Abstract

We proposed and demonstrated a coarse-fine method to achieve fast locating of external vibration for the phase-sensitive optical time-domain reflectometer (φ-OTDR) sensing system. Firstly, the acquired backscattered traces from heterodyne coherent φ-OTDR systems are spatially divided into a few segments along a sensing fiber for coarse locating, and most of the acquired data can be excluded by comparing the phase difference between the endpoints in adjacent segments. Secondly, the amplitude-based locating is implemented within the target segments for fine locating. By using the proposed coarse-fine locating method, we have numerically and experimentally investigated a distributed vibration sensor based on the heterodyne coherent φ-OTDR system with a 50-km-long sensing fiber. We find that the computation cost of signal processing for locating is significantly reduced in the long-haul sensing fiber, showing a potential application in real-time locating of external vibration.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

In recent years, the phase-sensitive optical time-domain reflectometer (φ-OTDR) has attracted much attention because of the capability of being a fully distributed vibration sensor [1–3]. The φ-OTDR system typically launches highly coherent probe optical pulses into a sensing fiber and receives the backscattered light to monitor external vibration disturbance along the sensing fiber through coherent detecting technique [4–8]. Different from the traditional OTDRs that only monitor optical intensity variation of backscattered light along the fiber, the φ-OTDR system is enabled to detect the phase variation of backscattered light [4–8]. By extracting the phase variation, the φ-OTDR technique is enabled to provide the information of the type of external vibration source. Therefore, the φ-OTDR based distributed sensors promise a broad range of applications including abnormal vibration detection along oil/gas pipes, intrusion alarm and location system, and distributed acoustic test for train tracking [9–12].

In order to locate the external vibration accurately along a sensing fiber in φ-OTDR systems, both the amplitude-based locating technology and phase-based locating technology have been proposed and explored by using various algorithms including moving average, wavelet transformation, 2D bilateral filtering algorithm, differential phase methods and so on [13–17]. For the amplitude-based locating technology, the main advantage is that false alarms for locating induced by signal fading can be suppressed through averaging method [13]. However, most of the amplitude-based locating methods need relatively complex algorithms to process all acquired sensing data point by point [5, 8], which has the serious computation cost problem. Hui et al. have demonstrated a graphics processing unit (GPU)-based system to perform parallel computation for every sensing points [18], which saves the total time for detection. Nevertheless, if a long range φ-OTDR system (for example >20 km) with fine locating resolution (for example <1 m) is constructed, a very large amount of sensing data need to be processed, which will require high performance hardware and affect its real-time feature [19, 20]. For the phase-based locating technology, the attractive merit is that the signal-to-noise ratio (SNR) for locating external vibration is relatively high [17, 21]. Pan’s works have demonstrated more than 10-dB improvement in SNR by using phase-based locating method [17]. However, a large number of false-alarm phase peaks unavoidably exist in φ-OTDR systems due to signal fading [22], which leads to a significant computation cost for discriminating such false-alarm phase peaks. In our previous works, we have proposed an effective method to discriminate the real external disturbance induced differential phase peaks from the fading ones [21]. The previous work focused on eliminating the false alarms and the computation was still time consuming.

In this work, we propose a coarse-fine method to achieve fast locating of external vibration along a sensing fiber for the heterodyne coherent φ-OTDR system. Since the external vibration can induce an additional phase beyond the vibration region while the signal fading has little influence on the phase beyond its location, we can firstly divide the backscattered trace into a few segments spaced by a long distance to realize coarse locating. Batches of sensing points along the fiber unrelated to external vibration are excluded. Secondly, we implement the amplitude-based locating process to realize fine locating within the target segment containing external vibration. Based on the proposed coarse-fine locating method, we have numerically and experimentally investigated a distributed vibration sensor based on the heterodyne coherent φ-OTDR system with a 50-km sensing fiber. Since most of sensing points that are idle and provide trivial information are discarded, we find that the coarse-fine locating method reduces the signal processing load significantly, especially for the long haul sensing fiber. Moreover, the results show the computation cost is insensitive to the sensing range.

2. Principle of the coarse-fine locating method

Generally, the φ-OTDR system launches optical pulses with frequency shift to a sensing fiber. The backscattered light and the local light are combined by a 3-dB coupler and detected by a balanced photodetector. The detected power PAC is given by [21,22]:

PACEsElocos(2πΔft+φz)
where Es and Elo are the amplitude of the backscattered light and local reference light, respectively. Δf is the shifting frequency. φz is the external vibration induced phase change at position z [8]. As shown in Fig. 1, the light pulse with an initial phase η0 propagates through the external disturbance region, picking up the phase shift ηd. Then the backscattered light successively returns to the port of light injection. A and B are two points before and behind the vibration position, respectively. The backscattered light from A is not affected by the vibration position, while the backscattered light from the B passes through the vibration and picks up the phase shift ηd again. As a result, we can determine whether it contains external vibration by comparing φA and φB, do not need to calculate each sensing point within the interval between A and B. It is noted that φz resulted from the refractive index variation along the fiber can be expressed as φz = 2ηz, which means that phase of the forward-propagation pulse light accumulates to ηz at position z along the sensing fiber and thus the backscattered light from position z experiences a round-trip phase shift of 2ηz [21, 23, 24].

 

Fig. 1 Principle of Rayleigh backscattering in φ-OTDR.

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Here we propose a coarse-fine locating method. Coarse locating is to search the segment where the vibration happens, while fine locating is to locate the accurate position within the target segment. In Fig. 2, the endpoints epi of these segments are selected as the observation points. By monitoring and comparing the phase difference of the adjacent observation points successively, we can determine whether external vibrations fall in the segment i. Finally, the sensing points within segment i are preserved for fine locating process [13, 17, 22, 25].

 

Fig. 2 Schematic diagram of coarse locating.

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In order to identify the phase difference between the observation points for coarse locating, the criterion based on correlation algorithm is taken. Pearson’s correlation coefficient r is commonly used to measure the linear relationship of discrete random signals, which is expressed as follows [26–28],

r(X,Y)=(XkX¯)(YkY¯)[(XkX¯)2(YkY¯)2]1/2
where X and Y denotes the random signals to be compared, X¯ and Y¯ denote the expectation of X and Y, respectively, k denotes the index of a value in the discrete signal. Since the range of r is [-1, 1] and strong correlation makes the r close to 1, a high similarity between the signals leads to a large r value.

To highlight the similarity between the adjacent observation points in the coarse locating process, we define a relevance coefficient si for segment i as:

si=s(φi1,φi)=1r(φi1,φi)
where φi denotes the phase of observation point epi. If φi differs from φi-1, si is relatively high and the segment i is considered to be the segment related to vibrations.

3. Experimental setup and results

3.1 Experimental setup

The experimental setup of a general heterodyne coherent φ-OTDR system is schematically shown in Fig. 3. A narrow linewidth laser (NLL, Koheras BasiK E15) launches continuous-wave (CW) light with a linewidth of 100 Hz into the sensing fiber. A 90:10 optical coupler separates 90% of light as the probe, and 10% of light as local reference light. An acoustic-optic modulator (AOM, Gooch & Housego T-M200-0.1C2J-3-F2S) driven by an arbitrary function generator (AFG, Tektronix AFG3252C) modulates the probe light into a pulse chain with pulse duration of 100 ns and repetition rate of 1.8 kHz, and introduces 200-MHz optical frequency shift to the pulse train. The power of the pulse light is amplified by an erbium-doped fiber amplifier (EDFA) and injected to the sensing fiber with length of 50 km. To simulate the external vibration source, a piezo transducer (PZT) driven by a sinusoidal voltage signal of 90 Hz is executed on 2 m sensing fiber at approximate 20 km. The backscattered light and local light are combined by using a 3-dB coupler. Then a balanced photodetector (BPD, Thorlabs PDB430C, 350 MHz) detects the coherent signal and extracts the beat signal. The output of the beat signal is sampled by a data acquisition card (DAQ, AlazarTech ATS9360, 12 bit) at a sample rate of 1 G/s, corresponding to a spatial step of about 0.1 m. The maximum of 60 beat signal traces can be acquired and stored, which is limited by the DAQ memory capacity. The traces are processed by inphase-quadrature (I/Q) demodulation method and phase unwrap technique in a personal computer (PC) [8, 17, 21].

 

Fig. 3 Schematic diagram of the heterodyne coherent φ-OTDR system: narrow linewidth laser (NLL); acoustic-optic modulator (AOM); erbium-doped fiber amplifier (EDFA); piezo transducer (PZT); balanced photodetector (BPD); data acquisition (DAQ); arbitrary function generator (AFG); personal computer (PC).

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3.2 Locating of the external vibrations

Firstly, the whole sensing fiber is divided into 100 segments with 500-m distance interval and 101 observation points to carry out the coarse-fine locating scheme. It is noted that in the experiment, an observation window at the end of every segment is required to demodulate the phase from the specified observation point. By using Eq. (3), the relevance coefficient was calculated for adjacent observation points, and the result of coarse locating is illustrated in Fig. 4(a). The peak indicates that the external vibration occurs within the 41st segment corresponding to the interval between 20 km and 20.5 km. The demodulated temporal phase profiles (φ) extracted from the successive endpoints ep40 (20.0 km), ep41 (20.5 km) and ep42 (21.0 km) are plotted together in Fig. 4(b). We find that φ41 and φ42 are almost the same, but different from φ40. Meanwhile, by subtracting the temporal phases from adjacent observation points (Δφ41 = φ41φ40, Δφ42 = φ42φ41 ), the temporal phase difference profiles (Δφ) are obtained, as shown in Fig. 4(c). The phase difference Δφ41 exhibits a sinusoidal signal that matches the applied PZT vibration, while the difference Δφ42 tends to zero. The non-zero difference manifests the sensing fiber is disturbed within the 41st segment. The SNR for the coarse locating in the relevance coefficients is approximate 44.55 dB. Here the SNR is calculated as 20*log(As/An), where As is the amplitude of the signal, An is the mean square root of the background noise [6]. According to the above coarse locating process, we can rapidly target the segment subjected to the external vibration and discard most of non-disturbance segments.

 

Fig. 4 Experimental result of coarse locating, (a) relevance coefficients for the segments; (b) the temporal phase profiles from endpoint ep40, ep41 and ep42, (c) the temporal phase difference profiles by subtracting the temporal phases.

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Secondly, the fine locating is implemented on the target segments for the accurate vibration location. Only 500-m sensing fiber needs to be investigated. In order to avoid the false-alarm phase peak induced by signal fading, we adopt the amplitude variance of every sensing point to identify the position of the vibration, shown in Fig. 5(a). It can be seen that the vibration is located at ~20.35 km from the peak and the spatial resolution is ~6.84 m from the inset graph in Fig. 5(a) [29]. Moreover, the vibration waveform is reproduced by the retrieved temporal phase difference and presented in Fig. 5(b) corresponding to the PZT sinusoidal vibration at 90 Hz [8, 17].

 

Fig. 5 Experimental results of fine locating, (a) amplitude variance of backscattered light from every sensing point in the 41st segment, (b) the retrieved temporal phase difference of backscattered light corresponding to the position of vibration at ~20.35 km.

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In order to study the feasibility of the coarse-fine locating method for monitoring multipoint vibrations simultaneously, we add another PZT vibration source at approximate 40 km driven by a sinusoidal signal of 60 Hz. Figure 6(a) shows the experimental results for simultaneous measurement of the two PZT vibrations by implementing coarse locating. Two peaks at the 41st and the 82nd segments are observed simultaneously, corresponding to the sensing fiber regions of 20.0 km ~20.5 km and 40.5 km ~41.0 km, respectively. The locating SNRs of 43.46 dB and 42.51 dB for the peaks reveal the excellent reliability of coarse locating. Then fine locating is performed on the two segments, and the locating results are shown in Figs. 6(b) and 6(d), respectively. Figures 6(c) and 6(e) exhibit the phase variation of backscattered light induced by the vibrations, which are exactly consistent with the ones applied on the PZTs. Note that the spatial resolution of ~7 m for vibration measurement comparable to the ones shown in previous reports is obtained in this work [5, 22]. By contrast, the computation load is greatly reduced through coarse locating.

 

Fig. 6 Location information of two PZT vibrations, (a) the result of coarse locating, (b) the result of fine locating for the 41st segment, (c) the temporal phase difference at ~20.35 km, (d) the result of fine locating for the 82nd segment, (e) the temporal phase difference at ~40.77 km.

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4. Discussion

We further investigate the overall computation cost for locating signal processing in the heterodyne coherent φ-OTDR system. Note that the computation cost is the main factor that affects the response speed of the sensing system, depending on the complexity of signal processing. Since each sensing point is subjected to the same demodulation, the computation cost depends on the amount of sensing points. Here, the computation cost Cdirect for direct locating (processing each sensing points one by one) can be expressed by:

Cdirect=qL
where q denotes the amount of sensing points per unit length and L denotes the length of entire sensing range. While the computation cost Ccf for the proposed coarse-fine locating method is given by:
Ccf=qw(L/Lseg+1)+qnLseg
where Lseg denotes the length of a segment for coarse locating, and n denotes the number of target segments. The operator ⌈⋅⌉ represents the operation of rounding up. w denotes the observation window length for each segment. In the experiment, q is 10 m−1 corresponding to the DAQ sample rate of 1 G/s and Lseg is 500 m. In order to achieve fast locating, the observation window length w should be as small as possible. Meanwhile, in order to guarantee the reliability of the coarse locating, the sensing points contained in the observation window should be enough to avoid that the observation point is selected at signal fading or vibration position. Here w is optimized to be 20 m covering 200 sensing points. Since the probability for quantities of sensing points suffering fading simultaneously is low [30], it is possible to obtain a sensing point selected as the endpoint that is free from fading within the 20-m window. Moreover, such observation point is selected that has the minimum phase difference from its adjacent sensing points to avoid vibration event [21].

Figure 7(a) compares the computation cost for direct locating and coarse-fine locating schemes when the sensing fiber length increases from 1 km to 50 km. We find that the computation cost for the coarse-fine locating is one order of magnitude less than that of the direct locating when the sensing fiber length exceeds 9 km with one intruder along the fiber. The computation cost by coarse-fine locating method grows gradually as the number of segments containing intruders increases. Noted that the coarse-fine locating method is insensitive relatively to the increasing sensing range compared with direct locating process, because most of the sensing points are excluded through the coarse locating process, which only consumes a few computations. Moreover, since the proposed coarse-fine locating method is a solution on software algorithm rather than hardware arrangement [6, 7, 31], it shows the compatibility to numerous coherent φ-OTDR. Thus, it is also applicable to the analog heterodyne demodulation scheme and FPGA-based real-time locating scheme [6, 32, 33], to further reduces the total computation cost in the long-range φ-OTDR system.

 

Fig. 7 Superiority of the coarse-fine locating method in computation cost, (a) comparison of computation cost with increasing sensing range, (b) the SNR variation for coarse locating with different length of segment.

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As the SNR for coarse locating might fluctuate with increasing the length of the divided segment, we further investigate the dependence of SNR on the segment length with single PZT at 20 km. Figure 7(b) shows that the SNR for coarse locating decreases with increasing the segment length. Because the phase noise induced by the laser source could accumulate with the distance growing [22], the segment length cannot be too large. Therefore, the segment length should be optimized by considering the responding speed and stability required in practical applications.

Further, we should discuss the potential limitations of the proposed coarse locating method. For the case that the phase change due to temperature fluctuations becomes significant over a segment, the relevance coefficient defined in Eq. (3) shows above zero even through there is no external vibration. However, the vibration still can be figured out as shown in Fig. 4(a), when the vibration induced peak is larger than the noise background that might be due to the temperature change. In order to minimize the effect of cross-talk from the temperature, an optimized threshold of relevance coefficient should be taken into account according to various practical applications. Another issue should be considered in the coarse locating process. If vibration sources act on the sensing fiber within one segment, we may face such case that the backscattered light phase change is cancelled out due to the similar magnitudes of compressing sections and expanding sections along the fiber, for example, two vibration sources with similar amplitudes and opposite phases. For this special case, the proposed coarse locating process has some limitations. Nevertheless, in practice, the external vibration disturbances generally have a certain bandwidth in vibration spectra [10–12]. As a result, it is quite rare to cancel out the phase changes induced by multiple frequencies simultaneously. Therefore, the proposed coarse locating method can satisfy most practical needs.

5. Conclusion

We present a coarse-fine locating method to improve capability of fast locating of external vibration based on heterodyne coherent φ-OTDR system. Instead of the direct locating by investigating the sensing points one by one, the location process is divided into two steps: coarse locating and fine locating. After the process of coarse locating, most sensing points that provide worthless information are excluded, but a few sensing points directly related to the vibration are preserved. Therefore, the computation cost for locating can be reduced largely. It demonstrates experimentally at the sensing fiber of about 50 km that the proposed method reduces the computation cost significantly, which indicates that the system respond speed can be optimized. Besides, the proposed method is simple and compatible to numerous coherent φ-OTDR systems on software algorithm. It is believed that the presented method can be made full use in real-time demanding cases such as train tracing, power grid monitoring, distributed acoustic sensing and etc.

Funding

National Key Research and Development Program of China (2016YFF0100600); Natural Science Foundation of China (Grant No. 61605108, 61635006, 61422507); Young Oriental Scholarship of Shanghai (QD2016025).

References and links

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2. X. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors (Basel) 12(7), 8601–8639 (2012). [CrossRef]   [PubMed]  

3. X. Fan, G. Yang, S. Wang, Q. Liu, and Z. He, “Distributed fiber-optic vibration sensing based on phase extraction from optical reflectometry,” J. Lightwave Technol. 35(16), 3281–3288 (2017). [CrossRef]  

4. X. Zhang, Z. Sun, Y. Shan, Y. Li, F. Wang, J. Zeng, and Y. Zhang, “A high performance distributed optical fiber sensor based on Φ-OTDR for dynamic strain measurement,” IEEE Photonics J. 9(3), 1–12 (2017).

5. G. Tu, X. Zhang, Y. Zhang, F. Zhu, L. Xia, and B. Nakarmi, “The development of an phi-OTDR system for quantitative vibration measurement,” IEEE Photonics Technol. Lett. 27(12), 1349–1352 (2015). [CrossRef]  

6. Z. Wang, L. Zhang, S. Wang, N. Xue, F. Peng, M. Fan, W. Sun, X. Qian, J. Rao, and Y. Rao, “Coherent Φ-OTDR based on I/Q demodulation and homodyne detection,” Opt. Express 24(2), 853–858 (2016). [CrossRef]   [PubMed]  

7. H. He, L. Y. Shao, Z. Li, Z. Zhang, X. Zou, B. Luo, W. Pan, and L. Yan, “Self-mixing demodulation for coherent phase-sensitive OTDR system,” Sensors (Basel) 16(5), 681 (2016). [CrossRef]   [PubMed]  

8. Y. Dong, X. Chen, E. Liu, C. Fu, H. Zhang, and Z. Lu, “Quantitative measurement of dynamic nanostrain based on a phase-sensitive optical time domain reflectometer,” Appl. Opt. 55(28), 7810–7815 (2016). [CrossRef]   [PubMed]  

9. F. Peng, H. Wu, X. H. Jia, Y. J. Rao, Z. N. Wang, and Z. P. Peng, “Ultra-long high-sensitivity Φ-OTDR for high spatial resolution intrusion detection of pipelines,” Opt. Express 22(11), 13804–13810 (2014). [CrossRef]   [PubMed]  

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12. F. Peng, N. Duan, Y. Rao, and J. Li, “Real-time position and speed monitoring of trains using phase-sensitive OTDR,” IEEE Photonics Technol. Lett. 26(20), 2055–2057 (2014). [CrossRef]  

13. Y. Lu, T. Zhu, L. Chen, and X. Bao, “Distributed vibration sensor based on coherent detection of phase-OTDR,” J. Lightwave Technol. 28(22), 3243–3249 (2010).

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References

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  1. J. C. Juarez, E. W. Maier, K. N. Choi, and H. F. Taylor, “Distributed fiber-optic intrusion sensor system,” J. Lightwave Technol. 23(6), 2081–2087 (2005).
    [Crossref]
  2. X. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors (Basel) 12(7), 8601–8639 (2012).
    [Crossref] [PubMed]
  3. X. Fan, G. Yang, S. Wang, Q. Liu, and Z. He, “Distributed fiber-optic vibration sensing based on phase extraction from optical reflectometry,” J. Lightwave Technol. 35(16), 3281–3288 (2017).
    [Crossref]
  4. X. Zhang, Z. Sun, Y. Shan, Y. Li, F. Wang, J. Zeng, and Y. Zhang, “A high performance distributed optical fiber sensor based on Φ-OTDR for dynamic strain measurement,” IEEE Photonics J. 9(3), 1–12 (2017).
  5. G. Tu, X. Zhang, Y. Zhang, F. Zhu, L. Xia, and B. Nakarmi, “The development of an phi-OTDR system for quantitative vibration measurement,” IEEE Photonics Technol. Lett. 27(12), 1349–1352 (2015).
    [Crossref]
  6. Z. Wang, L. Zhang, S. Wang, N. Xue, F. Peng, M. Fan, W. Sun, X. Qian, J. Rao, and Y. Rao, “Coherent Φ-OTDR based on I/Q demodulation and homodyne detection,” Opt. Express 24(2), 853–858 (2016).
    [Crossref] [PubMed]
  7. H. He, L. Y. Shao, Z. Li, Z. Zhang, X. Zou, B. Luo, W. Pan, and L. Yan, “Self-mixing demodulation for coherent phase-sensitive OTDR system,” Sensors (Basel) 16(5), 681 (2016).
    [Crossref] [PubMed]
  8. Y. Dong, X. Chen, E. Liu, C. Fu, H. Zhang, and Z. Lu, “Quantitative measurement of dynamic nanostrain based on a phase-sensitive optical time domain reflectometer,” Appl. Opt. 55(28), 7810–7815 (2016).
    [Crossref] [PubMed]
  9. F. Peng, H. Wu, X. H. Jia, Y. J. Rao, Z. N. Wang, and Z. P. Peng, “Ultra-long high-sensitivity Φ-OTDR for high spatial resolution intrusion detection of pipelines,” Opt. Express 22(11), 13804–13810 (2014).
    [Crossref] [PubMed]
  10. J. Tejedor, H. F. Martins, D. Piote, J. Macias-Guarasa, J. Pastor-Graells, S. Martin-Lopez, P. C. Guillén, F. De Smet, W. Postvoll, and M. González-Herráez, “Toward prevention of pipeline integrity threats using a smart fiber-optic surveillance system,” J. Lightwave Technol. 34(19), 4445–4453 (2016).
    [Crossref]
  11. Q. Sun, H. Feng, X. Yan, and Z. Zeng, “Recognition of a phase-sensitivity OTDR sensing system based on morphologic feature extraction,” Sensors (Basel) 15(7), 15179–15197 (2015).
    [Crossref] [PubMed]
  12. F. Peng, N. Duan, Y. Rao, and J. Li, “Real-time position and speed monitoring of trains using phase-sensitive OTDR,” IEEE Photonics Technol. Lett. 26(20), 2055–2057 (2014).
    [Crossref]
  13. Y. Lu, T. Zhu, L. Chen, and X. Bao, “Distributed vibration sensor based on coherent detection of phase-OTDR,” J. Lightwave Technol. 28(22), 3243–3249 (2010).
  14. Z. Qin, L. Chen, and X. Bao, “Continuous wavelet transform for non-stationary vibration detection with phase-OTDR,” Opt. Express 20(18), 20459–20465 (2012).
    [Crossref] [PubMed]
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2017 (7)

X. Fan, G. Yang, S. Wang, Q. Liu, and Z. He, “Distributed fiber-optic vibration sensing based on phase extraction from optical reflectometry,” J. Lightwave Technol. 35(16), 3281–3288 (2017).
[Crossref]

X. Zhang, Z. Sun, Y. Shan, Y. Li, F. Wang, J. Zeng, and Y. Zhang, “A high performance distributed optical fiber sensor based on Φ-OTDR for dynamic strain measurement,” IEEE Photonics J. 9(3), 1–12 (2017).

H. He, L. Shao, H. Li, W. Pan, B. Luo, X. Zou, and L. Yan, “SNR enhancement in phase-sensitive OTDR with adaptive 2-D Bilateral filtering algorithm,” IEEE Photonics J. 9(3), 1–10 (2017).

B. Lu, Z. Pan, Z. Wang, H. Zheng, Q. Ye, R. Qu, and H. Cai, “High spatial resolution phase-sensitive optical time domain reflectometer with a frequency-swept pulse,” Opt. Lett. 42(3), 391–394 (2017).
[Crossref] [PubMed]

J. Pastor-Graells, L. R. Cortés, M. R. Fernández-Ruiz, H. F. Martins, J. Azaña, S. Martin-Lopez, and M. Gonzalez-Herraez, “SNR enhancement in high-resolution phase-sensitive OTDR systems using chirped pulse amplification concepts,” Opt. Lett. 42(9), 1728–1731 (2017).
[Crossref] [PubMed]

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] [PubMed]

Y. Wang, B. Jin, Y. Wang, D. Wang, X. Liu, and Q. Bai, “Real-Time Distributed Vibration Monitoring System Using Φ-OTDR,” IEEE Sens. J. 17(5), 1333–1341 (2017).
[Crossref]

2016 (9)

C. Franciscangelis, W. Margulis, L. Kjellberg, I. Soderquist, and F. Fruett, “Real-time distributed fiber microphone based on phase-OTDR,” Opt. Express 24(26), 29597–29602 (2016).
[Crossref] [PubMed]

M. Ren, P. Lu, L. Chen, and X. Bao, “Theoretical and experimental analysis of Φ-OTDR based on polarization diversity detection,” IEEE Photonics Technol. Lett. 28(6), 697–700 (2016).
[Crossref]

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]

G. Yang, X. Fan, S. Wang, B. Wang, Q. Liu, and Z. He, “Long-range distributed vibration sensing based on phase extraction from phase-sensitive OTDR,” IEEE Photonics J. 8(3), 1–12 (2016).

J. Zhang, T. Zhu, H. Zhou, S. Huang, M. Liu, and W. Huang, “High spatial resolution distributed fiber system for multi-parameter sensing based on modulated pulses,” Opt. Express 24(24), 27482–27493 (2016).
[Crossref] [PubMed]

J. Tejedor, H. F. Martins, D. Piote, J. Macias-Guarasa, J. Pastor-Graells, S. Martin-Lopez, P. C. Guillén, F. De Smet, W. Postvoll, and M. González-Herráez, “Toward prevention of pipeline integrity threats using a smart fiber-optic surveillance system,” J. Lightwave Technol. 34(19), 4445–4453 (2016).
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Z. Wang, L. Zhang, S. Wang, N. Xue, F. Peng, M. Fan, W. Sun, X. Qian, J. Rao, and Y. Rao, “Coherent Φ-OTDR based on I/Q demodulation and homodyne detection,” Opt. Express 24(2), 853–858 (2016).
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H. He, L. Y. Shao, Z. Li, Z. Zhang, X. Zou, B. Luo, W. Pan, and L. Yan, “Self-mixing demodulation for coherent phase-sensitive OTDR system,” Sensors (Basel) 16(5), 681 (2016).
[Crossref] [PubMed]

Y. Dong, X. Chen, E. Liu, C. Fu, H. Zhang, and Z. Lu, “Quantitative measurement of dynamic nanostrain based on a phase-sensitive optical time domain reflectometer,” Appl. Opt. 55(28), 7810–7815 (2016).
[Crossref] [PubMed]

2015 (3)

G. Tu, X. Zhang, Y. Zhang, F. Zhu, L. Xia, and B. Nakarmi, “The development of an phi-OTDR system for quantitative vibration measurement,” IEEE Photonics Technol. Lett. 27(12), 1349–1352 (2015).
[Crossref]

Q. Sun, H. Feng, X. Yan, and Z. Zeng, “Recognition of a phase-sensitivity OTDR sensing system based on morphologic feature extraction,” Sensors (Basel) 15(7), 15179–15197 (2015).
[Crossref] [PubMed]

H. Wu, S. Xiao, X. Li, Z. Wang, J. Xu, and Y. Rao, “Separation and determination of the disturbing signals in phase-sensitive optical time domain reflectometry (Φ-OTDR),” J. Lightwave Technol. 33(15), 3156–3162 (2015).
[Crossref]

2014 (3)

2013 (2)

2012 (2)

2010 (1)

2005 (1)

1988 (1)

J. Lee Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Am. Stat. 42(1), 59–66 (1988).
[Crossref]

1896 (1)

K. Pearson, “Mathematical contributions to the theory of evolution. III. Regression, heredity, and panmixia,” Philosophical Trans. Royal Soc. London Series A 187(0), 253–318 (1896).
[Crossref]

Azaña, J.

Bai, Q.

Y. Wang, B. Jin, Y. Wang, D. Wang, X. Liu, and Q. Bai, “Real-Time Distributed Vibration Monitoring System Using Φ-OTDR,” IEEE Sens. J. 17(5), 1333–1341 (2017).
[Crossref]

Bao, X.

M. Ren, P. Lu, L. Chen, and X. Bao, “Theoretical and experimental analysis of Φ-OTDR based on polarization diversity detection,” IEEE Photonics Technol. Lett. 28(6), 697–700 (2016).
[Crossref]

Z. Qin, L. Chen, and X. Bao, “Continuous wavelet transform for non-stationary vibration detection with phase-OTDR,” Opt. Express 20(18), 20459–20465 (2012).
[Crossref] [PubMed]

X. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors (Basel) 12(7), 8601–8639 (2012).
[Crossref] [PubMed]

Y. Lu, T. Zhu, L. Chen, and X. Bao, “Distributed vibration sensor based on coherent detection of phase-OTDR,” J. Lightwave Technol. 28(22), 3243–3249 (2010).

Cai, H.

Cao, S.

Chen, L.

M. Ren, P. Lu, L. Chen, and X. Bao, “Theoretical and experimental analysis of Φ-OTDR based on polarization diversity detection,” IEEE Photonics Technol. Lett. 28(6), 697–700 (2016).
[Crossref]

Z. Qin, L. Chen, and X. Bao, “Continuous wavelet transform for non-stationary vibration detection with phase-OTDR,” Opt. Express 20(18), 20459–20465 (2012).
[Crossref] [PubMed]

X. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors (Basel) 12(7), 8601–8639 (2012).
[Crossref] [PubMed]

Y. Lu, T. Zhu, L. Chen, and X. Bao, “Distributed vibration sensor based on coherent detection of phase-OTDR,” J. Lightwave Technol. 28(22), 3243–3249 (2010).

Chen, N.

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]

Chen, X.

Chi, H.

Choi, K. N.

Clark, V. A.

O. J. Dunn and V. A. Clark, Applied Statistics: Analysis of Variance and Regression (1974).

Cortés, L. R.

De Smet, F.

Diao, D.

Dong, Y.

Duan, N.

F. Peng, N. Duan, Y. Rao, and J. Li, “Real-time position and speed monitoring of trains using phase-sensitive OTDR,” IEEE Photonics Technol. Lett. 26(20), 2055–2057 (2014).
[Crossref]

Dunn, O. J.

O. J. Dunn and V. A. Clark, Applied Statistics: Analysis of Variance and Regression (1974).

Fan, M.

Fan, X.

X. Fan, G. Yang, S. Wang, Q. Liu, and Z. He, “Distributed fiber-optic vibration sensing based on phase extraction from optical reflectometry,” J. Lightwave Technol. 35(16), 3281–3288 (2017).
[Crossref]

G. Yang, X. Fan, S. Wang, B. Wang, Q. Liu, and Z. He, “Long-range distributed vibration sensing based on phase extraction from phase-sensitive OTDR,” IEEE Photonics J. 8(3), 1–12 (2016).

Fang, Z.

Feng, H.

Q. Sun, H. Feng, X. Yan, and Z. Zeng, “Recognition of a phase-sensitivity OTDR sensing system based on morphologic feature extraction,” Sensors (Basel) 15(7), 15179–15197 (2015).
[Crossref] [PubMed]

Fernández-Ruiz, M. R.

Franciscangelis, C.

Fruett, F.

Fu, C.

Gonzalez-Herraez, M.

González-Herráez, M.

Gu, L.

Guillén, P. C.

He, H.

H. He, L. Shao, H. Li, W. Pan, B. Luo, X. Zou, and L. Yan, “SNR enhancement in phase-sensitive OTDR with adaptive 2-D Bilateral filtering algorithm,” IEEE Photonics J. 9(3), 1–10 (2017).

H. He, L. Y. Shao, Z. Li, Z. Zhang, X. Zou, B. Luo, W. Pan, and L. Yan, “Self-mixing demodulation for coherent phase-sensitive OTDR system,” Sensors (Basel) 16(5), 681 (2016).
[Crossref] [PubMed]

He, M.

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]

He, Q.

He, X.

He, Z.

X. Fan, G. Yang, S. Wang, Q. Liu, and Z. He, “Distributed fiber-optic vibration sensing based on phase extraction from optical reflectometry,” J. Lightwave Technol. 35(16), 3281–3288 (2017).
[Crossref]

G. Yang, X. Fan, S. Wang, B. Wang, Q. Liu, and Z. He, “Long-range distributed vibration sensing based on phase extraction from phase-sensitive OTDR,” IEEE Photonics J. 8(3), 1–12 (2016).

Huang, S.

Huang, W.

Hui, X.

Jia, X. H.

Jin, B.

Y. Wang, B. Jin, Y. Wang, D. Wang, X. Liu, and Q. Bai, “Real-Time Distributed Vibration Monitoring System Using Φ-OTDR,” IEEE Sens. J. 17(5), 1333–1341 (2017).
[Crossref]

Jin, X.

Juarez, J. C.

Kjellberg, L.

Lee Rodgers, J.

J. Lee Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Am. Stat. 42(1), 59–66 (1988).
[Crossref]

Li, H.

H. He, L. Shao, H. Li, W. Pan, B. Luo, X. Zou, and L. Yan, “SNR enhancement in phase-sensitive OTDR with adaptive 2-D Bilateral filtering algorithm,” IEEE Photonics J. 9(3), 1–10 (2017).

Li, J.

F. Peng, N. Duan, Y. Rao, and J. Li, “Real-time position and speed monitoring of trains using phase-sensitive OTDR,” IEEE Photonics Technol. Lett. 26(20), 2055–2057 (2014).
[Crossref]

Li, X.

Li, Y.

X. Zhang, Z. Sun, Y. Shan, Y. Li, F. Wang, J. Zeng, and Y. Zhang, “A high performance distributed optical fiber sensor based on Φ-OTDR for dynamic strain measurement,” IEEE Photonics J. 9(3), 1–12 (2017).

Li, Z.

H. He, L. Y. Shao, Z. Li, Z. Zhang, X. Zou, B. Luo, W. Pan, and L. Yan, “Self-mixing demodulation for coherent phase-sensitive OTDR system,” Sensors (Basel) 16(5), 681 (2016).
[Crossref] [PubMed]

Liu, E.

Liu, F.

Liu, H.

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]

Liu, M.

Liu, Q.

X. Fan, G. Yang, S. Wang, Q. Liu, and Z. He, “Distributed fiber-optic vibration sensing based on phase extraction from optical reflectometry,” J. Lightwave Technol. 35(16), 3281–3288 (2017).
[Crossref]

G. Yang, X. Fan, S. Wang, B. Wang, Q. Liu, and Z. He, “Long-range distributed vibration sensing based on phase extraction from phase-sensitive OTDR,” IEEE Photonics J. 8(3), 1–12 (2016).

Liu, X.

Y. Wang, B. Jin, Y. Wang, D. Wang, X. Liu, and Q. Bai, “Real-Time Distributed Vibration Monitoring System Using Φ-OTDR,” IEEE Sens. J. 17(5), 1333–1341 (2017).
[Crossref]

Lu, B.

Lu, P.

M. Ren, P. Lu, L. Chen, and X. Bao, “Theoretical and experimental analysis of Φ-OTDR based on polarization diversity detection,” IEEE Photonics Technol. Lett. 28(6), 697–700 (2016).
[Crossref]

Lu, Y.

Lu, Z.

Luo, B.

H. He, L. Shao, H. Li, W. Pan, B. Luo, X. Zou, and L. Yan, “SNR enhancement in phase-sensitive OTDR with adaptive 2-D Bilateral filtering algorithm,” IEEE Photonics J. 9(3), 1–10 (2017).

H. He, L. Y. Shao, Z. Li, Z. Zhang, X. Zou, B. Luo, W. Pan, and L. Yan, “Self-mixing demodulation for coherent phase-sensitive OTDR system,” Sensors (Basel) 16(5), 681 (2016).
[Crossref] [PubMed]

Macias-Guarasa, J.

Maier, E. W.

Margulis, W.

Martin-Lopez, S.

Martins, H. F.

Mei, X.

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]

Nakarmi, B.

G. Tu, X. Zhang, Y. Zhang, F. Zhu, L. Xia, and B. Nakarmi, “The development of an phi-OTDR system for quantitative vibration measurement,” IEEE Photonics Technol. Lett. 27(12), 1349–1352 (2015).
[Crossref]

Nicewander, W. A.

J. Lee Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Am. Stat. 42(1), 59–66 (1988).
[Crossref]

Pan, W.

H. He, L. Shao, H. Li, W. Pan, B. Luo, X. Zou, and L. Yan, “SNR enhancement in phase-sensitive OTDR with adaptive 2-D Bilateral filtering algorithm,” IEEE Photonics J. 9(3), 1–10 (2017).

H. He, L. Y. Shao, Z. Li, Z. Zhang, X. Zou, B. Luo, W. Pan, and L. Yan, “Self-mixing demodulation for coherent phase-sensitive OTDR system,” Sensors (Basel) 16(5), 681 (2016).
[Crossref] [PubMed]

Pan, Z.

Pang, F.

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]

Pastor-Graells, J.

Pearson, K.

K. Pearson, “Mathematical contributions to the theory of evolution. III. Regression, heredity, and panmixia,” Philosophical Trans. Royal Soc. London Series A 187(0), 253–318 (1896).
[Crossref]

Peng, F.

Peng, Z. P.

Piote, D.

Postvoll, W.

Qian, X.

Qin, Z.

Qu, R.

Rao, J.

Rao, Y.

Rao, Y. J.

Ren, M.

M. Ren, P. Lu, L. Chen, and X. Bao, “Theoretical and experimental analysis of Φ-OTDR based on polarization diversity detection,” IEEE Photonics Technol. Lett. 28(6), 697–700 (2016).
[Crossref]

Shan, Y.

X. Zhang, Z. Sun, Y. Shan, Y. Li, F. Wang, J. Zeng, and Y. Zhang, “A high performance distributed optical fiber sensor based on Φ-OTDR for dynamic strain measurement,” IEEE Photonics J. 9(3), 1–12 (2017).

Shao, L.

H. He, L. Shao, H. Li, W. Pan, B. Luo, X. Zou, and L. Yan, “SNR enhancement in phase-sensitive OTDR with adaptive 2-D Bilateral filtering algorithm,” IEEE Photonics J. 9(3), 1–10 (2017).

Shao, L. Y.

H. He, L. Y. Shao, Z. Li, Z. Zhang, X. Zou, B. Luo, W. Pan, and L. Yan, “Self-mixing demodulation for coherent phase-sensitive OTDR system,” Sensors (Basel) 16(5), 681 (2016).
[Crossref] [PubMed]

Soderquist, I.

Sun, Q.

Q. Sun, H. Feng, X. Yan, and Z. Zeng, “Recognition of a phase-sensitivity OTDR sensing system based on morphologic feature extraction,” Sensors (Basel) 15(7), 15179–15197 (2015).
[Crossref] [PubMed]

Sun, W.

Sun, Z.

X. Zhang, Z. Sun, Y. Shan, Y. Li, F. Wang, J. Zeng, and Y. Zhang, “A high performance distributed optical fiber sensor based on Φ-OTDR for dynamic strain measurement,” IEEE Photonics J. 9(3), 1–12 (2017).

Tao, J.

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]

Taylor, H. F.

Tejedor, J.

Tu, G.

G. Tu, X. Zhang, Y. Zhang, F. Zhu, L. Xia, and B. Nakarmi, “The development of an phi-OTDR system for quantitative vibration measurement,” IEEE Photonics Technol. Lett. 27(12), 1349–1352 (2015).
[Crossref]

Wang, B.

G. Yang, X. Fan, S. Wang, B. Wang, Q. Liu, and Z. He, “Long-range distributed vibration sensing based on phase extraction from phase-sensitive OTDR,” IEEE Photonics J. 8(3), 1–12 (2016).

Wang, D.

Y. Wang, B. Jin, Y. Wang, D. Wang, X. Liu, and Q. Bai, “Real-Time Distributed Vibration Monitoring System Using Φ-OTDR,” IEEE Sens. J. 17(5), 1333–1341 (2017).
[Crossref]

Wang, F.

X. Zhang, Z. Sun, Y. Shan, Y. Li, F. Wang, J. Zeng, and Y. Zhang, “A high performance distributed optical fiber sensor based on Φ-OTDR for dynamic strain measurement,” IEEE Photonics J. 9(3), 1–12 (2017).

Wang, S.

Wang, T.

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]

Wang, Y.

Y. Wang, B. Jin, Y. Wang, D. Wang, X. Liu, and Q. Bai, “Real-Time Distributed Vibration Monitoring System Using Φ-OTDR,” IEEE Sens. J. 17(5), 1333–1341 (2017).
[Crossref]

Y. Wang, B. Jin, Y. Wang, D. Wang, X. Liu, and Q. Bai, “Real-Time Distributed Vibration Monitoring System Using Φ-OTDR,” IEEE Sens. J. 17(5), 1333–1341 (2017).
[Crossref]

Wang, Z.

Wang, Z. N.

Wu, H.

Xia, L.

G. Tu, X. Zhang, Y. Zhang, F. Zhu, L. Xia, and B. Nakarmi, “The development of an phi-OTDR system for quantitative vibration measurement,” IEEE Photonics Technol. Lett. 27(12), 1349–1352 (2015).
[Crossref]

Xiao, S.

Xiao, X.

Xie, S.

Xu, J.

Xue, N.

Yan, L.

H. He, L. Shao, H. Li, W. Pan, B. Luo, X. Zou, and L. Yan, “SNR enhancement in phase-sensitive OTDR with adaptive 2-D Bilateral filtering algorithm,” IEEE Photonics J. 9(3), 1–10 (2017).

H. He, L. Y. Shao, Z. Li, Z. Zhang, X. Zou, B. Luo, W. Pan, and L. Yan, “Self-mixing demodulation for coherent phase-sensitive OTDR system,” Sensors (Basel) 16(5), 681 (2016).
[Crossref] [PubMed]

Yan, X.

Q. Sun, H. Feng, X. Yan, and Z. Zeng, “Recognition of a phase-sensitivity OTDR sensing system based on morphologic feature extraction,” Sensors (Basel) 15(7), 15179–15197 (2015).
[Crossref] [PubMed]

Yang, G.

X. Fan, G. Yang, S. Wang, Q. Liu, and Z. He, “Distributed fiber-optic vibration sensing based on phase extraction from optical reflectometry,” J. Lightwave Technol. 35(16), 3281–3288 (2017).
[Crossref]

G. Yang, X. Fan, S. Wang, B. Wang, Q. Liu, and Z. He, “Long-range distributed vibration sensing based on phase extraction from phase-sensitive OTDR,” IEEE Photonics J. 8(3), 1–12 (2016).

Ye, Q.

Ye, T.

Zeng, J.

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G. Tu, X. Zhang, Y. Zhang, F. Zhu, L. Xia, and B. Nakarmi, “The development of an phi-OTDR system for quantitative vibration measurement,” IEEE Photonics Technol. Lett. 27(12), 1349–1352 (2015).
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H. He, L. Y. Shao, Z. Li, Z. Zhang, X. Zou, B. Luo, W. Pan, and L. Yan, “Self-mixing demodulation for coherent phase-sensitive OTDR system,” Sensors (Basel) 16(5), 681 (2016).
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H. He, L. Shao, H. Li, W. Pan, B. Luo, X. Zou, and L. Yan, “SNR enhancement in phase-sensitive OTDR with adaptive 2-D Bilateral filtering algorithm,” IEEE Photonics J. 9(3), 1–10 (2017).

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Figures (7)

Fig. 1
Fig. 1 Principle of Rayleigh backscattering in φ-OTDR.
Fig. 2
Fig. 2 Schematic diagram of coarse locating.
Fig. 3
Fig. 3 Schematic diagram of the heterodyne coherent φ-OTDR system: narrow linewidth laser (NLL); acoustic-optic modulator (AOM); erbium-doped fiber amplifier (EDFA); piezo transducer (PZT); balanced photodetector (BPD); data acquisition (DAQ); arbitrary function generator (AFG); personal computer (PC).
Fig. 4
Fig. 4 Experimental result of coarse locating, (a) relevance coefficients for the segments; (b) the temporal phase profiles from endpoint ep40, ep41 and ep42, (c) the temporal phase difference profiles by subtracting the temporal phases.
Fig. 5
Fig. 5 Experimental results of fine locating, (a) amplitude variance of backscattered light from every sensing point in the 41st segment, (b) the retrieved temporal phase difference of backscattered light corresponding to the position of vibration at ~20.35 km.
Fig. 6
Fig. 6 Location information of two PZT vibrations, (a) the result of coarse locating, (b) the result of fine locating for the 41st segment, (c) the temporal phase difference at ~20.35 km, (d) the result of fine locating for the 82nd segment, (e) the temporal phase difference at ~40.77 km.
Fig. 7
Fig. 7 Superiority of the coarse-fine locating method in computation cost, (a) comparison of computation cost with increasing sensing range, (b) the SNR variation for coarse locating with different length of segment.

Equations (5)

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P A C E s E l o cos ( 2 π Δ f t + φ z )
r ( X , Y ) = ( X k X ¯ ) ( Y k Y ¯ ) [ ( X k X ¯ ) 2 ( Y k Y ¯ ) 2 ] 1 /2
s i = s ( φ i 1 , φ i ) = 1 r ( φ i 1 , φ i )
C d i r e c t = q L
C c f = q w ( L / L s e g + 1 ) + q n L s e g

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