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Conferences > OFS > 2018 > WF > WF14

Extending the Measurement of True Dynamic Strain via Chirped-Pulse Phase-Sensitive Optical Time Domain Reflectometry to 100’s of Microstrains

Hari Datta Bhatta, Luis Costa, Andres Garcia-Ruiz, Maria R. Fernandez-Ruiz, Hugo F. Martins, Moshe Tur, and Miguel Gonzalez-Herraez

Open Access Open Access

Abstract

It is experimentally demonstrated that a chirped pulse phase-sensitive OTDR can measure large and fast dynamic strains (~100’s of με, ~100’s of Hz) with SNR of > 24dB. Signal smoothing and impact of error accumulation are also discussed.

© 2018 The Author(s)

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  1. A. Motil, A. Bergman, and M. Tur, “[INVITED] State of the art of Brillouin fiber-optic distributed sensing,” Opt. Laser Technol., vol. 78, pp. 81–103, 2016.
    [Crossref]
  2. Z. N. Wang, J. Li, M. Q. Fan, L. Zhang, F. Peng, H. Wu, J. J. Zeng, Y. Zhou, and Y. J. Rao, “Phase-sensitive optical time-domain reflectometry with Brillouin amplification,” Opt. Lett., vol. 39, no. 15, p. 4313, 2014.
    [Crossref]
  3. H. F. Martins, S. Martin-Lopez, P. Corredera, J. D. Ania-Castanon, O. Frazao, and M. Gonzalez-Herraez, “Distributed vibration sensing over 125 km with enhanced SNR using Phi-OTDR over a URFL cavity,” J. Light. Technol., vol. 33, no. 12, pp. 26282632, 2015.
    [Crossref]
  4. G. J. Tu, X. P. Zhang, Y. X. Zhang, F. Zhu, L. Xia, and B. Nakarmi, “The Development of an Phi-OTDR System for Quantitative Vibration Measurement,” IeeePhotonics Technol. Lett., vol. 27, no. 12, pp. 1349–1352, 2015.
    [Crossref]
  5. A. Masoudi, M. Belal, and T. P. Newson, “A distributed optical fibre dynamic strain sensor based on phase-OTDR,” Meas. Sci. Technol., vol. 24, no. 8, 2013.
    [Crossref]
  6. L. Liokumovich, N. Ushakov, O. Kotov, M. Bisyarin, and A. Hartog, “Fundamentals of optical fiber sensing schemes based on coherent optical time domain reflectometry: Signal model under static fiber conditions,” J. Light. Technol., vol. 33, no. 17, pp. 11, 2015.
    [Crossref]
  7. M. R. Fernandez-Ruiz, J. Pastor-Graells, H. F. Martins, A. Garcia-Ruiz, S. Martin-Lopez, and M. Gonzalez-Herraez, “Laser Phase-noise Cancellation in Chirped-pulse Distributed Acoustic Sensors,” Journal of Lightwave Technology, 2017.
  8. M. A. Soto, X. Lu, H. F. Martins, M. Gonzalez-Herraez, and L. Thevenaz, “Distributed phase birefringence measurements based on polarization correlation in phase-sensitive optical time-domain reflectometers,” Opt. Express, vol. 23, no. 19, p. 24923, 2015.
    [Crossref]
  9. Y. Koyamada, M. Imahama, K. Kubota, and K. Hogari, “Fiber-optic distributed strain and temperature sensing with very high measurand resolution over long range using coherent OTDR,” J. Light. Technol., vol. 27, no. 9, pp. 1142–1146, 2009.
    [Crossref]
  10. Ling Zhou, Feng Wang, Xiangchuan Wang, Yun Pan, Zhenqin Sun, Ji Hua, and Xuping Zhang, “Distributed strain and vibration sensing system based on phase-sensitive OTDR,” IEEE Photonics Technol. Lett., vol. 27, no. 17, pp. 1884–1887, 2015.
    [Crossref]
  11. J. Pastor-Graells, H. F. Martins, A. Garcia-Ruiz, S. Martin-Lopez, and M. Gonzalez-Herraez, “Single-shot distributed temperature and strain tracking using direct detection phase-sensitive OTDR with chirped pulses,” Opt. Express, vol. 24, no. 12, p. 13121, 2016.
    [Crossref]

2017 (1)

M. R. Fernandez-Ruiz, J. Pastor-Graells, H. F. Martins, A. Garcia-Ruiz, S. Martin-Lopez, and M. Gonzalez-Herraez, “Laser Phase-noise Cancellation in Chirped-pulse Distributed Acoustic Sensors,” Journal of Lightwave Technology, 2017.

2016 (2)

2015 (5)

H. F. Martins, S. Martin-Lopez, P. Corredera, J. D. Ania-Castanon, O. Frazao, and M. Gonzalez-Herraez, “Distributed vibration sensing over 125 km with enhanced SNR using Phi-OTDR over a URFL cavity,” J. Light. Technol., vol. 33, no. 12, pp. 26282632, 2015.
[Crossref]

G. J. Tu, X. P. Zhang, Y. X. Zhang, F. Zhu, L. Xia, and B. Nakarmi, “The Development of an Phi-OTDR System for Quantitative Vibration Measurement,” IeeePhotonics Technol. Lett., vol. 27, no. 12, pp. 1349–1352, 2015.
[Crossref]

M. A. Soto, X. Lu, H. F. Martins, M. Gonzalez-Herraez, and L. Thevenaz, “Distributed phase birefringence measurements based on polarization correlation in phase-sensitive optical time-domain reflectometers,” Opt. Express, vol. 23, no. 19, p. 24923, 2015.
[Crossref]

L. Liokumovich, N. Ushakov, O. Kotov, M. Bisyarin, and A. Hartog, “Fundamentals of optical fiber sensing schemes based on coherent optical time domain reflectometry: Signal model under static fiber conditions,” J. Light. Technol., vol. 33, no. 17, pp. 11, 2015.
[Crossref]

Ling Zhou, Feng Wang, Xiangchuan Wang, Yun Pan, Zhenqin Sun, Ji Hua, and Xuping Zhang, “Distributed strain and vibration sensing system based on phase-sensitive OTDR,” IEEE Photonics Technol. Lett., vol. 27, no. 17, pp. 1884–1887, 2015.
[Crossref]

2014 (1)

2013 (1)

A. Masoudi, M. Belal, and T. P. Newson, “A distributed optical fibre dynamic strain sensor based on phase-OTDR,” Meas. Sci. Technol., vol. 24, no. 8, 2013.
[Crossref]

2009 (1)

Y. Koyamada, M. Imahama, K. Kubota, and K. Hogari, “Fiber-optic distributed strain and temperature sensing with very high measurand resolution over long range using coherent OTDR,” J. Light. Technol., vol. 27, no. 9, pp. 1142–1146, 2009.
[Crossref]

Ania-Castanon, J. D.

H. F. Martins, S. Martin-Lopez, P. Corredera, J. D. Ania-Castanon, O. Frazao, and M. Gonzalez-Herraez, “Distributed vibration sensing over 125 km with enhanced SNR using Phi-OTDR over a URFL cavity,” J. Light. Technol., vol. 33, no. 12, pp. 26282632, 2015.
[Crossref]

Belal, M.

A. Masoudi, M. Belal, and T. P. Newson, “A distributed optical fibre dynamic strain sensor based on phase-OTDR,” Meas. Sci. Technol., vol. 24, no. 8, 2013.
[Crossref]

Bergman, A.

A. Motil, A. Bergman, and M. Tur, “[INVITED] State of the art of Brillouin fiber-optic distributed sensing,” Opt. Laser Technol., vol. 78, pp. 81–103, 2016.
[Crossref]

Bisyarin, M.

L. Liokumovich, N. Ushakov, O. Kotov, M. Bisyarin, and A. Hartog, “Fundamentals of optical fiber sensing schemes based on coherent optical time domain reflectometry: Signal model under static fiber conditions,” J. Light. Technol., vol. 33, no. 17, pp. 11, 2015.
[Crossref]

Corredera, P.

H. F. Martins, S. Martin-Lopez, P. Corredera, J. D. Ania-Castanon, O. Frazao, and M. Gonzalez-Herraez, “Distributed vibration sensing over 125 km with enhanced SNR using Phi-OTDR over a URFL cavity,” J. Light. Technol., vol. 33, no. 12, pp. 26282632, 2015.
[Crossref]

Fan, M. Q.

Fernandez-Ruiz, M. R.

M. R. Fernandez-Ruiz, J. Pastor-Graells, H. F. Martins, A. Garcia-Ruiz, S. Martin-Lopez, and M. Gonzalez-Herraez, “Laser Phase-noise Cancellation in Chirped-pulse Distributed Acoustic Sensors,” Journal of Lightwave Technology, 2017.

Frazao, O.

H. F. Martins, S. Martin-Lopez, P. Corredera, J. D. Ania-Castanon, O. Frazao, and M. Gonzalez-Herraez, “Distributed vibration sensing over 125 km with enhanced SNR using Phi-OTDR over a URFL cavity,” J. Light. Technol., vol. 33, no. 12, pp. 26282632, 2015.
[Crossref]

Garcia-Ruiz, A.

M. R. Fernandez-Ruiz, J. Pastor-Graells, H. F. Martins, A. Garcia-Ruiz, S. Martin-Lopez, and M. Gonzalez-Herraez, “Laser Phase-noise Cancellation in Chirped-pulse Distributed Acoustic Sensors,” Journal of Lightwave Technology, 2017.

J. Pastor-Graells, H. F. Martins, A. Garcia-Ruiz, S. Martin-Lopez, and M. Gonzalez-Herraez, “Single-shot distributed temperature and strain tracking using direct detection phase-sensitive OTDR with chirped pulses,” Opt. Express, vol. 24, no. 12, p. 13121, 2016.
[Crossref]

Gonzalez-Herraez, M.

M. R. Fernandez-Ruiz, J. Pastor-Graells, H. F. Martins, A. Garcia-Ruiz, S. Martin-Lopez, and M. Gonzalez-Herraez, “Laser Phase-noise Cancellation in Chirped-pulse Distributed Acoustic Sensors,” Journal of Lightwave Technology, 2017.

J. Pastor-Graells, H. F. Martins, A. Garcia-Ruiz, S. Martin-Lopez, and M. Gonzalez-Herraez, “Single-shot distributed temperature and strain tracking using direct detection phase-sensitive OTDR with chirped pulses,” Opt. Express, vol. 24, no. 12, p. 13121, 2016.
[Crossref]

M. A. Soto, X. Lu, H. F. Martins, M. Gonzalez-Herraez, and L. Thevenaz, “Distributed phase birefringence measurements based on polarization correlation in phase-sensitive optical time-domain reflectometers,” Opt. Express, vol. 23, no. 19, p. 24923, 2015.
[Crossref]

H. F. Martins, S. Martin-Lopez, P. Corredera, J. D. Ania-Castanon, O. Frazao, and M. Gonzalez-Herraez, “Distributed vibration sensing over 125 km with enhanced SNR using Phi-OTDR over a URFL cavity,” J. Light. Technol., vol. 33, no. 12, pp. 26282632, 2015.
[Crossref]

Hartog, A.

L. Liokumovich, N. Ushakov, O. Kotov, M. Bisyarin, and A. Hartog, “Fundamentals of optical fiber sensing schemes based on coherent optical time domain reflectometry: Signal model under static fiber conditions,” J. Light. Technol., vol. 33, no. 17, pp. 11, 2015.
[Crossref]

Hogari, K.

Y. Koyamada, M. Imahama, K. Kubota, and K. Hogari, “Fiber-optic distributed strain and temperature sensing with very high measurand resolution over long range using coherent OTDR,” J. Light. Technol., vol. 27, no. 9, pp. 1142–1146, 2009.
[Crossref]

Hua, Ji

Ling Zhou, Feng Wang, Xiangchuan Wang, Yun Pan, Zhenqin Sun, Ji Hua, and Xuping Zhang, “Distributed strain and vibration sensing system based on phase-sensitive OTDR,” IEEE Photonics Technol. Lett., vol. 27, no. 17, pp. 1884–1887, 2015.
[Crossref]

Imahama, M.

Y. Koyamada, M. Imahama, K. Kubota, and K. Hogari, “Fiber-optic distributed strain and temperature sensing with very high measurand resolution over long range using coherent OTDR,” J. Light. Technol., vol. 27, no. 9, pp. 1142–1146, 2009.
[Crossref]

Kotov, O.

L. Liokumovich, N. Ushakov, O. Kotov, M. Bisyarin, and A. Hartog, “Fundamentals of optical fiber sensing schemes based on coherent optical time domain reflectometry: Signal model under static fiber conditions,” J. Light. Technol., vol. 33, no. 17, pp. 11, 2015.
[Crossref]

Koyamada, Y.

Y. Koyamada, M. Imahama, K. Kubota, and K. Hogari, “Fiber-optic distributed strain and temperature sensing with very high measurand resolution over long range using coherent OTDR,” J. Light. Technol., vol. 27, no. 9, pp. 1142–1146, 2009.
[Crossref]

Kubota, K.

Y. Koyamada, M. Imahama, K. Kubota, and K. Hogari, “Fiber-optic distributed strain and temperature sensing with very high measurand resolution over long range using coherent OTDR,” J. Light. Technol., vol. 27, no. 9, pp. 1142–1146, 2009.
[Crossref]

Li, J.

Liokumovich, L.

L. Liokumovich, N. Ushakov, O. Kotov, M. Bisyarin, and A. Hartog, “Fundamentals of optical fiber sensing schemes based on coherent optical time domain reflectometry: Signal model under static fiber conditions,” J. Light. Technol., vol. 33, no. 17, pp. 11, 2015.
[Crossref]

Lu, X.

Martin-Lopez, S.

M. R. Fernandez-Ruiz, J. Pastor-Graells, H. F. Martins, A. Garcia-Ruiz, S. Martin-Lopez, and M. Gonzalez-Herraez, “Laser Phase-noise Cancellation in Chirped-pulse Distributed Acoustic Sensors,” Journal of Lightwave Technology, 2017.

J. Pastor-Graells, H. F. Martins, A. Garcia-Ruiz, S. Martin-Lopez, and M. Gonzalez-Herraez, “Single-shot distributed temperature and strain tracking using direct detection phase-sensitive OTDR with chirped pulses,” Opt. Express, vol. 24, no. 12, p. 13121, 2016.
[Crossref]

H. F. Martins, S. Martin-Lopez, P. Corredera, J. D. Ania-Castanon, O. Frazao, and M. Gonzalez-Herraez, “Distributed vibration sensing over 125 km with enhanced SNR using Phi-OTDR over a URFL cavity,” J. Light. Technol., vol. 33, no. 12, pp. 26282632, 2015.
[Crossref]

Martins, H. F.

M. R. Fernandez-Ruiz, J. Pastor-Graells, H. F. Martins, A. Garcia-Ruiz, S. Martin-Lopez, and M. Gonzalez-Herraez, “Laser Phase-noise Cancellation in Chirped-pulse Distributed Acoustic Sensors,” Journal of Lightwave Technology, 2017.

J. Pastor-Graells, H. F. Martins, A. Garcia-Ruiz, S. Martin-Lopez, and M. Gonzalez-Herraez, “Single-shot distributed temperature and strain tracking using direct detection phase-sensitive OTDR with chirped pulses,” Opt. Express, vol. 24, no. 12, p. 13121, 2016.
[Crossref]

M. A. Soto, X. Lu, H. F. Martins, M. Gonzalez-Herraez, and L. Thevenaz, “Distributed phase birefringence measurements based on polarization correlation in phase-sensitive optical time-domain reflectometers,” Opt. Express, vol. 23, no. 19, p. 24923, 2015.
[Crossref]

H. F. Martins, S. Martin-Lopez, P. Corredera, J. D. Ania-Castanon, O. Frazao, and M. Gonzalez-Herraez, “Distributed vibration sensing over 125 km with enhanced SNR using Phi-OTDR over a URFL cavity,” J. Light. Technol., vol. 33, no. 12, pp. 26282632, 2015.
[Crossref]

Masoudi, A.

A. Masoudi, M. Belal, and T. P. Newson, “A distributed optical fibre dynamic strain sensor based on phase-OTDR,” Meas. Sci. Technol., vol. 24, no. 8, 2013.
[Crossref]

Motil, A.

A. Motil, A. Bergman, and M. Tur, “[INVITED] State of the art of Brillouin fiber-optic distributed sensing,” Opt. Laser Technol., vol. 78, pp. 81–103, 2016.
[Crossref]

Nakarmi, B.

G. J. Tu, X. P. Zhang, Y. X. Zhang, F. Zhu, L. Xia, and B. Nakarmi, “The Development of an Phi-OTDR System for Quantitative Vibration Measurement,” IeeePhotonics Technol. Lett., vol. 27, no. 12, pp. 1349–1352, 2015.
[Crossref]

Newson, T. P.

A. Masoudi, M. Belal, and T. P. Newson, “A distributed optical fibre dynamic strain sensor based on phase-OTDR,” Meas. Sci. Technol., vol. 24, no. 8, 2013.
[Crossref]

Pan, Yun

Ling Zhou, Feng Wang, Xiangchuan Wang, Yun Pan, Zhenqin Sun, Ji Hua, and Xuping Zhang, “Distributed strain and vibration sensing system based on phase-sensitive OTDR,” IEEE Photonics Technol. Lett., vol. 27, no. 17, pp. 1884–1887, 2015.
[Crossref]

Pastor-Graells, J.

M. R. Fernandez-Ruiz, J. Pastor-Graells, H. F. Martins, A. Garcia-Ruiz, S. Martin-Lopez, and M. Gonzalez-Herraez, “Laser Phase-noise Cancellation in Chirped-pulse Distributed Acoustic Sensors,” Journal of Lightwave Technology, 2017.

J. Pastor-Graells, H. F. Martins, A. Garcia-Ruiz, S. Martin-Lopez, and M. Gonzalez-Herraez, “Single-shot distributed temperature and strain tracking using direct detection phase-sensitive OTDR with chirped pulses,” Opt. Express, vol. 24, no. 12, p. 13121, 2016.
[Crossref]

Peng, F.

Rao, Y. J.

Soto, M. A.

Sun, Zhenqin

Ling Zhou, Feng Wang, Xiangchuan Wang, Yun Pan, Zhenqin Sun, Ji Hua, and Xuping Zhang, “Distributed strain and vibration sensing system based on phase-sensitive OTDR,” IEEE Photonics Technol. Lett., vol. 27, no. 17, pp. 1884–1887, 2015.
[Crossref]

Thevenaz, L.

Tu, G. J.

G. J. Tu, X. P. Zhang, Y. X. Zhang, F. Zhu, L. Xia, and B. Nakarmi, “The Development of an Phi-OTDR System for Quantitative Vibration Measurement,” IeeePhotonics Technol. Lett., vol. 27, no. 12, pp. 1349–1352, 2015.
[Crossref]

Tur, M.

A. Motil, A. Bergman, and M. Tur, “[INVITED] State of the art of Brillouin fiber-optic distributed sensing,” Opt. Laser Technol., vol. 78, pp. 81–103, 2016.
[Crossref]

Ushakov, N.

L. Liokumovich, N. Ushakov, O. Kotov, M. Bisyarin, and A. Hartog, “Fundamentals of optical fiber sensing schemes based on coherent optical time domain reflectometry: Signal model under static fiber conditions,” J. Light. Technol., vol. 33, no. 17, pp. 11, 2015.
[Crossref]

Wang, Feng

Ling Zhou, Feng Wang, Xiangchuan Wang, Yun Pan, Zhenqin Sun, Ji Hua, and Xuping Zhang, “Distributed strain and vibration sensing system based on phase-sensitive OTDR,” IEEE Photonics Technol. Lett., vol. 27, no. 17, pp. 1884–1887, 2015.
[Crossref]

Wang, Xiangchuan

Ling Zhou, Feng Wang, Xiangchuan Wang, Yun Pan, Zhenqin Sun, Ji Hua, and Xuping Zhang, “Distributed strain and vibration sensing system based on phase-sensitive OTDR,” IEEE Photonics Technol. Lett., vol. 27, no. 17, pp. 1884–1887, 2015.
[Crossref]

Wang, Z. N.

Wu, H.

Xia, L.

G. J. Tu, X. P. Zhang, Y. X. Zhang, F. Zhu, L. Xia, and B. Nakarmi, “The Development of an Phi-OTDR System for Quantitative Vibration Measurement,” IeeePhotonics Technol. Lett., vol. 27, no. 12, pp. 1349–1352, 2015.
[Crossref]

Zeng, J. J.

Zhang, L.

Zhang, X. P.

G. J. Tu, X. P. Zhang, Y. X. Zhang, F. Zhu, L. Xia, and B. Nakarmi, “The Development of an Phi-OTDR System for Quantitative Vibration Measurement,” IeeePhotonics Technol. Lett., vol. 27, no. 12, pp. 1349–1352, 2015.
[Crossref]

Zhang, Xuping

Ling Zhou, Feng Wang, Xiangchuan Wang, Yun Pan, Zhenqin Sun, Ji Hua, and Xuping Zhang, “Distributed strain and vibration sensing system based on phase-sensitive OTDR,” IEEE Photonics Technol. Lett., vol. 27, no. 17, pp. 1884–1887, 2015.
[Crossref]

Zhang, Y. X.

G. J. Tu, X. P. Zhang, Y. X. Zhang, F. Zhu, L. Xia, and B. Nakarmi, “The Development of an Phi-OTDR System for Quantitative Vibration Measurement,” IeeePhotonics Technol. Lett., vol. 27, no. 12, pp. 1349–1352, 2015.
[Crossref]

Zhou, Ling

Ling Zhou, Feng Wang, Xiangchuan Wang, Yun Pan, Zhenqin Sun, Ji Hua, and Xuping Zhang, “Distributed strain and vibration sensing system based on phase-sensitive OTDR,” IEEE Photonics Technol. Lett., vol. 27, no. 17, pp. 1884–1887, 2015.
[Crossref]

Zhou, Y.

Zhu, F.

G. J. Tu, X. P. Zhang, Y. X. Zhang, F. Zhu, L. Xia, and B. Nakarmi, “The Development of an Phi-OTDR System for Quantitative Vibration Measurement,” IeeePhotonics Technol. Lett., vol. 27, no. 12, pp. 1349–1352, 2015.
[Crossref]

IEEE Photonics Technol. Lett. (1)

Ling Zhou, Feng Wang, Xiangchuan Wang, Yun Pan, Zhenqin Sun, Ji Hua, and Xuping Zhang, “Distributed strain and vibration sensing system based on phase-sensitive OTDR,” IEEE Photonics Technol. Lett., vol. 27, no. 17, pp. 1884–1887, 2015.
[Crossref]

IeeePhotonics Technol. Lett. (1)

G. J. Tu, X. P. Zhang, Y. X. Zhang, F. Zhu, L. Xia, and B. Nakarmi, “The Development of an Phi-OTDR System for Quantitative Vibration Measurement,” IeeePhotonics Technol. Lett., vol. 27, no. 12, pp. 1349–1352, 2015.
[Crossref]

J. Light. Technol. (3)

L. Liokumovich, N. Ushakov, O. Kotov, M. Bisyarin, and A. Hartog, “Fundamentals of optical fiber sensing schemes based on coherent optical time domain reflectometry: Signal model under static fiber conditions,” J. Light. Technol., vol. 33, no. 17, pp. 11, 2015.
[Crossref]

H. F. Martins, S. Martin-Lopez, P. Corredera, J. D. Ania-Castanon, O. Frazao, and M. Gonzalez-Herraez, “Distributed vibration sensing over 125 km with enhanced SNR using Phi-OTDR over a URFL cavity,” J. Light. Technol., vol. 33, no. 12, pp. 26282632, 2015.
[Crossref]

Y. Koyamada, M. Imahama, K. Kubota, and K. Hogari, “Fiber-optic distributed strain and temperature sensing with very high measurand resolution over long range using coherent OTDR,” J. Light. Technol., vol. 27, no. 9, pp. 1142–1146, 2009.
[Crossref]

Journal of Lightwave Technology (1)

M. R. Fernandez-Ruiz, J. Pastor-Graells, H. F. Martins, A. Garcia-Ruiz, S. Martin-Lopez, and M. Gonzalez-Herraez, “Laser Phase-noise Cancellation in Chirped-pulse Distributed Acoustic Sensors,” Journal of Lightwave Technology, 2017.

Meas. Sci. Technol. (1)

A. Masoudi, M. Belal, and T. P. Newson, “A distributed optical fibre dynamic strain sensor based on phase-OTDR,” Meas. Sci. Technol., vol. 24, no. 8, 2013.
[Crossref]

Opt. Express (2)

Opt. Laser Technol. (1)

A. Motil, A. Bergman, and M. Tur, “[INVITED] State of the art of Brillouin fiber-optic distributed sensing,” Opt. Laser Technol., vol. 78, pp. 81–103, 2016.
[Crossref]

Opt. Lett. (1)

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