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

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References

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    [Crossref] [PubMed]

2017 (7)

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).

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]

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]

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]

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. 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]

2016 (9)

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]

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]

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]

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]

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).

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]

2015 (3)

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]

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]

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]

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

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]

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]

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

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]

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).
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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).
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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]

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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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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]

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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).
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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]

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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).
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Ye, T.

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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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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. 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).
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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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