Abstract

A phase demodulation method for quasi-distributed acoustic sensing (DAS) systems based on a dual-identical-chirped-pulse and weak fiber Bragg gratings (WFBGs) is proposed. Compared to the use of Rayleigh backscattering light in optical fibers, the implementation of WFBGs can contribute to obtaining an optical signal with a higher signal-to-noise ratio (SNR). The dual-identical-chirped-pulse is generated by a time-delay fiber, and the sinusoidal carrier is generated by the interference between the two chirped pulses reflected by adjacent WFBGs. The phase of the sinusoidal carrier represents the dynamic strain change posed on the sensing fiber. Discrete Fourier transform is used to directly retrieve the phase information. The performance of the phase demodulation from interference signals under different sinusoidal carrier frequencies and SNRs is numerically investigated. The piezoelectric transducer is employed to emulate the sound in the experiment to verify the effectiveness of our method. It is shown that the dynamic strain can be well reconstructed at the end of a 101.64 km fiber when the signal SNR is down to 3.234 dB. Our proposed method enables the application of the long-distance sensing in quasi-DAS systems.

© 2020 Chinese Laser Press

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2019 (1)

2018 (4)

2017 (4)

2016 (4)

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

G. Allwood, G. Wild, and S. Hinckley, “Optical fiber sensors in physical intrusion detection systems: a review,” IEEE Sens. J. 16, 5497–5509 (2016).
[Crossref]

A. Masoudi and T. P. Newson, “Contributed review: distributed optical fibre dynamic strain sensing,” Rev. Sci. Instrum. 87, 011501 (2016).
[Crossref]

J. Luo, Z. Xie, and M. Xie, “Interpolated DFT algorithms with zero padding for classic windows,” Mech. Syst. Signal Process. 70–71, 1011–1025 (2016).
[Crossref]

2015 (1)

2014 (3)

2013 (1)

2012 (1)

2010 (2)

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

D. Belega, D. Dallet, and D. Petri, “Accuracy of sine wave frequency estimation by multipoint interpolated DFT approach,” IEEE Trans. Instrum. Meas. 59, 2808–2815 (2010).
[Crossref]

2009 (1)

S. Schuster, S. Scheiblhofer, and A. Stelzer, “The influence of windowing on bias and variance of DFT-based frequency and phase estimation,” IEEE Trans. Instrum. Meas. 58, 1975–1990 (2009).
[Crossref]

2005 (1)

D. Agrez, “Improving phase estimation with leakage minimization,” IEEE Trans. Instrum. Meas. 54, 1347–1353 (2005).
[Crossref]

Aghayev, R.

P. Jousset, T. Reinsch, T. Ryberg, H. Blanck, A. Clarke, R. Aghayev, G. P. Hersir, J. Henninges, M. Weber, and C. M. Krawczyk, “Dynamic strain determination using fibre-optic cables allows imaging of seismological and structural features,” Nat. Commun. 9, 2509 (2018).
[Crossref]

Agrez, D.

D. Agrez, “Improving phase estimation with leakage minimization,” IEEE Trans. Instrum. Meas. 54, 1347–1353 (2005).
[Crossref]

Allwood, G.

G. Allwood, G. Wild, and S. Hinckley, “Optical fiber sensors in physical intrusion detection systems: a review,” IEEE Sens. J. 16, 5497–5509 (2016).
[Crossref]

Am, A. B.

Arbel, D.

Bao, X.

Belega, D.

D. Belega and D. Petri, “Sine-wave parameter estimation by interpolated DFT method based on new cosine windows with high interference rejection capability,” Digit. Signal Process. 33, 60–70 (2014).
[Crossref]

D. Belega, D. Dallet, and D. Petri, “Accuracy of sine wave frequency estimation by multipoint interpolated DFT approach,” IEEE Trans. Instrum. Meas. 59, 2808–2815 (2010).
[Crossref]

Blanck, H.

P. Jousset, T. Reinsch, T. Ryberg, H. Blanck, A. Clarke, R. Aghayev, G. P. Hersir, J. Henninges, M. Weber, and C. M. Krawczyk, “Dynamic strain determination using fibre-optic cables allows imaging of seismological and structural features,” Nat. Commun. 9, 2509 (2018).
[Crossref]

Cai, H.

Cao, L.

Cao, S.

Chen, D.

Chen, L.

Clarke, A.

P. Jousset, T. Reinsch, T. Ryberg, H. Blanck, A. Clarke, R. Aghayev, G. P. Hersir, J. Henninges, M. Weber, and C. M. Krawczyk, “Dynamic strain determination using fibre-optic cables allows imaging of seismological and structural features,” Nat. Commun. 9, 2509 (2018).
[Crossref]

Dallet, D.

D. Belega, D. Dallet, and D. Petri, “Accuracy of sine wave frequency estimation by multipoint interpolated DFT approach,” IEEE Trans. Instrum. Meas. 59, 2808–2815 (2010).
[Crossref]

Di Pasquale, F.

Dong, B.

Dong, X.

Duan, N.

Eyal, A.

Fan, M.

Fan, X.

Faralli, S.

Fu, X.

Gong, J.

Gu, L.

Guo, H. G.

Guo, Q.

He, X.

He, Z.

Henninges, J.

P. Jousset, T. Reinsch, T. Ryberg, H. Blanck, A. Clarke, R. Aghayev, G. P. Hersir, J. Henninges, M. Weber, and C. M. Krawczyk, “Dynamic strain determination using fibre-optic cables allows imaging of seismological and structural features,” Nat. Commun. 9, 2509 (2018).
[Crossref]

Hersir, G. P.

P. Jousset, T. Reinsch, T. Ryberg, H. Blanck, A. Clarke, R. Aghayev, G. P. Hersir, J. Henninges, M. Weber, and C. M. Krawczyk, “Dynamic strain determination using fibre-optic cables allows imaging of seismological and structural features,” Nat. Commun. 9, 2509 (2018).
[Crossref]

Hinckley, S.

G. Allwood, G. Wild, and S. Hinckley, “Optical fiber sensors in physical intrusion detection systems: a review,” IEEE Sens. J. 16, 5497–5509 (2016).
[Crossref]

Ji, W.

Jiang, D. S.

Jousset, P.

P. Jousset, T. Reinsch, T. Ryberg, H. Blanck, A. Clarke, R. Aghayev, G. P. Hersir, J. Henninges, M. Weber, and C. M. Krawczyk, “Dynamic strain determination using fibre-optic cables allows imaging of seismological and structural features,” Nat. Commun. 9, 2509 (2018).
[Crossref]

Krawczyk, C. M.

P. Jousset, T. Reinsch, T. Ryberg, H. Blanck, A. Clarke, R. Aghayev, G. P. Hersir, J. Henninges, M. Weber, and C. M. Krawczyk, “Dynamic strain determination using fibre-optic cables allows imaging of seismological and structural features,” Nat. Commun. 9, 2509 (2018).
[Crossref]

Li, J.

Li, X. L.

Li, Z.

Liu, F.

Liu, Q.

Liu, X. H.

Lu, B.

Lu, Y.

Luo, J.

J. Luo, Z. Xie, and M. Xie, “Interpolated DFT algorithms with zero padding for classic windows,” Mech. Syst. Signal Process. 70–71, 1011–1025 (2016).
[Crossref]

Masoudi, A.

A. Masoudi and T. P. Newson, “Contributed review: distributed optical fibre dynamic strain sensing,” Rev. Sci. Instrum. 87, 011501 (2016).
[Crossref]

Muanenda, Y.

Newson, T. P.

A. Masoudi and T. P. Newson, “Contributed review: distributed optical fibre dynamic strain sensing,” Rev. Sci. Instrum. 87, 011501 (2016).
[Crossref]

Oton, C. J.

Pan, Z.

Peng, F.

Peng, G. D.

Petri, D.

D. Belega and D. Petri, “Sine-wave parameter estimation by interpolated DFT method based on new cosine windows with high interference rejection capability,” Digit. Signal Process. 33, 60–70 (2014).
[Crossref]

D. Belega, D. Dallet, and D. Petri, “Accuracy of sine wave frequency estimation by multipoint interpolated DFT approach,” IEEE Trans. Instrum. Meas. 59, 2808–2815 (2010).
[Crossref]

Qian, X.

Qu, R.

Rao, J.

Rao, Y.

Rao, Y.-J.

Reinsch, T.

P. Jousset, T. Reinsch, T. Ryberg, H. Blanck, A. Clarke, R. Aghayev, G. P. Hersir, J. Henninges, M. Weber, and C. M. Krawczyk, “Dynamic strain determination using fibre-optic cables allows imaging of seismological and structural features,” Nat. Commun. 9, 2509 (2018).
[Crossref]

Ryberg, T.

P. Jousset, T. Reinsch, T. Ryberg, H. Blanck, A. Clarke, R. Aghayev, G. P. Hersir, J. Henninges, M. Weber, and C. M. Krawczyk, “Dynamic strain determination using fibre-optic cables allows imaging of seismological and structural features,” Nat. Commun. 9, 2509 (2018).
[Crossref]

Scheiblhofer, S.

S. Schuster, S. Scheiblhofer, and A. Stelzer, “The influence of windowing on bias and variance of DFT-based frequency and phase estimation,” IEEE Trans. Instrum. Meas. 58, 1975–1990 (2009).
[Crossref]

Schuster, S.

S. Schuster, S. Scheiblhofer, and A. Stelzer, “The influence of windowing on bias and variance of DFT-based frequency and phase estimation,” IEEE Trans. Instrum. Meas. 58, 1975–1990 (2009).
[Crossref]

Shan, Y.

Shang, Y.

Shillig, T. J.

Shiloh, L.

Stelzer, A.

S. Schuster, S. Scheiblhofer, and A. Stelzer, “The influence of windowing on bias and variance of DFT-based frequency and phase estimation,” IEEE Trans. Instrum. Meas. 58, 1975–1990 (2009).
[Crossref]

Sun, W.

Tang, J. T.

Tong, Y.

Wang, A.

Wang, C.

Wang, D. Y.

Wang, J.

Wang, Q.

Wang, S.

Wang, Y.

Wang, Z.

Weber, M.

P. Jousset, T. Reinsch, T. Ryberg, H. Blanck, A. Clarke, R. Aghayev, G. P. Hersir, J. Henninges, M. Weber, and C. M. Krawczyk, “Dynamic strain determination using fibre-optic cables allows imaging of seismological and structural features,” Nat. Commun. 9, 2509 (2018).
[Crossref]

Wild, G.

G. Allwood, G. Wild, and S. Hinckley, “Optical fiber sensors in physical intrusion detection systems: a review,” IEEE Sens. J. 16, 5497–5509 (2016).
[Crossref]

Xie, M.

J. Luo, Z. Xie, and M. Xie, “Interpolated DFT algorithms with zero padding for classic windows,” Mech. Syst. Signal Process. 70–71, 1011–1025 (2016).
[Crossref]

Xie, S.

Xie, Z.

J. Luo, Z. Xie, and M. Xie, “Interpolated DFT algorithms with zero padding for classic windows,” Mech. Syst. Signal Process. 70–71, 1011–1025 (2016).
[Crossref]

Xue, N.

Yang, G.

Ye, Q.

Yu, H.

Yu, H. H.

Yu, H. Y.

Zabihi, M.

Zhang, L.

Zhang, M.

Zhang, X.

Zhang, Y.

Zheng, H.

Zheng, X.

Zheng, Y. Z.

Zhu, T.

Chin. Opt. Lett. (1)

Digit. Signal Process. (1)

D. Belega and D. Petri, “Sine-wave parameter estimation by interpolated DFT method based on new cosine windows with high interference rejection capability,” Digit. Signal Process. 33, 60–70 (2014).
[Crossref]

IEEE Sens. J. (1)

G. Allwood, G. Wild, and S. Hinckley, “Optical fiber sensors in physical intrusion detection systems: a review,” IEEE Sens. J. 16, 5497–5509 (2016).
[Crossref]

IEEE Trans. Instrum. Meas. (3)

D. Belega, D. Dallet, and D. Petri, “Accuracy of sine wave frequency estimation by multipoint interpolated DFT approach,” IEEE Trans. Instrum. Meas. 59, 2808–2815 (2010).
[Crossref]

D. Agrez, “Improving phase estimation with leakage minimization,” IEEE Trans. Instrum. Meas. 54, 1347–1353 (2005).
[Crossref]

S. Schuster, S. Scheiblhofer, and A. Stelzer, “The influence of windowing on bias and variance of DFT-based frequency and phase estimation,” IEEE Trans. Instrum. Meas. 58, 1975–1990 (2009).
[Crossref]

J. Lightwave Technol. (6)

Mech. Syst. Signal Process. (1)

J. Luo, Z. Xie, and M. Xie, “Interpolated DFT algorithms with zero padding for classic windows,” Mech. Syst. Signal Process. 70–71, 1011–1025 (2016).
[Crossref]

Nat. Commun. (1)

P. Jousset, T. Reinsch, T. Ryberg, H. Blanck, A. Clarke, R. Aghayev, G. P. Hersir, J. Henninges, M. Weber, and C. M. Krawczyk, “Dynamic strain determination using fibre-optic cables allows imaging of seismological and structural features,” Nat. Commun. 9, 2509 (2018).
[Crossref]

Opt. Express (6)

Opt. Lett. (2)

Rev. Sci. Instrum. (1)

A. Masoudi and T. P. Newson, “Contributed review: distributed optical fibre dynamic strain sensing,” Rev. Sci. Instrum. 87, 011501 (2016).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. Schematic diagram of a WFBGs array system.
Fig. 2.
Fig. 2. DFT simulation results. (a) 3D spatial-temporal profile of original a 20 MHz sinusoidal signal with a varying phase without noise. (b) Phase demodulation result of a 20 MHz sinusoidal signal without noise. (c) 3D spatial-temporal profile of a 20 MHz noise-added sinusoidal signal with a varying phase. (d) Two noise-added signal traces at the moments of t=0 and t=0.1  ms. (e) Phase demodulation result of a 20 MHz noise-loaded sinusoidal signal. (f) R-squared and RMSE of phase demodulation results at different SNRs.
Fig. 3.
Fig. 3. Raw beat frequency signal at 2 km. (a) 3D spatial-temporal profile at the sensing section. (b) All-fiber signal at the moment t=0 and t=0.1  ms. (c) Sensing section signal at the moment t=0 and t=0.1  ms.
Fig. 4.
Fig. 4. Phase demodulation results of different types of PZTs. (a) Reconstructed signal waveforms for PZT1 at different voltages. (b) Demodulation results and fitting curves of different amplitude signals for PZT1. (c) Reconstructed signal waveforms for PZT2 at different voltages. (d) Demodulation results and fitting curves of different amplitude signals for PZT2.
Fig. 5.
Fig. 5. Time-domain and frequency-domain plots of PZT at different frequencies. (a) Time-domain information of the phase demodulation result of the 0.8 kHz signal. (b) Time-domain information of phase demodulation result of the 1.0 kHz signal. (c) Time-domain information of phase demodulation result of the 1.2 kHz signal. (d) Frequency-domain information of demodulation results for 0.8, 1.0, and 1.2 kHz signals.
Fig. 6.
Fig. 6. Raw beat frequency signal and phase demodulation results at 101 km. (a) 3D spatial-temporal profile at the sensing section. (b) Sensing section signal and power spectrum at the moment t=0 and t=0.1  ms. (c) The signal demodulation result of the sensing section 1. (d) The signal demodulation result of the sensing section 2.

Equations (5)

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

Em+1=Rm+1E0exp{j2π[f0+f1+k2(t+δT)](t+δT)},t[0,T],
Em+1=Rm+1E0exp{j2π[(f0+f1+k2t+kδT)t+(f0+f1+k2δT)δT]}Rm+1E0exp{j2π[(f0+f1+k2t)t+(f0+f1)δT]}Rm+1E0exp{j2π[(f0+f1+k2t)t+cλδT]}=Rm+1E0exp{j2π[(f0+f1+k2t)t+nΔlλ]}=Rm+1E0exp{j2π[(f0+f1+k2t)t]+jΔφ},t[0,T],
Em=RmE0exp{j2π[f0+f1+k2(t+ΔT)](t+ΔT)},t[0,T],
ΔT=nΔLc,
IAC=RmRm+1E02cos[2π(kΔT)tΔφ+2π(f0+f1+k2ΔT)ΔT]=cos(2πωtΔφ+φ0),t[0,TΔT],

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