Abstract

An interferometric fiber-optic vibration sensing system using the phase-generated carrier (PGC) method is proposed and experimentally demonstrated. The sensing section consists of a Sagnac interferometer combined with a Mach–Zehnder interferometer, a length of sensing fiber is shared between the two interferometers. The PGC demodulation scheme is used to demodulate the time-varying phase shifts induced by vibrations. Spatial information can be extracted from the demodulated results. A prototype sensing system with a 628 m long sensing fiber has been tested and a spatial resolution better than 12 m is successfully achieved.

© 2013 Optical Society of America

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References

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  1. J. C. Juarez, E. W. Maier, C. Kyoo Nam, and H. F. Taylor, “Distributed fiber-optic intrusion sensor system,” J. Lightwave Technol. 23, 2081–2087 (2005).
    [CrossRef]
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    [CrossRef]
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  4. S. Liang, C. Zhang, W. Lin, L. Li, C. Li, X. Feng, and B. Lin, “Fiber-optic intrinsic distributed acoustic emission sensor for large structure health monitoring,” Opt. Lett. 34, 1858–1860 (2009).
    [CrossRef]
  5. Y. Wang and Z. Jiang, “Application of Golay codes to distributed optical fiber sensor for long-distance oil pipeline leakage and external damage detection,” Chin. Opt. Lett. 4, 141–144 (2006).
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    [CrossRef]
  7. J. P. Dakin, D. A. Pearce, C. A. Wade, and A. Strong, “A novel distributed optical fibre sensing system, enabling location of disturbances in a Sagnac loop interferometer,” Proc. SPIE 838, 325–328 (1987).
    [CrossRef]
  8. F. Xiaojun, “A variable-loop Sagnac interferometer for distributed impact sensing,” J. Lightwave Technol. 14, 2250–2254 (1996).
    [CrossRef]
  9. X. Fang, “Fiber-optic distributed sensing by a two-loop Sagnac interferometer,” Opt. Lett. 21, 444–446 (1996).
    [CrossRef]
  10. G. Zhang, C. Xi, Y. Liang, and H. Zuo, “Dual-Sagnac optical fiber sensor used in acoustic emission source location,” in Proceedings of IEEE Conference on Cross Strait Quad-Regional Radio Science and Wireless Technology (IEEE, 2011), pp. 1598–1602.
  11. S. J. Spammer, P. L. Swart, and A. A. Chtcherbakov, “Distributed dual-wavelength Sagnac impact sensor,” Microw. Opt. Technol. Lett. 17, 170–173 (1998).
    [CrossRef]
  12. W. Xu, C. Zhang, S. Liang, L. Li, W. Lin, and Y. Yang, “Fiber-optic distributed sensor based on a Sagnac interferometer with a time delay loop for detecting time-varying disturbance,” Microwave Opt. Technol. Lett. 51, 2564–2567 (2009).
    [CrossRef]
  13. S. J. Spammer, P. L. Swart, and A. A. Chtcherbakov, “Merged Sagnac–Michelson interferometer for distributed disturbance detection,” J. Lightwave Technol. 15, 972–976 (1997).
    [CrossRef]
  14. Q. Sun, D. Liu, J. Wang, and H. Liu, “Distributed fiber-optic vibration sensor using a ring Mach–Zehnder interferometer,” Opt. Commun. 281, 1538–1544 (2008).
    [CrossRef]
  15. X. Hong, J. Wu, C. Zuo, F. Liu, H. Guo, and K. Xu, “Dual Michelson interferometers for distributed vibration detection,” Appl. Opt. 50, 4333–4338 (2011).
    [CrossRef]
  16. S. J. Spammer, P. L. Swart, and A. Booysen, “Interferometric distributed optical-fiber sensor,” Appl. Opt. 35, 4522–4525 (1996).
    [CrossRef]
  17. A. D. Kersey, A. C. Lewin, and D. A. Jackson, “Pseudo-heterodyne detection scheme for the fibre gyroscope,” Electron. Lett. 20, 368–370 (1984).
    [CrossRef]
  18. W. Jianfei, L. Hong, M. Zhou, and H. Yongming, “Experimental research of an all-polarization-maintaining optical fiber vector hydrophone,” J. Lightwave Technol. 30, 1178–1184 (2012).
    [CrossRef]
  19. L. Wang, J. He, F. Li, and Y. Liu, “Ultra low frequency phase generated carrier demodulation technique for fiber sensors,” Chin. J. Lasers 38, 405001 (2011).
    [CrossRef]
  20. A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE Trans. Microwave Theory Tech. 30, 1635–1641 (1982).
    [CrossRef]
  21. D. A. Brown, C. B. Cameron, R. M. Keolian, D. L. Gardner, and S. L. Garrett, “A symmetric 3×3 coupler based demodulator for fiber optic interferometric sensors,” Proc. SPIE 1584, 328–335 (1991).
    [CrossRef]

2012 (1)

2011 (2)

X. Hong, J. Wu, C. Zuo, F. Liu, H. Guo, and K. Xu, “Dual Michelson interferometers for distributed vibration detection,” Appl. Opt. 50, 4333–4338 (2011).
[CrossRef]

L. Wang, J. He, F. Li, and Y. Liu, “Ultra low frequency phase generated carrier demodulation technique for fiber sensors,” Chin. J. Lasers 38, 405001 (2011).
[CrossRef]

2009 (2)

W. Xu, C. Zhang, S. Liang, L. Li, W. Lin, and Y. Yang, “Fiber-optic distributed sensor based on a Sagnac interferometer with a time delay loop for detecting time-varying disturbance,” Microwave Opt. Technol. Lett. 51, 2564–2567 (2009).
[CrossRef]

S. Liang, C. Zhang, W. Lin, L. Li, C. Li, X. Feng, and B. Lin, “Fiber-optic intrinsic distributed acoustic emission sensor for large structure health monitoring,” Opt. Lett. 34, 1858–1860 (2009).
[CrossRef]

2008 (1)

Q. Sun, D. Liu, J. Wang, and H. Liu, “Distributed fiber-optic vibration sensor using a ring Mach–Zehnder interferometer,” Opt. Commun. 281, 1538–1544 (2008).
[CrossRef]

2007 (1)

2006 (1)

2005 (2)

1998 (2)

S. J. Spammer, P. L. Swart, and A. A. Chtcherbakov, “Distributed dual-wavelength Sagnac impact sensor,” Microw. Opt. Technol. Lett. 17, 170–173 (1998).
[CrossRef]

A. A. Chtcherbakov, P. L. Swart, and S. J. Spammer, “Mach–Zehnder and modified Sagnac-distributed fiber-optic impact sensor,” Appl. Opt. 37, 3432–3437 (1998).
[CrossRef]

1997 (1)

S. J. Spammer, P. L. Swart, and A. A. Chtcherbakov, “Merged Sagnac–Michelson interferometer for distributed disturbance detection,” J. Lightwave Technol. 15, 972–976 (1997).
[CrossRef]

1996 (3)

1991 (1)

D. A. Brown, C. B. Cameron, R. M. Keolian, D. L. Gardner, and S. L. Garrett, “A symmetric 3×3 coupler based demodulator for fiber optic interferometric sensors,” Proc. SPIE 1584, 328–335 (1991).
[CrossRef]

1987 (1)

J. P. Dakin, D. A. Pearce, C. A. Wade, and A. Strong, “A novel distributed optical fibre sensing system, enabling location of disturbances in a Sagnac loop interferometer,” Proc. SPIE 838, 325–328 (1987).
[CrossRef]

1984 (1)

A. D. Kersey, A. C. Lewin, and D. A. Jackson, “Pseudo-heterodyne detection scheme for the fibre gyroscope,” Electron. Lett. 20, 368–370 (1984).
[CrossRef]

1982 (1)

A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE Trans. Microwave Theory Tech. 30, 1635–1641 (1982).
[CrossRef]

Booysen, A.

Brown, D. A.

D. A. Brown, C. B. Cameron, R. M. Keolian, D. L. Gardner, and S. L. Garrett, “A symmetric 3×3 coupler based demodulator for fiber optic interferometric sensors,” Proc. SPIE 1584, 328–335 (1991).
[CrossRef]

Cameron, C. B.

D. A. Brown, C. B. Cameron, R. M. Keolian, D. L. Gardner, and S. L. Garrett, “A symmetric 3×3 coupler based demodulator for fiber optic interferometric sensors,” Proc. SPIE 1584, 328–335 (1991).
[CrossRef]

Chtcherbakov, A. A.

A. A. Chtcherbakov, P. L. Swart, and S. J. Spammer, “Mach–Zehnder and modified Sagnac-distributed fiber-optic impact sensor,” Appl. Opt. 37, 3432–3437 (1998).
[CrossRef]

S. J. Spammer, P. L. Swart, and A. A. Chtcherbakov, “Distributed dual-wavelength Sagnac impact sensor,” Microw. Opt. Technol. Lett. 17, 170–173 (1998).
[CrossRef]

S. J. Spammer, P. L. Swart, and A. A. Chtcherbakov, “Merged Sagnac–Michelson interferometer for distributed disturbance detection,” J. Lightwave Technol. 15, 972–976 (1997).
[CrossRef]

Dakin, J. P.

J. P. Dakin, D. A. Pearce, C. A. Wade, and A. Strong, “A novel distributed optical fibre sensing system, enabling location of disturbances in a Sagnac loop interferometer,” Proc. SPIE 838, 325–328 (1987).
[CrossRef]

Dandridge, A.

A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE Trans. Microwave Theory Tech. 30, 1635–1641 (1982).
[CrossRef]

Fang, X.

Feng, X.

Gao, J.

Gardner, D. L.

D. A. Brown, C. B. Cameron, R. M. Keolian, D. L. Gardner, and S. L. Garrett, “A symmetric 3×3 coupler based demodulator for fiber optic interferometric sensors,” Proc. SPIE 1584, 328–335 (1991).
[CrossRef]

Garrett, S. L.

D. A. Brown, C. B. Cameron, R. M. Keolian, D. L. Gardner, and S. L. Garrett, “A symmetric 3×3 coupler based demodulator for fiber optic interferometric sensors,” Proc. SPIE 1584, 328–335 (1991).
[CrossRef]

Giallorenzi, T. G.

A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE Trans. Microwave Theory Tech. 30, 1635–1641 (1982).
[CrossRef]

Guo, H.

He, J.

L. Wang, J. He, F. Li, and Y. Liu, “Ultra low frequency phase generated carrier demodulation technique for fiber sensors,” Chin. J. Lasers 38, 405001 (2011).
[CrossRef]

Hong, L.

Hong, X.

Jackson, D. A.

A. D. Kersey, A. C. Lewin, and D. A. Jackson, “Pseudo-heterodyne detection scheme for the fibre gyroscope,” Electron. Lett. 20, 368–370 (1984).
[CrossRef]

Jianfei, W.

Jiang, Z.

Juarez, J. C.

Keolian, R. M.

D. A. Brown, C. B. Cameron, R. M. Keolian, D. L. Gardner, and S. L. Garrett, “A symmetric 3×3 coupler based demodulator for fiber optic interferometric sensors,” Proc. SPIE 1584, 328–335 (1991).
[CrossRef]

Kersey, A. D.

A. D. Kersey, A. C. Lewin, and D. A. Jackson, “Pseudo-heterodyne detection scheme for the fibre gyroscope,” Electron. Lett. 20, 368–370 (1984).
[CrossRef]

Kyoo Nam, C.

Lewin, A. C.

A. D. Kersey, A. C. Lewin, and D. A. Jackson, “Pseudo-heterodyne detection scheme for the fibre gyroscope,” Electron. Lett. 20, 368–370 (1984).
[CrossRef]

Li, C.

Li, F.

L. Wang, J. He, F. Li, and Y. Liu, “Ultra low frequency phase generated carrier demodulation technique for fiber sensors,” Chin. J. Lasers 38, 405001 (2011).
[CrossRef]

Li, L.

S. Liang, C. Zhang, W. Lin, L. Li, C. Li, X. Feng, and B. Lin, “Fiber-optic intrinsic distributed acoustic emission sensor for large structure health monitoring,” Opt. Lett. 34, 1858–1860 (2009).
[CrossRef]

W. Xu, C. Zhang, S. Liang, L. Li, W. Lin, and Y. Yang, “Fiber-optic distributed sensor based on a Sagnac interferometer with a time delay loop for detecting time-varying disturbance,” Microwave Opt. Technol. Lett. 51, 2564–2567 (2009).
[CrossRef]

Liang, S.

W. Xu, C. Zhang, S. Liang, L. Li, W. Lin, and Y. Yang, “Fiber-optic distributed sensor based on a Sagnac interferometer with a time delay loop for detecting time-varying disturbance,” Microwave Opt. Technol. Lett. 51, 2564–2567 (2009).
[CrossRef]

S. Liang, C. Zhang, W. Lin, L. Li, C. Li, X. Feng, and B. Lin, “Fiber-optic intrinsic distributed acoustic emission sensor for large structure health monitoring,” Opt. Lett. 34, 1858–1860 (2009).
[CrossRef]

Liang, Y.

G. Zhang, C. Xi, Y. Liang, and H. Zuo, “Dual-Sagnac optical fiber sensor used in acoustic emission source location,” in Proceedings of IEEE Conference on Cross Strait Quad-Regional Radio Science and Wireless Technology (IEEE, 2011), pp. 1598–1602.

Lin, B.

Lin, W.

S. Liang, C. Zhang, W. Lin, L. Li, C. Li, X. Feng, and B. Lin, “Fiber-optic intrinsic distributed acoustic emission sensor for large structure health monitoring,” Opt. Lett. 34, 1858–1860 (2009).
[CrossRef]

W. Xu, C. Zhang, S. Liang, L. Li, W. Lin, and Y. Yang, “Fiber-optic distributed sensor based on a Sagnac interferometer with a time delay loop for detecting time-varying disturbance,” Microwave Opt. Technol. Lett. 51, 2564–2567 (2009).
[CrossRef]

Liu, D.

Q. Sun, D. Liu, J. Wang, and H. Liu, “Distributed fiber-optic vibration sensor using a ring Mach–Zehnder interferometer,” Opt. Commun. 281, 1538–1544 (2008).
[CrossRef]

Liu, F.

Liu, H.

Q. Sun, D. Liu, J. Wang, and H. Liu, “Distributed fiber-optic vibration sensor using a ring Mach–Zehnder interferometer,” Opt. Commun. 281, 1538–1544 (2008).
[CrossRef]

Liu, Y.

L. Wang, J. He, F. Li, and Y. Liu, “Ultra low frequency phase generated carrier demodulation technique for fiber sensors,” Chin. J. Lasers 38, 405001 (2011).
[CrossRef]

Maier, E. W.

Pearce, D. A.

J. P. Dakin, D. A. Pearce, C. A. Wade, and A. Strong, “A novel distributed optical fibre sensing system, enabling location of disturbances in a Sagnac loop interferometer,” Proc. SPIE 838, 325–328 (1987).
[CrossRef]

Spammer, S. J.

S. J. Spammer, P. L. Swart, and A. A. Chtcherbakov, “Distributed dual-wavelength Sagnac impact sensor,” Microw. Opt. Technol. Lett. 17, 170–173 (1998).
[CrossRef]

A. A. Chtcherbakov, P. L. Swart, and S. J. Spammer, “Mach–Zehnder and modified Sagnac-distributed fiber-optic impact sensor,” Appl. Opt. 37, 3432–3437 (1998).
[CrossRef]

S. J. Spammer, P. L. Swart, and A. A. Chtcherbakov, “Merged Sagnac–Michelson interferometer for distributed disturbance detection,” J. Lightwave Technol. 15, 972–976 (1997).
[CrossRef]

S. J. Spammer, P. L. Swart, and A. Booysen, “Interferometric distributed optical-fiber sensor,” Appl. Opt. 35, 4522–4525 (1996).
[CrossRef]

Strong, A.

J. P. Dakin, D. A. Pearce, C. A. Wade, and A. Strong, “A novel distributed optical fibre sensing system, enabling location of disturbances in a Sagnac loop interferometer,” Proc. SPIE 838, 325–328 (1987).
[CrossRef]

Sun, Q.

Q. Sun, D. Liu, J. Wang, and H. Liu, “Distributed fiber-optic vibration sensor using a ring Mach–Zehnder interferometer,” Opt. Commun. 281, 1538–1544 (2008).
[CrossRef]

Swart, P. L.

S. J. Spammer, P. L. Swart, and A. A. Chtcherbakov, “Distributed dual-wavelength Sagnac impact sensor,” Microw. Opt. Technol. Lett. 17, 170–173 (1998).
[CrossRef]

A. A. Chtcherbakov, P. L. Swart, and S. J. Spammer, “Mach–Zehnder and modified Sagnac-distributed fiber-optic impact sensor,” Appl. Opt. 37, 3432–3437 (1998).
[CrossRef]

S. J. Spammer, P. L. Swart, and A. A. Chtcherbakov, “Merged Sagnac–Michelson interferometer for distributed disturbance detection,” J. Lightwave Technol. 15, 972–976 (1997).
[CrossRef]

S. J. Spammer, P. L. Swart, and A. Booysen, “Interferometric distributed optical-fiber sensor,” Appl. Opt. 35, 4522–4525 (1996).
[CrossRef]

Taylor, H. F.

Tveten, A. B.

A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE Trans. Microwave Theory Tech. 30, 1635–1641 (1982).
[CrossRef]

Wade, C. A.

J. P. Dakin, D. A. Pearce, C. A. Wade, and A. Strong, “A novel distributed optical fibre sensing system, enabling location of disturbances in a Sagnac loop interferometer,” Proc. SPIE 838, 325–328 (1987).
[CrossRef]

Wang, J.

Q. Sun, D. Liu, J. Wang, and H. Liu, “Distributed fiber-optic vibration sensor using a ring Mach–Zehnder interferometer,” Opt. Commun. 281, 1538–1544 (2008).
[CrossRef]

Wang, L.

L. Wang, J. He, F. Li, and Y. Liu, “Ultra low frequency phase generated carrier demodulation technique for fiber sensors,” Chin. J. Lasers 38, 405001 (2011).
[CrossRef]

Wang, Y.

Wu, J.

Xi, C.

G. Zhang, C. Xi, Y. Liang, and H. Zuo, “Dual-Sagnac optical fiber sensor used in acoustic emission source location,” in Proceedings of IEEE Conference on Cross Strait Quad-Regional Radio Science and Wireless Technology (IEEE, 2011), pp. 1598–1602.

Xiaojun, F.

F. Xiaojun, “A variable-loop Sagnac interferometer for distributed impact sensing,” J. Lightwave Technol. 14, 2250–2254 (1996).
[CrossRef]

Xu, K.

Xu, W.

W. Xu, C. Zhang, S. Liang, L. Li, W. Lin, and Y. Yang, “Fiber-optic distributed sensor based on a Sagnac interferometer with a time delay loop for detecting time-varying disturbance,” Microwave Opt. Technol. Lett. 51, 2564–2567 (2009).
[CrossRef]

Yang, Y.

W. Xu, C. Zhang, S. Liang, L. Li, W. Lin, and Y. Yang, “Fiber-optic distributed sensor based on a Sagnac interferometer with a time delay loop for detecting time-varying disturbance,” Microwave Opt. Technol. Lett. 51, 2564–2567 (2009).
[CrossRef]

Yongming, H.

Zhang, C.

W. Xu, C. Zhang, S. Liang, L. Li, W. Lin, and Y. Yang, “Fiber-optic distributed sensor based on a Sagnac interferometer with a time delay loop for detecting time-varying disturbance,” Microwave Opt. Technol. Lett. 51, 2564–2567 (2009).
[CrossRef]

S. Liang, C. Zhang, W. Lin, L. Li, C. Li, X. Feng, and B. Lin, “Fiber-optic intrinsic distributed acoustic emission sensor for large structure health monitoring,” Opt. Lett. 34, 1858–1860 (2009).
[CrossRef]

Zhang, G.

G. Zhang, C. Xi, Y. Liang, and H. Zuo, “Dual-Sagnac optical fiber sensor used in acoustic emission source location,” in Proceedings of IEEE Conference on Cross Strait Quad-Regional Radio Science and Wireless Technology (IEEE, 2011), pp. 1598–1602.

Zhao, G.

Zhao, Y.

Zhou, M.

Zhu, L.

Zuo, C.

Zuo, H.

G. Zhang, C. Xi, Y. Liang, and H. Zuo, “Dual-Sagnac optical fiber sensor used in acoustic emission source location,” in Proceedings of IEEE Conference on Cross Strait Quad-Regional Radio Science and Wireless Technology (IEEE, 2011), pp. 1598–1602.

Appl. Opt. (4)

Chin. J. Lasers (1)

L. Wang, J. He, F. Li, and Y. Liu, “Ultra low frequency phase generated carrier demodulation technique for fiber sensors,” Chin. J. Lasers 38, 405001 (2011).
[CrossRef]

Chin. Opt. Lett. (2)

Electron. Lett. (1)

A. D. Kersey, A. C. Lewin, and D. A. Jackson, “Pseudo-heterodyne detection scheme for the fibre gyroscope,” Electron. Lett. 20, 368–370 (1984).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE Trans. Microwave Theory Tech. 30, 1635–1641 (1982).
[CrossRef]

J. Lightwave Technol. (4)

J. C. Juarez, E. W. Maier, C. Kyoo Nam, and H. F. Taylor, “Distributed fiber-optic intrusion sensor system,” J. Lightwave Technol. 23, 2081–2087 (2005).
[CrossRef]

S. J. Spammer, P. L. Swart, and A. A. Chtcherbakov, “Merged Sagnac–Michelson interferometer for distributed disturbance detection,” J. Lightwave Technol. 15, 972–976 (1997).
[CrossRef]

F. Xiaojun, “A variable-loop Sagnac interferometer for distributed impact sensing,” J. Lightwave Technol. 14, 2250–2254 (1996).
[CrossRef]

W. Jianfei, L. Hong, M. Zhou, and H. Yongming, “Experimental research of an all-polarization-maintaining optical fiber vector hydrophone,” J. Lightwave Technol. 30, 1178–1184 (2012).
[CrossRef]

Microw. Opt. Technol. Lett. (1)

S. J. Spammer, P. L. Swart, and A. A. Chtcherbakov, “Distributed dual-wavelength Sagnac impact sensor,” Microw. Opt. Technol. Lett. 17, 170–173 (1998).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

W. Xu, C. Zhang, S. Liang, L. Li, W. Lin, and Y. Yang, “Fiber-optic distributed sensor based on a Sagnac interferometer with a time delay loop for detecting time-varying disturbance,” Microwave Opt. Technol. Lett. 51, 2564–2567 (2009).
[CrossRef]

Opt. Commun. (1)

Q. Sun, D. Liu, J. Wang, and H. Liu, “Distributed fiber-optic vibration sensor using a ring Mach–Zehnder interferometer,” Opt. Commun. 281, 1538–1544 (2008).
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (2)

D. A. Brown, C. B. Cameron, R. M. Keolian, D. L. Gardner, and S. L. Garrett, “A symmetric 3×3 coupler based demodulator for fiber optic interferometric sensors,” Proc. SPIE 1584, 328–335 (1991).
[CrossRef]

J. P. Dakin, D. A. Pearce, C. A. Wade, and A. Strong, “A novel distributed optical fibre sensing system, enabling location of disturbances in a Sagnac loop interferometer,” Proc. SPIE 838, 325–328 (1987).
[CrossRef]

Other (1)

G. Zhang, C. Xi, Y. Liang, and H. Zuo, “Dual-Sagnac optical fiber sensor used in acoustic emission source location,” in Proceedings of IEEE Conference on Cross Strait Quad-Regional Radio Science and Wireless Technology (IEEE, 2011), pp. 1598–1602.

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Figures (6)

Fig. 1.
Fig. 1.

Schematic diagram of the Sagnac and Mach–Zehnder vibration sensing system.

Fig. 2.
Fig. 2.

PGC demodulation scheme. , multiplier; LPF, low pass filter; d/dt, derivative; , integrator; HPF, high pass filter.

Fig. 3.
Fig. 3.

Relationship between U0 and ϕm.

Fig. 4.
Fig. 4.

Schematic of the experimental setup.

Fig. 5.
Fig. 5.

(a) original signals and (b) demodulated signals of SI and MZI, disturbance occurs at 313 m.

Fig. 6.
Fig. 6.

Locating results and deviations.

Equations (10)

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

I=A+Bcos(Δφ),
φ(t)=ϕmsinωc(t+t0),
I1=14Ein2{1cos[ϕmsinωc(t+t0)ϕmsinωc(t+t0τd1)+ψ(tτ2)ψ(tτ1)+φ0]},
I1=14Ein2{1cos[ϕmτd1ωccosωc(t+t0)Δτdψdt+φ0]},
Δτ=τ2τ1=2znc.
I2=14Ein2{1cos[ϕmsinωc(t+t0τd2)ψ(tτ3)+φ0]}
x1(t)=Ein416J1(ϕmτd1ωc)J2(ϕmτd1ωc)2zncdψdt.
x2(t)=Ein416J1(ϕm)J2(ϕm)cosωcτd2sin2ωcτd2dψdt.
z=x1(t)x2(t)ξc2Kn,
K=J1(ϕmτd1ωc)J2(ϕmτd1ωc)J1(ϕm)J2(ϕm)cosωcτd2sin2ωcτd2,

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