogated using pulse
xx, xy, yx and yy.
T if nT
T
if nT
Let E 1 (n) = [E1x (n) E1y (n)] e
and E 2 (n) = [E2x (n) E2y (n)] e
be the Jones vectors of the
rst and the second interrogation pulse leaving the source within the n'th TDM repetition period, respectively.
interrogation pulses between two orthogonal SOPs
pairs with all four combinations of the two SOPs, denoted polarization channels
sc
sc
Proc. of SPIE Vol. 7004 70044Z-2
The term e
represents a dierential phase modulation where fsc is called the sub-carrier frequency. The
electric eld phasor of the k'th pulse within the reected pulse trains originating from the rst and the second
interrogation pulse are given by
E d1 (k; n) = h((k)E 1 (n)
(1)
(2)
E d2 (k; n) = 0h(k 1)E (n) :: kk >= 00 ;
2
ifsc nT
where h(k), k = 0; 1; : : : is a 2 2 complex Jones matrix describing the polarization resolved impulse response
from the sensor group. h(0) represents the transmission through the lead ber and the reection of the rst
FBG, while h(1) is the transmission through the lead bers and the reection from the second FBG. Relative to
h(0), h(1) includes information about the state of the rst sensor. h(2) includes information about the second
sensor, but also a third order multiple reection within the rst sensor.
Fig. 1 shows the combined pulse train received from a sensor group when interrogated by the two interrogation
pulses. The pulse trains originating from the two interrogation pulses will overlap, and the total intensity
It (k; n), comprises a non-interfering term Ip (k; n) and an interference term I (k; n). The interference signal can
be extracted from the total intensity in a frequency band around the sub-carrier frequency fsc . The interference
term gives rise to a time varying amplitude (illustrated as hatched pulses in the gure). Note that the amplitude
of the rst pulse in the reected pulse train has no interference term, since E d2 (0; n) is zero. The length of
the pulse train is in principle innite, due to the multiple reection within the sensor group. However, only
It (1; n)-It (5; n) is needed for demodulation of the 5 sensors. The pulses after the sixth pulse do not include rst
order reections. These tail pulses must fade out to an amplitude determined by the maximum allowed crosstalk
level before a new pulse train can be received.
The interference between two reected eld phasors are given by,
I (k; n) = 2Ref
= 2Re
n
E y (k; n)E (k; n)g = 2RefE y (n)hy (k 1)h(k)E (n)g = 2RefE y (n)H (k)E (n)g o
(3)
y
y
y
y
d2
d1
1
2
1
2
Hxx E2x (n)E1x (n) + Hxy E2x (n)E1y (n) + Hyx E2y (n)E1x (n) + Hyy E2y (n)E1y (n) ei2fsc nT
for k > 1 and is zero for k = 0. Here, y is the conjugate transpose matrix operation, and H , H , H and H
are the components of the matrix H (k) = hy (k 1)h(k). In polarization channels xx, we have E1 = E2 = 0,
and only the rst term in the last line of (3) is non-zero enables extracting of H from I (k; n). In channel xy,
we have E1 = E2 = 0 which enables extracting H , and in similar ways for H and H .
When H (k) is determined, a measure h~ (k) for the impulse response can be calculated successively using,
(4)
h~ (k) = h~ (k 1)y 1 H (k) = h~ (k 1)y 1 h(k 1)y h(k):
xx
xy
yx
y
yy
y
xx
y
x
yx
xy
yy
In (4), h~ (0) is the starting point
p for the successive calculations, representing the reection from the rst
grating. We therefore set h~ (0) = It (0; n)I , where I is the identity matrix.
The impulse response h~ serves as the input to the polarization-resolved layer-peeling inverse scattering algorithm to extract the phase of the individual sensors in the group, as previously described for reconstruction of
the spatial prole of FBGs from measured impulse responses. 6 The layer-peeling algorithm is based on the fact
that the rst non-zero sample in the impulse response is the reection of the rst layer. Knowing the response
of the rst layer, the response from the remaining layers, without the rst layer in front, can be calculated.
The rst non-zero sample of the resulting impulse response equals T1 1 1 , and can be factorized to nd the
Jones matrix 1 describing the forward transmission through sensor coil 1 and the Jones matrix 1 describing
reection from the second FBG (see Fig. 2), provided that either the sensor loss( jj1 jj) or the FBG reectivity
(jj1 jj) is known. Layers are stripped o in iterative steps until the transmission matrix has been found for
all sensors, without contributions from multiple reections.
The sensor phase is calculated as the phase of the determinant of . The phase of the determinant is
the sum of the one way phase delay of the two polarization eigenmodes of the sensor coil, or equivalently the
j
j
Proc. of SPIE Vol. 7004 70044Z-3
average of the two way phase delays of the eigenmodes. This means that the sensor phase is independent on
the birefringence of the lead cables. Thus, the problems with polarization-induced noise and fading caused by
polarization uctuations in the lead ber are also eliminated by this approach.
3. EXPERIMENTS
Suppression of crosstalk was tested on a sensor group consisting of 6 FBGs with reectivities 5 % at 1557.4 nm
as shown in Fig. 1. The dual pass delay between subsequent FBGs was 100 ns. A DFB ber laser operating at
1557.4 nm was used as source, and the TDM repetition period was T =1.22 s. The number of TDM repetition
periods per sub-carrier period was 12, and the four polarization channels where time division multiplexed so
that three samples per sub-carrier periods were received from each polarization channel. The response of each
polarization channel was decimated to 7.5 kHz, and the layer-peeling algorithm was applied to the decimated
data to remove crosstalk. The sensor phases were extracted from the data using the determinant approach, as
described above.
A 97 Hz signal was applied to the PZT of sensor coil 1, producing a phase modulation of 1.6 rad p-p. The
crosstalk to sensor 2,3,4 and 5 was recorded for a period of 2 hours. Figure 3 shows the accumulated probability
for crosstalk from sensor 1. The gure shows that the probability for < 40 dB crosstalk is >97 % for all sensors.
This is an signicant improvement compared demodulation without the layer-peeling algorithm (by extracting
the phase of the determinant of (k ) before removing crosstalk), in which case the measured crosstalk was 15-20
dB higher.
H
Acc. probability
1
Sensor 2
Sensor 3
Sensor 4
Sensor 5
0.8
2
3
0.6
0.4
4
5
0.2
0
−65
−60
−55
−50
−45
Crosstalk [dB]
−40
−35
−30
Figure 3. Accumulated probability for crosstalk from sensor 1 to other sensors.
REFERENCES
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DWDM," Journal of Lightwave Technology 19(5), pp. 687{699, 2001.
4. J. Dakin, C. Wade, and M. Henning, \Novel optical ber hydrophone array using a single laser source and
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Conference of Optical Fiber Sensors , 2008.
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7. A. Kersey, K. Dorsey, and A. Dandridge, \Cross talk in a ber-optic Fabry-Perot sensor array with ring
reectors," Optics Letters 14(1), pp. 93{95, 1989.
Proc. of SPIE Vol. 7004 70044Z-4