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Abstract
Polarization fading degrades the performance of phase-sensitive optical time-domain reflectometry (φ-OTDR) seriously and has to be suppressed. A novel scheme is proposed in this paper to combat polarization fading, which features a quite simple transceiver structure by exploiting both polarization diversity through delayed polarization multiplexing and the aperiodic autocorrelation of pseudorandom binary sequence. The components of Jones matrix of a sensing fiber are then shown at those four peaks of aperiodic autocorrelation and can be obtained directly without complicated computation to give a polarization independent phase variation due to vibration. Moreover, the scheme does not require stringent match between the delayed time and the spacing between sensors. The proposed scheme is demonstrated through experiment on a weak fiber Bragg grating (WFBG) array, which shows a high crosstalk rejection ratio among sensors of more than 50 dB and a high dynamic range of more than 30 dB.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Distributed optical fiber sensors (DOFS) have huge advantage on monitoring of large-scale structures [1,2]. As a typical implementation of DOFS, phase-sensitive optical time-domain reflectometry (φ-OTDR) is considered to be suitable for measurement of vibration and acoustic wave through demodulation of phase change of optical field [3,4]. Benefitting from the very short wavelength in micrometer range, the phase change is very sensitive to refractive index and length change of fiber and hence distributed measurement with high sensitivity can be realized, making φ-OTDR very attractive in recent years [5,6].
Because optical phase change is also sensitive to the frequency change of laser source, a laser with very narrow linewidth and low-frequency drift is necessary for φ-OTDR. However, such laser sources with very high coherence lead to coherent fading in Rayleigh scattering based φ-OTDR systems [7,8]. Recently, φ-OTDR based on weak FBG (WFBG) arrays embedded in fiber have been proposed, which generally do not suffer from coherent fading. Moreover, because the reflectivity of WFBGs is higher than that of Rayleigh scattering, the sensitivity of WFBG based φ-OTDR is also improved quite a lot over Rayleigh scattering based systems [9,10].
Φ-OTDR can be implemented through direct detection [11,12] and coherent detection [13,14]. Benefitting from a high-power laser as the local oscillator (LO), coherent detection can effectively enhance the received signal-to-noise ratio (SNR), making the sensitivity and measurement range improved. However, the LO used in coherent detection brings polarization related problem as the demodulated signal is maximized only when polarizations of received signal and the LO are aligned [15,16]. Because polarizations of reflected signals at various positions of sensing fiber are quite different and the polarization of LO is fixed, polarization fading due to polarization mismatch between signal and LO is inevitable [17]. The configuration of direct detection is normally simpler than that of coherent detection. However, for WFBG based φ-OTDR, polarization fading is still an important problem and has to be suppressed for direct detection schemes because reflections from two adjacent WFBGs are very likely polarization mismatched due to birefringence of fiber, especially when the spacing of WFBGs is in range of meters [18].
To suppress polarization fading in φ-OTDR, some kind of polarization diversity has to be introduced [19]. If direct detection is used, polarization diversity is generally introduced at the transmitter site, such as those schemes based on double pulses with orthogonal polarizations or pulse polarization switching [20]. The basic idea of such schemes is to maximize the visibility of the received signal through combining outputs due to introduced polarization diversity. Besides optical intensity, some direct detection schemes can also explore the phase information of received optical field. With phase information of received optical field, Jones matrix to describe the birefringence of the sensing fiber can be obtained in theory through the relationship between the input and the output optical field [21,22]. Polarization fading can then be fully suppressed and the interference due to polarization variation can be eliminated after knowing the Jones matrix of the sensing fiber. However, there are usually some stringent requirements on the polarization diversity introduced at the transmitter site to meet, such as that the delay between pulses has to match the spacing of WFBGs which may be hard to fulfill in practice, especially for long range sensing. Compared to direct detection, coherent detection can get the phase information of received optical field directly and hence is more powerful in combating polarization fading. Polarization diversity can therefore be employed in both transmitter and receiver sites. An implementation of such scheme is based on polarization multiplexing with phase coding at transmitter site and a polarization diversity receiver with multi-input multi-output (MIMO) algorithm. Correlations among coding sequences are exploited to assist in distinguishing multiplexed polarization states. An impressive performance has been demonstrated at a cost of fairly complicated transceiver structures and algorithm [23,24]. Besides those improvements on sensing scheme to combat polarization fading, some algorithms have also been proposed to enhance performance at fading [25–27].
In this paper, a novel φ-OTDR scheme to suppress polarization fading is proposed for WFBG sensor array based on delayed polarization multiplexing and bipolar phase coding. The scheme is implemented in a quite simple transceiver structure and requires no stringent timing match between delay time and the spacing of WFBGs. Although delayed polarization multiplexing with phase coding has been proposed for distributed sensing [28], those two channels multiplexed through polarization multiplexing are actually uncorrelated to each other and hence the polarization information is not explored there. In this paper, through exploiting the correlation of coding sequence, the Jones matrix of the sensor array and hence the polarization independent phase variation due to vibration can be obtained directly without complicated algorithms.
2. Principle
When birefringence is considered, the input and output can be related through Jones matrix to describe the transmission through a section of fiber as the following
To obtain $\mathbf{H}$, the basic idea of the proposed scheme in this paper is to exploit both polarization diversity through delayed polarization multiplexing and the aperiodic autocorrelation of pseudorandom binary sequence. The scheme is shown in Fig. 1. The optical field of a laser output coded by a binary sequence can be written as:
where ${A_s}$ is the amplitude of the optical field with laser phase noise included, ${\omega _0}$ is the laser frequency, ${P_s}$ is the binary sequence. The optical field has a linear polarization. Polarization multiplexing is then introduced by splitting the optical field into two orthogonal polarizations with one on slow axis and the other on fast axis. A relative time delay of τ is introduced between two branches through a section of delay fiber. Those two branches are then recombined to form the input optical field ${\mathbf{E}_\mathbf{i}}$ with delayed polarization multiplexing, which can be written asWhen this input optical field passes through a section of fiber with birefringence, according to Eq. (1), the output optical field ${\mathbf{E}_\mathbf{o}}$ is related to the Jones matrix $\mathbf{H}$ of the fiber by
It then shows that those two multiplexed polarizations are coupled with each other. At the receiver site, the polarization coordinate is normally the same as that of transmitter since the laser source is also used as the local oscillator for receiving. Therefore, if a receiver with polarization diversity is employed as shown in Fig. (1), both outputs of the receiver contain information from both multiplexed polarizations and the received signal matrix $\mathbf{R}$ can be written as the following
To untangle coupled polarizations from $\mathbf{R}$, the binary sequence $P_s$ is deliberately chosen so that its aperiodic autocorrelation is as close to a delta function as possible and can be expressed by
where ${\otimes} $ denotes convolution. $\delta (t )$ is the delta function and $c(t )$ denotes sidelobes of the aperiodic autocorrelation which is normally much smaller than $\delta (t )$ in amplitude. The received signal matrix $\mathbf{R}$ is then correlated with the binary sequence and the result isFor received signal at each polarization, the first term at the right side of Eq. (7) then shows that there are two correlation peaks in time domain spaced by the delay time τ for polarization multiplexing as shown at the left-bottom corner in Fig. 1. Therefore, the delay in polarization multiplexing is to make those two multiplexed polarizations distinguishable at receiver site and is irrelevant to the spacing between WFBGs.
Moreover, amplitudes of correlation peaks are proportional to corresponding components of $\mathbf{H}$. Therefore, amplitudes of these correlation peaks can be extracted to form a matrix $\mathbf{T}$ denoting the transmission of this section of fiber for the polarization multiplexing signal, which is written as
It then follows that
The second term at the right side of Eq. (7) stands for sidelobes of aperiodic autocorrelation which presents itself as crosstalk among sensors as shown in Fig. 2 and should be minimized as low as possible. For binary sequence, there is generally no sequence with zero sidelobe of aperiodic autocorrelation everywhere. However, for a given binary sequence, the aperiodic autocorrelation at some relative delay can be zero or very close to zero. This may be useful for distributed sensors based on WFBG array as the delay for polarization multiplexing and the spacing between WFBGs can be deliberately selected to make sensing signal received with almost zero sidelobe and hence minimize crosstalk. Figure 2 (a) and (b) shows calculated sidelobes power relative to the main peak at various delay offsets for aperiodic autocorrelation of 63-bit pseudorandom binary sequence (PRBS). On the other hand, to make use of this point, the position and spacing of WFBGs have to be precisely controlled, which puts stringent requirement on fabrication and engineering implementation. Therefore, a delay with a relative high sidelobe of about -26.4 dB is chosen in experiment to demonstrate performance basically realizable in all conditions.
3. Experimental result
The experiment setup is shown in Fig. 3. A laser at 1550.12 nm with a narrow linewidth less than 3 kHz emits a beam with high coherence at a power level of 10 dBm. The light is equally split into two branches. One acts as the carrier of modulation and the other is the local oscillation (LO). The carrier is modulated by an electro-optic modulator (EOM) driven by PRBS codes generated by an arbitrary waveform generator (AWG). The EOM is biased at its minimum optical power transmission point and PRBS codes are in bi-polar format. Therefore, a binary phase shift keying modulation is used. The light after modulation is sent into a polarization multiplexer for delayed polarization multiplexing. The polarization multiplexer splits the output of the EOM equally into two branches at first by a polarization maintaining coupler (PMC) and delays one of them through a section of polarization maintaining fiber (PMF). To make code sequences of both polarizations sampled correctly in demodulation, the relative delay should be as close to integer multiple of bit duration as possible. Given that the bit duration is in nanosecond, it then requires that the length of delay fiber should be controlled to a precision of centimeter range, which is easily achievable in practice. In experiment, the delay is 5 bits and hence a delay fiber of 4.11 m is used. Then those two branches of light at two orthogonal polarization states are multiplexed through a polarization beam combiner (PBC). The output of the polarization multiplexer is launched into a WFBG array through an optical circulator after amplified by an erbium doped fiber amplifier (EDFA). The central wavelength of all WFBGs in the array is at 1550.1 nm with a reflectivity of -30 dB. The length of the array is 50 m and the spacing between two adjacent WFBGs is 5 m. The PRBS sequence is repeatedly launched in an interval of 20 µs which is much larger than the round-trip time (RTT) of the 50 m sensor array. Generally, the interval should be at least greater than the RTT of the sensor array plus the time duration of the entire code sequence. A 63-bit PRBS sequence is used in experiment with 4 ns duration of each bit to reach a spatial resolution of about 0.4 m so that each WFBG of the array can be resolved. This spatial resolution is determined by the width of the correlation peak of PRBS sequence given by Eq. (6) and hence is just the length with its RTT equal to the duration of one bit.
A piezoelectric transducer (PZT) is inserted in the WFBG array and is placed between the 2nd and the 3rd WFBG to work as a source of vibration. The optical pulse train reflected by the WFBG array is directed by the optical circulator to the receiver which is essentially an optical coherent receiver with polarization diversity. The received pulse train is split at first into two orthogonal polarizations denoted by X and Y in Fig. 3 by a polarization beam splitter (PBS) and each of them is then mixed with the LO derived from the laser source at a 90°optical hybrid. Each 90° optical hybrid outputs in-phase (I) and quadrature (Q) signals representing the complex amplitude of the reflected optical signal due to the mixing at one polarization. Therefore, 4 outputs, Xi, Xq, Yi and Yq, are obtained after balanced photodetection as shown in Fig. 3, and then are sampled and digitized at a rate of 250 MSps by an oscilloscope. Waveform samples of 4 outputs obtained by the oscilloscope are also shown as insets in Fig. 3.
After digitization by the oscilloscope, demodulation of vibration signal is then carried out through algorithm in computer. At first, complex signals for both polarizations are formed by combing the in-phase term with its corresponding quadrature signal. The received optical power of each polarization can then be obtained by taking the square of the modulus of the complex signal, which generally gives noise-like waveforms as shown by insets in Fig. 3 due to coding of the optical signal. To decode, the complex signals are then correlated with the transmitted PRBS code at both polarizations, which then makes reflections of WFBGs shown up as some discrete peaks along temporal axis according to their distance to the receiver as shown in the right-bottom corner in Fig. 3.
The reflection of the second WFBG is shown in Fig. 4. Reflections obtained at X- and Y-polarization of the receiver are shown in Fig. 4(a) and (b), respectively. Several repeated measurements are shown by overlapped traces which are in agreement very well. 10 WFBGs are inscribed into the sensing fiber. However, 22 reflections are identified after decoding as shown in the inset of Fig. 4. The first two reflections actually come from the splice fusion of sensing fiber and the circulator. The received optical power for each WFBG is not the same due to subtle difference in the reflectivity of WFBGs. Due to the delayed polarization multiplexing, there are two reflections from the WFBG with a spacing time equal to the delayed time between the two multiplexed polarizations. Therefore, those two reflections are actually from two orthogonal polarization states multiplexed at the transmitter and they can be distinguished in time domain through their relative time delay. The coupling between transmitted two polarizations and received two polarizations are then given by those four peaks shown in Fig. 4 and hence those four components, Hxx, Hxy, Hyx and Hyy, of the transmission matrix $\mathbf{T}$ given by Eq. (8) can be obtained.
Fig. 4. (a) The reflection of the second WFBG received by X-port. (b) The reflection of the second WFBG received by Y-port.
The temporal variation of each peak is then calculated and their phase variations are obtained from the complex amplitude of those peaks. The demodulated vibration signal is then given by the phase difference of two adjacent WFBGs. Without vibration applied, the phase stability of each sensor of the array is measured and shown in Fig. 5(a). Phase variation details of the 5th sensors is also given in Fig. 5(b). The peak-to-peak phase variation is found to be within 25 mrad. Vibration is then applied through the PZT placed between the 2nd and the 3rd WFBGs, which has a phase modulation coefficient of 6 rad/V. When a sinusoid driving signal at 1 kHz with an amplitude of 2.5 V is applied, the received waveform after demodulation is shown as the dashed line in Fig. 6(a). The recovered vibration signal has an amplitude of about 14.7 rad and is in consistence with the phase modulation coefficient of the PZT. The waveform obtained at other sensors when the vibration is applied is also plotted in Fig. 6(a) which represents the crosstalk from the sensor between the 2nd and the 3rd WFBGs to other sensors. Phase variation details of the 7th sensors is also given in Fig. 6(b) to demonstrate the crosstalk level. A peak-to-peak crosstalk of about 70 mrad is observed.
In the experiment, a PRBS code sequence of 63 bit is employed. With 4 ns per bit, the duration of the entire coded optical pulse train is 252 ns and covers a spatial range of about 25 m with 5 WFBGs inside. Due to sidelobes of the aperiodic autocorrelation of PRBS, demodulation of some WFBG will have some part of information from other WFBGs shown up which is known as the major source of crosstalk among WFBGs. To quantify the rejection ratio of crosstalk, power spectrums of waveform at all sensors are calculated and shown in Fig. 7. The crosstalk of the 1 kHz vibration at other sensors is shown as minor peaks at 1 kHz, which gives rejection ratio of more than 52 dB. The inset of Fig. 7 shows the crosstalk power at various sensors. As expected, the power of crosstalk is about -26 dB at neighboring sensors and is highest among all sensors. The crosstalk level drops to about -35 dB at sensors within the coverage of the length of one code sequence. At those sensors beyond the length of one code sequence, the crosstalk level barely drops to the level of background noise of about -45 dB.
The response of the sensor to various PZT input voltage is measured and a linear relationship is observed as demonstrated in Fig. 8(a). The dynamic range is shown to be more than 30 dB and the slope of the curve is about 6 rad/V which is in consistence with the phase modulation coefficient of the PZT. The sensitivity of the sensor is also measured based on the power spectral density (PSD) of received signal after demodulation. The PZT is driven at a constant amplitude of 2.5 V to produce a phase variation amplitude of about 15 rad. The corresponding PSD of the signal is then obtained and the noise power is estimated based on its ratio to the power of the phase variation signal. An observation window of 100 ms for spectral analysis is employed in measurement which results in a spectral resolution of 10 Hz. The PSD of the noise is then given by the ratio between the noise power and the spectral resolution, which also gives the minimum phase amplitude that the sensor can perceive and is known as the sensitivity of the sensor. By tuning the driving frequency of PZT from 1 kHz to 5 kHz, a sensitivity of about 267 µrad/Hz0.5 according to the noise level is observed in this frequency range as demonstrated in Fig. 8(b).
Fig. 8. (a) Phase magnitude at various driving voltages of PZT. (b) sensitivity at various vibration frequencies according to the noise level after demodulation.
5. Conclusion
A novel scheme of polarization fading suppression for φ-OTDR is demonstrated through polarization multiplexing of light waves with phase coded by pseudorandom binary sequence. By introducing some amount of time delay between those two polarizations in polarization multiplexing, components of Jones matrix of the sensing fiber can be obtained directly without complicated computation through those four aperiodic autocorrelation peaks of the binary sequence, which then gives the polarization independent phase variation due to vibration through the determinant of the Jones matrix. The scheme is demonstrated through experiment on a WFBG array with 10 elements, which shows a high crosstalk rejection ratio among sensors of more than 50 dB and a high dynamic range of more than 30 dB. A sensitivity of about 267 µrad/Hz0.5 is observed for vibration frequency range from 1 kHz to 5 kHz according to the noise level after demodulation.
Funding
National Natural Science Foundation of China (61875246, 62075086).
Acknowledgments
This work was supported in part by National Natural Science Foundation of China (NSFC) under Grant 61875246 and 62075086.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. P. Lu, N. Lalam, M. Badar, B. Liu, B. T. Chorpening, M. P. Buric, and P. R. Ohodnicki, “Distributed optical fiber sensing: Review and perspective,” Appl. Phys. Rev. 6(4), 041302 (2019). [CrossRef]
2. J. Huang, X. Lan, M. Luo, and H. Xiao, “Spatially continuous distributed fiber optic sensing using optical carrier based microwave interferometry,” Opt. Express 22(15), 18757–18769 (2014). [CrossRef]
3. M. Ren, P. Lu, L. Chen, and X. Bao, “Study of Ф-OTDR stability for dynamic strain measurement in piezoelectric vibration,” Photonic Sens. 6(3), 199–208 (2016). [CrossRef]
4. Z. Huang, C. Wu, Z. Wang, J. Wang, and L. Liu, “Distributed measurement of axes misaligned splicing and multi-stress in polarization-maintaining fiber based on polarization-OTDR,” Opt. Commun. 423, 96–99 (2018). [CrossRef]
5. T. F. B. Marie, Y. Bin, H. Dezhi, and A. Bowen, “Principle and application state of fully distributed fiber optic vibration detection technology based on Φ-OTDR: A review,” IEEE Sens. J. 21(15), 16428–16442 (2021). [CrossRef]
6. X. He, S. Xie, F. Liu, S. Cao, L. Gu, X. Zheng, and M. Zhang, “Multi-event waveform-retrieved distributed optical fiber acoustic sensor using dual-pulse heterodyne phase-sensitive OTDR,” Opt. Lett. 42(3), 442–445 (2017). [CrossRef]
7. X. Zhong, C. Zhang, L. Li, S. Liang, Q. Li, Q. Lü, X. Ding, and Q. Cao, “Influences of laser source on phase-sensitivity optical time-domain reflectometer-based distributed intrusion sensor,” Appl. Opt. 53(21), 4645 (2014). [CrossRef]
8. F. Zhu, X. Zhang, L. Xia, Z. Guo, and Y. Zhang, “Active compensation method for light source frequency drifting in Φ-OTDR sensing system,” IEEE Photonics Technol. Lett. 27(24), 2523–2526 (2015). [CrossRef]
9. T. Liu, F. Wang, X. Zhang, Q. Yuan, J. Niu, L. Zhang, and T. Wei, “Interrogation of ultra-weak FBG array using double-pulse and heterodyne detection,” IEEE Photonics Technol. Lett. 30(8), 677–680 (2018). [CrossRef]
10. M. Wu, X. Fan, Q. Liu, and Z. He, “Highly sensitive quasi-distributed fiber-optic acoustic sensing system by interrogating a weak reflector array,” Opt. Lett. 43(15), 3594–3597 (2018). [CrossRef]
11. Y. Muanenda, C. J. Oton, S. Faralli, and F. D. Pasquale, “A Cost-Effective Distributed Acoustic Sensor Using a Commercial Off-the-Shelf DFB Laser and Direct Detection Phase-OTDR,” IEEE Photonics J. 8(1), 1–10 (2016). [CrossRef]
12. J. Pastor-Graells, H. Martins, A. Garcia-Ruiz, S. Martin-Lopez, and M. Gonzalez-Herraez, “Single-shot distributed temperature and strain tracking using direct detection phase-sensitive OTDR with chirped pulses,” Opt. Express 24(12), 13121–13133 (2016). [CrossRef]
13. F. Pang, M. He, H. Liu, X. Mei, J. Tao, T. Zhang, X. Zhang, N. Chen, and T. Wang, “A Fading-Discrimination Method for Distributed Vibration Sensor Using Coherent Detection of φ -OTDR,” IEEE Photonics Technol. Lett. 28(23), 2752–2755 (2016). [CrossRef]
14. W. Chen, J. Jiang, K. Liu, S. Wang, Z. Ma, Z. Ding, T. Xu, and T. Liu, “Coherent OTDR using flexible all-digital orthogonal phase code pulse for distributed sensing,” IEEE Access 8, 85395–85400 (2020). [CrossRef]
15. X. Zhang, Q. Wang, F. Xiong, D. Zhang, M. Chen, X. Chen, Z. Ding, Y. Zhang, T. Zhou, and F. Wang, “Performance enhancement method for phase-sensitive optical time-domain reflectometer system based on suppression of fading induced false alarms,” Opt. Eng. 59(04), 1 (2020). [CrossRef]
16. J. J. Mompó, L. Shiloh, N. Arbel, N. Levanon, A. Loayssa, and A. Eyal, “Distributed dynamic strain sensing via perfect periodic coherent codes and a polarization diversity receiver,” J. Lightwave Technol. 37(18), 4597–4602 (2019). [CrossRef]
17. Z. Wang, J. Zeng, J. Li, M. Fan, H. Wu, F. Peng, L. Zhang, Y. Zhou, and Y. Rao, “Ultra-long phase-sensitive OTDR with hybrid distributed amplification,” Opt. Lett. 39(20), 5866–5869 (2014). [CrossRef]
18. Z. Ren, K. Cui, R. Zhu, W. Peng, and J. Qian, “Efficient and compact inline interferometric fiber sensor array based on fiber Bragg grating and rectangular-pulse binary phase modulation,” IEEE Sens. J. 18(23), 9556–9561 (2018). [CrossRef]
19. L. Xiao, Y. Wang, Y. Li, Q. Bai, X. Liu, and B. Jin, “Polarization Fading Suppression for Optical Fiber Sensing: A Review,” IEEE Sens. J. 22(9), 8295–8312 (2022). [CrossRef]
20. X. Fu, Z. Deng, Q. Wei, and Z. Li, “Polarization fading suppression in distributed interferometric sensing by matched interference between polarization-switched pulses,” Opt. Express 30(11), 19705–19715 (2022). [CrossRef]
21. Z. Hu, P. Jiang, L. Ma, and Y. Hu, “Suppression of polarization induced signal fading and phase noise utilizing orthogonal-polarization switching method,” Chin. J. Laser 43(9), 0910001 (2016). [CrossRef]
22. F. Wang, Y. Liu, T. Wei, Y. Zhang, W. Ji, M. Zong, and X. Zhang, “Polarization fading elimination for ultra-weak FBG array-based Phi-OTDR using a composite double probe pulse approach,” Opt. Express 27(15), 20468–20478 (2019). [CrossRef]
23. C. Dorize and E. Awwad, “Enhancing the performance of coherent OTDR systems with polarization diversity complementary codes,” Opt. Express 26(10), 12878–12890 (2018). [CrossRef]
24. C. Dorize, E. Awwad, and J. Renaudier, “High Sensitivity φ-OTDR Over Long Distance With Polarization Multiplexed Codes,” IEEE Photonics Technol. Lett. 31(20), 1654–1657 (2019). [CrossRef]
25. F. Gu, Y. Li, Y. Song, J. Chen, J. Zhang, and M. Zhang, “Performance comparison of combining algorithms for polarization-diversity receiving in phase-sensitive OTDR,” Opt. Commun. 435, 140–144 (2019). [CrossRef]
26. G. Tu, M. Zhao, Z. Tang, K. Qian, and B. Yu, “Fading noise suppression in Φ-OTDR based on nearest neighbor analysis,” J. Lightwave Technol. 38(23), 6691–6698 (2020). [CrossRef]
27. M. Sagues, E. Piñeiro, E. Cerri, A. Minardo, A. Eyal, and A. Loayssa, “Two-wavelength phase-sensitive OTDR sensor using perfect periodic correlation codes for measurement range enhancement, noise reduction and fading compensation,” Opt. Express 29(4), 6021–6035 (2021). [CrossRef]
28. H. Martins, K. Shi, B. Thomsen, S. Martin-Lopez, M. Gonzalez-Herraez, and S. Savory, “Real time dynamic strain monitoring of optical links using the backreflection of live PSK data,” Opt. Express 24(19), 22303–22318 (2016). [CrossRef]
29. P. Jiang, L. Ma, Z. Hu, and Y. Hu, “Low-crosstalk and polarization-independent inline interferometric fiber sensor array based on fiber Bragg gratings,” J. Lightwave Technol. 34(18), 4232–4239 (2016). [CrossRef]
