Abstract

For a distributed fiber-optic vibration sensor (DFVS), the vibration signal extracted from the phase of backscattering has a linear response to the applied vibration, and is more attractive than that from the intensity term. However, the large phase noise at a random weak-fading-point seriously limits the sensor's credibility. In this paper, a novel phase-detection DFVS is developed, which effectively eliminates the weak-fading-point. The relationship between phase noise and the intensity of backscattering is analyzed, and the inner-pulse frequency-division method and rotated-vector-sum method are introduced to effectively suppress phase noise. In experiments, two simultaneous vibrations along the 35-kilometer-long fiber are clearly detected by phase detection with the signal-to-noise ratio (SNR) over 26 dB. The spatial resolution approaches 5 m and the vibration response bandwidth is 1.25 kHz.

© 2017 Optical Society of America

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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 (2005).
    [Crossref]
  2. 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).
  3. Z. Qin, T. Zhu, L. Chen, and X. Bao, “High sensitivity distributed vibration sensor based on polarization-maintaining configurations of phase-OTDR,” IEEE Photon. Technol. Lett. 23(15), 1091–1093 (2011).
    [Crossref]
  4. Z. Qin, L. Chen, and X. Bao, “Wavelet denoising method for improving detection performance of distributed vibration sensor,” IEEE Photon. Technol. Lett. 24(7), 542–544 (2012).
    [Crossref]
  5. P. Healey, “Fading in heterodyne OTDR,” Electron. Lett. 20(1), 30–32 (1984).
    [Crossref]
  6. Z. Pan, K. Liang, Q. Ye, H. Cai, R. Qu, and Z. Fang, “Phase-sensitive OTDR system based on digital coherent detection,” in Optical Sensors and Biophotonics, (Optical Society of America, 2011), paper 83110S.
  7. H. F. Martins, K. Shi, B. C. Thomsen, S. Martin-Lopez, M. Gonzalez-Herraez, and S. J. Savory, “Real time dynamic strain monitoring of optical links using the backreflection of live PSK data,” Opt. Express 24(19), 22303–22318 (2016).
    [Crossref] [PubMed]
  8. Z. Pan, K. Liang, J. Zhou, Q. Ye, H. Cai, and R. Qu, “Interference-fading-free phase-demodulated OTDR system,” Proc. SPIE,  8421, 842129 (2012).
    [Crossref]
  9. J. Zhou, Z. Q. Pan, Q. Ye, H. W. Cai, R. H. Qu, and Z. J. Fang, “Phase demodulation technology using a multi-frequency source discrimination of interference-fading induced false alarm in a ϕ-OTDR system,” Chin. J. Lasers 40(9), 0905003 (2013).
    [Crossref]
  10. Q. Liu, X. Fan, and Z. He, “Time-gated digital optical frequency domain reflectometry with 1.6-m spatial resolution over entire 110-km range,” Opt. Express 23(20), 25988–25995 (2015).
    [Crossref] [PubMed]
  11. S. Wang, X. Fan, Q. Liu, and Z. He, “Distributed fiber-optic vibration sensing based on phase extraction from time-gated digital OFDR,” Opt. Express 23(26), 33301–33309 (2015).
    [Crossref]
  12. D. Chen, Q. Liu, X. Fan, and Z. He, “Distributed fiber-optic acoustic sensor with enhanced response bandwidth and high signal-to-noise ratio,” J. Lightwave Technol. to be published.
  13. Y. Namihira, “Opto-elastic constant in single mode optical fibers,” J. Lightwave Technol. 3(5), 1078–1083 (1985).
    [Crossref]
  14. A. Bertholds and R. Dandliker, “Determination of the individual strain-optic coefficients in single-mode optical fibers,” J. Lightwave Technol. 6(1), 17–20 (1988).
    [Crossref]
  15. D. A. Jackson, R. Priest, A. Dandridge, and A. B. Tveten, “Elimination of drift in a single-mode optical fiber interferometer using a piezoelectrically stretched coiled fiber,” Appl. Opt. 19(17), 2926–2929 (1980).
    [Crossref] [PubMed]
  16. 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 Photon. J. 8(3), 1–12 (2016).
  17. J. Zhou, Z. Pan, Q. Ye, H. Cai, R. Qu, and Z. Fang, “Characteristics and explanations of interference fading of a ϕ-OTDR with a multi-frequency source,” J. Lightwave Technol. 31(17), 2947–2954 (2013).
    [Crossref]
  18. K. Shimizu, T. Horiguchi, and Y. Koyamada, “Characteristics and reduction of coherent fading noise in rayleigh backscattering measurement for optical fibers and components,” J. Lightwave Technol. 10(7), 982–987 (1992).
    [Crossref]

2016 (2)

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 Photon. J. 8(3), 1–12 (2016).

H. F. Martins, K. Shi, B. C. Thomsen, S. Martin-Lopez, M. Gonzalez-Herraez, and S. J. Savory, “Real time dynamic strain monitoring of optical links using the backreflection of live PSK data,” Opt. Express 24(19), 22303–22318 (2016).
[Crossref] [PubMed]

2015 (2)

2013 (2)

J. Zhou, Z. Pan, Q. Ye, H. Cai, R. Qu, and Z. Fang, “Characteristics and explanations of interference fading of a ϕ-OTDR with a multi-frequency source,” J. Lightwave Technol. 31(17), 2947–2954 (2013).
[Crossref]

J. Zhou, Z. Q. Pan, Q. Ye, H. W. Cai, R. H. Qu, and Z. J. Fang, “Phase demodulation technology using a multi-frequency source discrimination of interference-fading induced false alarm in a ϕ-OTDR system,” Chin. J. Lasers 40(9), 0905003 (2013).
[Crossref]

2012 (2)

Z. Qin, L. Chen, and X. Bao, “Wavelet denoising method for improving detection performance of distributed vibration sensor,” IEEE Photon. Technol. Lett. 24(7), 542–544 (2012).
[Crossref]

Z. Pan, K. Liang, J. Zhou, Q. Ye, H. Cai, and R. Qu, “Interference-fading-free phase-demodulated OTDR system,” Proc. SPIE,  8421, 842129 (2012).
[Crossref]

2011 (1)

Z. Qin, T. Zhu, L. Chen, and X. Bao, “High sensitivity distributed vibration sensor based on polarization-maintaining configurations of phase-OTDR,” IEEE Photon. Technol. Lett. 23(15), 1091–1093 (2011).
[Crossref]

2010 (1)

2005 (1)

1992 (1)

K. Shimizu, T. Horiguchi, and Y. Koyamada, “Characteristics and reduction of coherent fading noise in rayleigh backscattering measurement for optical fibers and components,” J. Lightwave Technol. 10(7), 982–987 (1992).
[Crossref]

1988 (1)

A. Bertholds and R. Dandliker, “Determination of the individual strain-optic coefficients in single-mode optical fibers,” J. Lightwave Technol. 6(1), 17–20 (1988).
[Crossref]

1985 (1)

Y. Namihira, “Opto-elastic constant in single mode optical fibers,” J. Lightwave Technol. 3(5), 1078–1083 (1985).
[Crossref]

1984 (1)

P. Healey, “Fading in heterodyne OTDR,” Electron. Lett. 20(1), 30–32 (1984).
[Crossref]

1980 (1)

Bao, X.

Z. Qin, L. Chen, and X. Bao, “Wavelet denoising method for improving detection performance of distributed vibration sensor,” IEEE Photon. Technol. Lett. 24(7), 542–544 (2012).
[Crossref]

Z. Qin, T. Zhu, L. Chen, and X. Bao, “High sensitivity distributed vibration sensor based on polarization-maintaining configurations of phase-OTDR,” IEEE Photon. Technol. Lett. 23(15), 1091–1093 (2011).
[Crossref]

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).

Bertholds, A.

A. Bertholds and R. Dandliker, “Determination of the individual strain-optic coefficients in single-mode optical fibers,” J. Lightwave Technol. 6(1), 17–20 (1988).
[Crossref]

Cai, H.

J. Zhou, Z. Pan, Q. Ye, H. Cai, R. Qu, and Z. Fang, “Characteristics and explanations of interference fading of a ϕ-OTDR with a multi-frequency source,” J. Lightwave Technol. 31(17), 2947–2954 (2013).
[Crossref]

Z. Pan, K. Liang, J. Zhou, Q. Ye, H. Cai, and R. Qu, “Interference-fading-free phase-demodulated OTDR system,” Proc. SPIE,  8421, 842129 (2012).
[Crossref]

Z. Pan, K. Liang, Q. Ye, H. Cai, R. Qu, and Z. Fang, “Phase-sensitive OTDR system based on digital coherent detection,” in Optical Sensors and Biophotonics, (Optical Society of America, 2011), paper 83110S.

Cai, H. W.

J. Zhou, Z. Q. Pan, Q. Ye, H. W. Cai, R. H. Qu, and Z. J. Fang, “Phase demodulation technology using a multi-frequency source discrimination of interference-fading induced false alarm in a ϕ-OTDR system,” Chin. J. Lasers 40(9), 0905003 (2013).
[Crossref]

Chen, D.

D. Chen, Q. Liu, X. Fan, and Z. He, “Distributed fiber-optic acoustic sensor with enhanced response bandwidth and high signal-to-noise ratio,” J. Lightwave Technol. to be published.

Chen, L.

Z. Qin, L. Chen, and X. Bao, “Wavelet denoising method for improving detection performance of distributed vibration sensor,” IEEE Photon. Technol. Lett. 24(7), 542–544 (2012).
[Crossref]

Z. Qin, T. Zhu, L. Chen, and X. Bao, “High sensitivity distributed vibration sensor based on polarization-maintaining configurations of phase-OTDR,” IEEE Photon. Technol. Lett. 23(15), 1091–1093 (2011).
[Crossref]

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).

Choi, K. N.

Dandliker, R.

A. Bertholds and R. Dandliker, “Determination of the individual strain-optic coefficients in single-mode optical fibers,” J. Lightwave Technol. 6(1), 17–20 (1988).
[Crossref]

Dandridge, A.

Fan, X.

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 Photon. J. 8(3), 1–12 (2016).

Q. Liu, X. Fan, and Z. He, “Time-gated digital optical frequency domain reflectometry with 1.6-m spatial resolution over entire 110-km range,” Opt. Express 23(20), 25988–25995 (2015).
[Crossref] [PubMed]

S. Wang, X. Fan, Q. Liu, and Z. He, “Distributed fiber-optic vibration sensing based on phase extraction from time-gated digital OFDR,” Opt. Express 23(26), 33301–33309 (2015).
[Crossref]

D. Chen, Q. Liu, X. Fan, and Z. He, “Distributed fiber-optic acoustic sensor with enhanced response bandwidth and high signal-to-noise ratio,” J. Lightwave Technol. to be published.

Fang, Z.

J. Zhou, Z. Pan, Q. Ye, H. Cai, R. Qu, and Z. Fang, “Characteristics and explanations of interference fading of a ϕ-OTDR with a multi-frequency source,” J. Lightwave Technol. 31(17), 2947–2954 (2013).
[Crossref]

Z. Pan, K. Liang, Q. Ye, H. Cai, R. Qu, and Z. Fang, “Phase-sensitive OTDR system based on digital coherent detection,” in Optical Sensors and Biophotonics, (Optical Society of America, 2011), paper 83110S.

Fang, Z. J.

J. Zhou, Z. Q. Pan, Q. Ye, H. W. Cai, R. H. Qu, and Z. J. Fang, “Phase demodulation technology using a multi-frequency source discrimination of interference-fading induced false alarm in a ϕ-OTDR system,” Chin. J. Lasers 40(9), 0905003 (2013).
[Crossref]

Gonzalez-Herraez, M.

He, Z.

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 Photon. J. 8(3), 1–12 (2016).

Q. Liu, X. Fan, and Z. He, “Time-gated digital optical frequency domain reflectometry with 1.6-m spatial resolution over entire 110-km range,” Opt. Express 23(20), 25988–25995 (2015).
[Crossref] [PubMed]

S. Wang, X. Fan, Q. Liu, and Z. He, “Distributed fiber-optic vibration sensing based on phase extraction from time-gated digital OFDR,” Opt. Express 23(26), 33301–33309 (2015).
[Crossref]

D. Chen, Q. Liu, X. Fan, and Z. He, “Distributed fiber-optic acoustic sensor with enhanced response bandwidth and high signal-to-noise ratio,” J. Lightwave Technol. to be published.

Healey, P.

P. Healey, “Fading in heterodyne OTDR,” Electron. Lett. 20(1), 30–32 (1984).
[Crossref]

Horiguchi, T.

K. Shimizu, T. Horiguchi, and Y. Koyamada, “Characteristics and reduction of coherent fading noise in rayleigh backscattering measurement for optical fibers and components,” J. Lightwave Technol. 10(7), 982–987 (1992).
[Crossref]

Jackson, D. A.

Juarez, J. C.

Koyamada, Y.

K. Shimizu, T. Horiguchi, and Y. Koyamada, “Characteristics and reduction of coherent fading noise in rayleigh backscattering measurement for optical fibers and components,” J. Lightwave Technol. 10(7), 982–987 (1992).
[Crossref]

Liang, K.

Z. Pan, K. Liang, J. Zhou, Q. Ye, H. Cai, and R. Qu, “Interference-fading-free phase-demodulated OTDR system,” Proc. SPIE,  8421, 842129 (2012).
[Crossref]

Z. Pan, K. Liang, Q. Ye, H. Cai, R. Qu, and Z. Fang, “Phase-sensitive OTDR system based on digital coherent detection,” in Optical Sensors and Biophotonics, (Optical Society of America, 2011), paper 83110S.

Liu, Q.

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 Photon. J. 8(3), 1–12 (2016).

S. Wang, X. Fan, Q. Liu, and Z. He, “Distributed fiber-optic vibration sensing based on phase extraction from time-gated digital OFDR,” Opt. Express 23(26), 33301–33309 (2015).
[Crossref]

Q. Liu, X. Fan, and Z. He, “Time-gated digital optical frequency domain reflectometry with 1.6-m spatial resolution over entire 110-km range,” Opt. Express 23(20), 25988–25995 (2015).
[Crossref] [PubMed]

D. Chen, Q. Liu, X. Fan, and Z. He, “Distributed fiber-optic acoustic sensor with enhanced response bandwidth and high signal-to-noise ratio,” J. Lightwave Technol. to be published.

Lu, Y.

Maier, E. W.

Martin-Lopez, S.

Martins, H. F.

Namihira, Y.

Y. Namihira, “Opto-elastic constant in single mode optical fibers,” J. Lightwave Technol. 3(5), 1078–1083 (1985).
[Crossref]

Pan, Z.

J. Zhou, Z. Pan, Q. Ye, H. Cai, R. Qu, and Z. Fang, “Characteristics and explanations of interference fading of a ϕ-OTDR with a multi-frequency source,” J. Lightwave Technol. 31(17), 2947–2954 (2013).
[Crossref]

Z. Pan, K. Liang, J. Zhou, Q. Ye, H. Cai, and R. Qu, “Interference-fading-free phase-demodulated OTDR system,” Proc. SPIE,  8421, 842129 (2012).
[Crossref]

Z. Pan, K. Liang, Q. Ye, H. Cai, R. Qu, and Z. Fang, “Phase-sensitive OTDR system based on digital coherent detection,” in Optical Sensors and Biophotonics, (Optical Society of America, 2011), paper 83110S.

Pan, Z. Q.

J. Zhou, Z. Q. Pan, Q. Ye, H. W. Cai, R. H. Qu, and Z. J. Fang, “Phase demodulation technology using a multi-frequency source discrimination of interference-fading induced false alarm in a ϕ-OTDR system,” Chin. J. Lasers 40(9), 0905003 (2013).
[Crossref]

Priest, R.

Qin, Z.

Z. Qin, L. Chen, and X. Bao, “Wavelet denoising method for improving detection performance of distributed vibration sensor,” IEEE Photon. Technol. Lett. 24(7), 542–544 (2012).
[Crossref]

Z. Qin, T. Zhu, L. Chen, and X. Bao, “High sensitivity distributed vibration sensor based on polarization-maintaining configurations of phase-OTDR,” IEEE Photon. Technol. Lett. 23(15), 1091–1093 (2011).
[Crossref]

Qu, R.

J. Zhou, Z. Pan, Q. Ye, H. Cai, R. Qu, and Z. Fang, “Characteristics and explanations of interference fading of a ϕ-OTDR with a multi-frequency source,” J. Lightwave Technol. 31(17), 2947–2954 (2013).
[Crossref]

Z. Pan, K. Liang, J. Zhou, Q. Ye, H. Cai, and R. Qu, “Interference-fading-free phase-demodulated OTDR system,” Proc. SPIE,  8421, 842129 (2012).
[Crossref]

Z. Pan, K. Liang, Q. Ye, H. Cai, R. Qu, and Z. Fang, “Phase-sensitive OTDR system based on digital coherent detection,” in Optical Sensors and Biophotonics, (Optical Society of America, 2011), paper 83110S.

Qu, R. H.

J. Zhou, Z. Q. Pan, Q. Ye, H. W. Cai, R. H. Qu, and Z. J. Fang, “Phase demodulation technology using a multi-frequency source discrimination of interference-fading induced false alarm in a ϕ-OTDR system,” Chin. J. Lasers 40(9), 0905003 (2013).
[Crossref]

Savory, S. J.

Shi, K.

Shimizu, K.

K. Shimizu, T. Horiguchi, and Y. Koyamada, “Characteristics and reduction of coherent fading noise in rayleigh backscattering measurement for optical fibers and components,” J. Lightwave Technol. 10(7), 982–987 (1992).
[Crossref]

Taylor, H. F.

Thomsen, B. C.

Tveten, A. B.

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 Photon. J. 8(3), 1–12 (2016).

Wang, S.

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 Photon. J. 8(3), 1–12 (2016).

S. Wang, X. Fan, Q. Liu, and Z. He, “Distributed fiber-optic vibration sensing based on phase extraction from time-gated digital OFDR,” Opt. Express 23(26), 33301–33309 (2015).
[Crossref]

Yang, G.

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 Photon. J. 8(3), 1–12 (2016).

Ye, Q.

J. Zhou, Z. Q. Pan, Q. Ye, H. W. Cai, R. H. Qu, and Z. J. Fang, “Phase demodulation technology using a multi-frequency source discrimination of interference-fading induced false alarm in a ϕ-OTDR system,” Chin. J. Lasers 40(9), 0905003 (2013).
[Crossref]

J. Zhou, Z. Pan, Q. Ye, H. Cai, R. Qu, and Z. Fang, “Characteristics and explanations of interference fading of a ϕ-OTDR with a multi-frequency source,” J. Lightwave Technol. 31(17), 2947–2954 (2013).
[Crossref]

Z. Pan, K. Liang, J. Zhou, Q. Ye, H. Cai, and R. Qu, “Interference-fading-free phase-demodulated OTDR system,” Proc. SPIE,  8421, 842129 (2012).
[Crossref]

Z. Pan, K. Liang, Q. Ye, H. Cai, R. Qu, and Z. Fang, “Phase-sensitive OTDR system based on digital coherent detection,” in Optical Sensors and Biophotonics, (Optical Society of America, 2011), paper 83110S.

Zhou, J.

J. Zhou, Z. Q. Pan, Q. Ye, H. W. Cai, R. H. Qu, and Z. J. Fang, “Phase demodulation technology using a multi-frequency source discrimination of interference-fading induced false alarm in a ϕ-OTDR system,” Chin. J. Lasers 40(9), 0905003 (2013).
[Crossref]

J. Zhou, Z. Pan, Q. Ye, H. Cai, R. Qu, and Z. Fang, “Characteristics and explanations of interference fading of a ϕ-OTDR with a multi-frequency source,” J. Lightwave Technol. 31(17), 2947–2954 (2013).
[Crossref]

Z. Pan, K. Liang, J. Zhou, Q. Ye, H. Cai, and R. Qu, “Interference-fading-free phase-demodulated OTDR system,” Proc. SPIE,  8421, 842129 (2012).
[Crossref]

Zhu, T.

Z. Qin, T. Zhu, L. Chen, and X. Bao, “High sensitivity distributed vibration sensor based on polarization-maintaining configurations of phase-OTDR,” IEEE Photon. Technol. Lett. 23(15), 1091–1093 (2011).
[Crossref]

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).

Appl. Opt. (1)

Chin. J. Lasers (1)

J. Zhou, Z. Q. Pan, Q. Ye, H. W. Cai, R. H. Qu, and Z. J. Fang, “Phase demodulation technology using a multi-frequency source discrimination of interference-fading induced false alarm in a ϕ-OTDR system,” Chin. J. Lasers 40(9), 0905003 (2013).
[Crossref]

Electron. Lett. (1)

P. Healey, “Fading in heterodyne OTDR,” Electron. Lett. 20(1), 30–32 (1984).
[Crossref]

IEEE Photon. J. (1)

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 Photon. J. 8(3), 1–12 (2016).

IEEE Photon. Technol. Lett. (2)

Z. Qin, T. Zhu, L. Chen, and X. Bao, “High sensitivity distributed vibration sensor based on polarization-maintaining configurations of phase-OTDR,” IEEE Photon. Technol. Lett. 23(15), 1091–1093 (2011).
[Crossref]

Z. Qin, L. Chen, and X. Bao, “Wavelet denoising method for improving detection performance of distributed vibration sensor,” IEEE Photon. Technol. Lett. 24(7), 542–544 (2012).
[Crossref]

J. Lightwave Technol. (6)

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 (2005).
[Crossref]

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).

J. Zhou, Z. Pan, Q. Ye, H. Cai, R. Qu, and Z. Fang, “Characteristics and explanations of interference fading of a ϕ-OTDR with a multi-frequency source,” J. Lightwave Technol. 31(17), 2947–2954 (2013).
[Crossref]

K. Shimizu, T. Horiguchi, and Y. Koyamada, “Characteristics and reduction of coherent fading noise in rayleigh backscattering measurement for optical fibers and components,” J. Lightwave Technol. 10(7), 982–987 (1992).
[Crossref]

Y. Namihira, “Opto-elastic constant in single mode optical fibers,” J. Lightwave Technol. 3(5), 1078–1083 (1985).
[Crossref]

A. Bertholds and R. Dandliker, “Determination of the individual strain-optic coefficients in single-mode optical fibers,” J. Lightwave Technol. 6(1), 17–20 (1988).
[Crossref]

Opt. Express (3)

Proc. SPIE (1)

Z. Pan, K. Liang, J. Zhou, Q. Ye, H. Cai, and R. Qu, “Interference-fading-free phase-demodulated OTDR system,” Proc. SPIE,  8421, 842129 (2012).
[Crossref]

Other (2)

Z. Pan, K. Liang, Q. Ye, H. Cai, R. Qu, and Z. Fang, “Phase-sensitive OTDR system based on digital coherent detection,” in Optical Sensors and Biophotonics, (Optical Society of America, 2011), paper 83110S.

D. Chen, Q. Liu, X. Fan, and Z. He, “Distributed fiber-optic acoustic sensor with enhanced response bandwidth and high signal-to-noise ratio,” J. Lightwave Technol. to be published.

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Figures (8)

Fig. 1
Fig. 1 The schematic setup; AWG: arbitrary waveform generator; AOM: acousto-optic modulator; ADC: analog-to-digital converter; BPD: balanced photodetector; PZT: cylinder piezoelectric transducer.
Fig. 2
Fig. 2 (a) Probability density function of δθ; (b) Relation between the variance of δθ and the SNR of intensity.
Fig. 3
Fig. 3 (a) Addition of two complex reflection coefficients; (b) rotated-vector-sum method without phase extraction noise; (c) rotated-vector-sum method with phase extraction noise.
Fig. 4
Fig. 4 The experimental system; Amp: electrical signal amplifier; EDFA: erbium-doped fiber amplifier; PC: polarization controller.
Fig. 5
Fig. 5 (a) A normalized reflection intensity trace demodulated from the section |#1| of the 1-st probe pulse and (b) 80 differential phase traces demodulated from the section #1 of 80 probe pulses; (c)(d) traces zooming around the position of two vibrations.
Fig. 6
Fig. 6 (a) A normalized reflection intensity trace after average and (b) 80 differential phase traces without phase errors; (c)(d) traces zooming around the position of two vibrations.
Fig. 7
Fig. 7 The traces of the variance of δθ, (a) along the whole FUT and (b) zooming on a segment of the FUT.
Fig. 8
Fig. 8 (a) A normalized reflection intensity trace after average and (b) 50 differential phase traces without phase errors; (c) The vibration located at the distance of 9.93 km and (d) the vibration located at the distance of 34.6 km; (e)(f) Power spectrum.

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

s ( t ) = rect ( t τ p ) exp { j 2 π f 0 t + j π κ t 2 } ,
E P ( t ) = rect ( t τ p ) exp { j ω c t + j 2 π f 0 t + j π κ t 2 } ,
E L ( t ) = exp { j ω c t } ,
E s ( t ) = i = 1 N a i r i rect ( t τ i τ p ) exp { j ω c ( t τ i ) + j 2 π f 0 ( t τ i ) + j π κ ( t τ i ) 2 } ,
i ( t ) Re { E s ( t ) E L * ( t ) } = i = 1 N a i r i rect ( t τ i τ p ) cos { 2 π f 0 ( t τ i ) + π κ ( t τ i ) 2 ω c τ i } .
i ( t ) = 0 T a ( τ ) r ( τ ) rect ( t τ τ p ) exp { j 2 π f 0 ( t τ ) + j π κ ( t τ ) 2 j ω c τ } d τ = h ( t ) s ( t ) ,
h ( t ) = a ( t ) r ( t ) exp { j ω c t } .
r c ( t ) = i ( t ) s * ( t ) = h ( t ) R ( t ) ,
R ( t ) = s ( t ) s * ( t ) = rect ( t 2 τ p ) sin [ π κ t ( τ p | t | ) ] π K t exp { j 2 π ( f 0 + κ τ p 2 ) t } .
Δ Z = v g 2 Δ F ,
h ( z ) = a ( z ) r ( z ) exp { j 0 z β ( x ) d x } ,
Δ θ A , B = angle { h ( z A ) } angle { h ( z B ) } = ( 1 + γ ) β L ε z + C ,
r c ( k ) = | r c ( k ) | exp { j θ c ( k ) } = i = k M k + M R k + M i h i ,
r c ( k ) = i = k M k + M R k + M i h i exp { j k ε z i } ,
r c ( k ) = i = k M k + M R k + M i h i ( 1 + j k ε z i ) = r c ( k ) + j k i = k M k + M ε z i R k + M i h i ,
ε z ¯ = i = k M k + M ε z i R k + M i h i i = k M k + M R k + M i h i = ε z a ¯ j ε z b ¯
r c ( k ) = r c ( k ) exp { j k ε z ¯ } = r c ( k ) exp { k ε z b ¯ } exp { j k ε z a ¯ } .
σ θ 2 = 1 SNR .
δ θ ave = arctan [ i = 1 K | r i | sin ( δ θ i ) i = 1 K | r i | cos ( δ θ i ) ] i = 1 K | r i | δ θ i i = 1 K | r i | ,
σ θ ave 2 = i = 1 K | r i | 2 σ θ i 2 ( i = 1 K | r i | ) 2 .
G ( K , A K ) = σ θ ave 2 σ θ 1 2 = K A K 2 ,
α K + 1 > K + 1 K K A K .
σ r 2 = 1 + Δ F 2 F + 1 K ,

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