Abstract

We present a slope-assisted BOTDA system based on the vector stimulated Brillouin scattering (SBS) and frequency-agile technique (FAT) for the wide-strain-range dynamic measurement. A dimensionless coefficient K defined as the ratio of Brillouin phase-shift to gain is employed to demodulate the strain of the fiber, and it is immune to the power fluctuation of pump pulse and has a linear relation of the frequency detuning for the continuous pump and Stokes waves. For a 30ns-square pump pulse, the available frequency span of the K spectrum can reach up to 200MHz, which is larger than fourfold of 48MHz-linewidth of Brillouin gain spectrum. For a single-slope assisted BOTDA, dynamic strain measurement with the maximum strain of 2467.4με and the vibration frequency components of 10.44Hz and 20.94Hz is obtained. For a multi-slope-assisted BOTDA, dynamic measurement with the strain variation up to 5372.9με and the vibration frequency components of 5.58Hz and 11.14Hz is achieved by using FAT to extend the strain range.

© 2017 Optical Society of America

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  1. X. Bao and L. Chen, “Recent Progress in Brillouin Scattering Based Fiber Sensors,” Sensors (Basel) 11(12), 4152–4187 (2011).
    [Crossref] [PubMed]
  2. L. Thévenaz, “Brillouin distributed time-domain sensing in optical fibers: state of the art and perspectives,” Front. Optoelectron. China 3(1), 13–21 (2010).
    [Crossref]
  3. N. Hayashi, Y. Mizuno, and K. Nakamura, “Simplified Configuration of Brillouin Optical Correlation-Domain Reflectometry,” IEEE Photonics J. 6(5), 1–7 (2014).
    [Crossref]
  4. N. Hayashi, Y. Mizuno, and K. Nakamura, “Alternative Implementation of Simplified Brillouin Optical Correlation-Domain Reflectometry,” IEEE Photonics J. 6(6), 1–8 (2014).
    [Crossref]
  5. N. Hayashi, Y. Mizuno, and K. Nakamura, “Simplified Brillouin Optical Correlation-Domain Reflectometry Using Polymer Optical Fiber,” IEEE Photonics J. 7(1), 1–7 (2015).
    [Crossref]
  6. K. Hotate, “Fiber distributed Brillouin sensing with optical correlation domain techniques,” Opt. Fiber Technol. 19(66, Part B), 700–719 (2013).
    [Crossref]
  7. K. Hotate and M. Tanaka, “Distributed fiber Brillouin strain sensing with 1-cm spatial resolution by correlation-based continuous-wave technique,” IEEE Photonics Technol. Lett. 14(2), 179–181 (2002).
    [Crossref]
  8. K. Y. Song, Z. He, and K. Hotate, “Distributed strain measurement with millimeter-order spatial resolution based on Brillouin optical correlation domain analysis,” Opt. Lett. 31(17), 2526–2528 (2006).
    [Crossref] [PubMed]
  9. D. Garus, T. Gogolla, K. Krebber, and F. Schliep, “Distributed sensing technique based on Brillouin optical-fiber frequency-domain analysis,” Opt. Lett. 21(17), 1402–1404 (1996).
    [Crossref] [PubMed]
  10. D. Garcus, T. Gogolla, K. Krebber, and F. Schliep, “Brillouin optical-fiber frequency-domain analysis for distributed temperature and strain measurements,” J. Lightwave Technol. 15(4), 654–662 (1997).
    [Crossref]
  11. A. Minardo, R. Bernini, and L. Zeni, “Brillouin optical frequency domain analysis in polymer optical fiber,” (2014), pp. 91576V–91576V–91574.
  12. R. Bernini, A. Minardo, and L. Zeni, “Distributed Sensing at Centimeter-Scale Spatial Resolution by BOFDA: Measurements and Signal Processing,” IEEE Photonics J. 4(1), 48–56 (2012).
    [Crossref]
  13. Z. Ma, M. Zhang, Y. Liu, X. Bao, H. Liu, Y. Zhang, and Y. Wang, “Incoherent Brillouin Optical Time-Domain Reflectometry With Random State Correlated Brillouin Spectrum,” IEEE Photonics J. 7(4), 1–7 (2015).
    [Crossref]
  14. Y. Weng, E. Ip, Z. Pan, and T. Wang, “Single-end simultaneous temperature and strain sensing techniques based on Brillouin optical time domain reflectometry in few-mode fibers,” Opt. Express 23(7), 9024–9039 (2015).
    [Crossref] [PubMed]
  15. 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. 39(15), 4313–4316 (2014).
    [Crossref] [PubMed]
  16. Y. Dong, H. Zhang, L. Chen, and X. Bao, “2 cm spatial-resolution and 2 km range Brillouin optical fiber sensor using a transient differential pulse pair,” Appl. Opt. 51(9), 1229–1235 (2012).
    [Crossref] [PubMed]
  17. Y. Dong, L. Chen, and X. Bao, “Extending the Sensing Range of Brillouin Optical Time-Domain Analysis Combining Frequency-Division Multiplexing and In-Line EDFAs,” J. Lightwave Technol. 30(8), 1161–1167 (2012).
    [Crossref]
  18. Y. Dong, P. Xu, H. Zhang, Z. Lu, L. Chen, and X. Bao, “Characterization of evolution of mode coupling in a graded-index polymer optical fiber by using Brillouin optical time-domain analysis,” Opt. Express 22(22), 26510–26516 (2014).
    [Crossref] [PubMed]
  19. A. Minardo, R. Bernini, and L. Zeni, “Analysis of SNR penalty in Brillouin optical time-domain analysis sensors induced by laser source phase noise,” J. Opt. 18(2), 025601 (2016).
    [Crossref]
  20. A. Dominguez-Lopez, X. Angulo-Vinuesa, A. Lopez-Gil, S. Martin-Lopez, and M. Gonzalez-Herraez, “Non-local effects in dual-probe-sideband Brillouin optical time domain analysis,” Opt. Express 23(8), 10341–10352 (2015).
    [Crossref] [PubMed]
  21. J. Urricelqui, M. Sagues, and A. Loayssa, “Phasorial differential pulse-width pair technique for long-range Brillouin optical time-domain analysis sensors,” Opt. Express 22(14), 17403–17408 (2014).
    [Crossref] [PubMed]
  22. L. Thévenaz, S. F. Mafang, and J. Lin, “Effect of pulse depletion in a Brillouin optical time-domain analysis system,” Opt. Express 21(12), 14017–14035 (2013).
    [Crossref] [PubMed]
  23. Y. Mao, N. Guo, K. L. Yu, H. Y. Tam, and C. Lu, “1-cm-Spatial-Resolution Brillouin Optical Time-Domain Analysis Based on Bright Pulse Brillouin Gain and Complementary Code,” IEEE Photonics J. 4(6), 2243–2248 (2012).
    [Crossref]
  24. A. W. Brown, B. G. Colpitts, and K. Brown, “Dark-Pulse Brillouin Optical Time-Domain Sensor With 20-mm Spatial Resolution,” J. Lightwave Technol. 25(1), 381–386 (2007).
    [Crossref]
  25. P. Xu, Y. Dong, J. Zhang, D. Zhou, T. Jiang, J. Xu, H. Zhang, T. Zhu, Z. Lu, L. Chen, and X. Bao, “Bend-insensitive distributed sensing in singlemode-multimode-singlemode optical fiber structure by using Brillouin optical time-domain analysis,” Opt. Express 23(17), 22714–22722 (2015).
    [Crossref] [PubMed]
  26. A. Minardo, A. Coscetta, L. Zeni, and R. Bernini, “High-Spatial Resolution DPP-BOTDA by Real-Time Balanced Detection,” IEEE Photonics Technol. Lett. 26(12), 1251–1254 (2014).
    [Crossref]
  27. Y. Koyamada, Y. Sakairi, N. Takeuchi, and S. Adachi, “Novel Technique to Improve Spatial Resolution in Brillouin Optical Time-Domain Reflectometry,” IEEE Photonics Technol. Lett. 19(23), 1910–1912 (2007).
    [Crossref]
  28. W. Li, X. Bao, Y. Li, and L. Chen, “Differential pulse-width pair BOTDA for high spatial resolution sensing,” Opt. Express 16(26), 21616–21625 (2008).
    [Crossref] [PubMed]
  29. M. A. Soto, G. Bolognini, F. Di Pasquale, and L. Thévenaz, “Long-range Brillouin optical time-domain analysis sensor employing pulse coding techniques,” Meas. Sci. Technol. 21(9), 094024 (2010).
    [Crossref]
  30. X. Angulo-Vinuesa, S. Martin-Lopez, P. Corredera, and M. Gonzalez-Herraez, “Raman-assisted Brillouin optical time-domain analysis with sub-meter resolution over 100 km,” Opt. Express 20(11), 12147–12154 (2012).
    [Crossref] [PubMed]
  31. Z. Li, L. Yan, L. Shao, W. Pan, and B. Luo, “Coherent BOTDA sensor with intensity modulated local light and IQ demodulation,” Opt. Express 23(12), 16407–16415 (2015).
    [Crossref] [PubMed]
  32. Y. Lu, Z. Qin, P. Lu, D. Zhou, L. Chen, and X. Bao, “Distributed Strain and Temperature Measurement by Brillouin Beat Spectrum,” IEEE Photonics Technol. Lett. 25(11), 1050–1053 (2013).
    [Crossref]
  33. Y. Peled, A. Motil, and M. Tur, “Fast Brillouin optical time domain analysis for dynamic sensing,” Opt. Express 20(8), 8584–8591 (2012).
    [Crossref] [PubMed]
  34. Y. Dong, D. Ba, T. Jiang, D. Zhou, H. Zhang, C. Zhu, Z. Lu, H. Li, L. Chen, and X. Bao, “High-Spatial-Resolution Fast BOTDA for Dynamic Strain Measurement Based on Differential Double-Pulse and Second-Order Sideband of Modulation,” IEEE Photonics J. 5(3), 2600407 (2013).
    [Crossref]
  35. Y. Peled, A. Motil, L. Yaron, and M. Tur, “Slope-assisted fast distributed sensing in optical fibers with arbitrary Brillouin profile,” Opt. Express 19(21), 19845–19854 (2011).
    [Crossref] [PubMed]
  36. R. Bernini, A. Minardo, and L. Zeni, “Dynamic strain measurement in optical fibers by stimulated Brillouin scattering,” Opt. Lett. 34(17), 2613–2615 (2009).
    [Crossref] [PubMed]
  37. Q. Cui, S. Pamukcu, W. Xiao, and M. Pervizpour, “Truly Distributed Fiber Vibration Sensor Using Pulse Base BOTDA With Wide Dynamic Range,” IEEE Photonics Technol. Lett. 23(24), 1887–1889 (2011).
    [Crossref]
  38. A. Minardo, A. Coscetta, R. Bernini, and L. Zeni, “Heterodyne slope-assisted Brillouin optical time-domain analysis for dynamic strain measurements,” J. Opt. 18(2), 025606 (2016).
    [Crossref]
  39. A. Motil, O. Danon, Y. Peled, and M. Tur, “Pump-Power-Independent Double Slope-Assisted Distributed and Fast Brillouin Fiber-Optic Sensor,” IEEE Photonics Technol. Lett. 26(8), 797–800 (2014).
    [Crossref]
  40. D. Ba, B. Wang, D. Zhou, M. Yin, Y. Dong, H. Li, Z. Lu, and Z. Fan, “Distributed measurement of dynamic strain based on multi-slope assisted fast BOTDA,” Opt. Express 24(9), 9781–9793 (2016).
    [Crossref] [PubMed]
  41. R. W. Boyd, Nonlinear Optics (Academic) 3rd edition, Chap. 9.
  42. A. Zornoza, M. Sagues, and A. Loayssa, “Self-Heterodyne Detection for SNR Improvement and Distributed Phase-Shift Measurements in BOTDA,” J. Lightwave Technol. 30(8), 1066–1072 (2012).
    [Crossref]
  43. J. Urricelqui, M. Sagues, and A. Loayssa, “BOTDA measurements tolerant to non-local effects by using a phase-modulated probe wave and RF demodulation,” Opt. Express 21(14), 17186–17194 (2013).
    [Crossref] [PubMed]
  44. X. Tu, Q. Sun, W. Chen, M. Chen, and Z. Meng, “Vector Brillouin Optical Time-Domain Analysis With Heterodyne Detection and IQ Demodulation Algorithm,” IEEE Photonics J. 6(2), 1–8 (2014).
    [Crossref]
  45. J. Urricelqui, A. Zornoza, M. Sagues, and A. Loayssa, “Dynamic BOTDA measurements based on Brillouin phase-shift and RF demodulation,” Opt. Express 20(24), 26942–26949 (2012).
    [Crossref] [PubMed]
  46. M. Pagani, D. Marpaung, and B. J. Eggleton, “Ultra-wideband microwave photonic phase shifter with configurable amplitude response,” Opt. Lett. 39(20), 5854–5857 (2014).
    [Crossref] [PubMed]
  47. areZ. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, “Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber,” J. Opt. Soc. Am. B 22(11), 2378–2384 (2005).
    [Crossref]
  48. A. Lopez-Gil, M. A. Soto, X. Angulo-Vinuesa, A. Dominguez-Lopez, S. Martin-Lopez, L. Thévenaz, and M. Gonzalez-Herraez, “Evaluation of the accuracy of BOTDA systems based on the phase spectral response,” Opt. Express 24(15), 17200–17214 (2016).
    [Crossref] [PubMed]
  49. Z. Li, L. Yan, L. Shao, W. Pan, B. Luo, J. Liang, and H. He, “Coherent BOTDA Sensor With Single-Sideband Modulated Probe Light,” IEEE Photonics J. 8(1), 1–8 (2016).

2016 (5)

A. Minardo, R. Bernini, and L. Zeni, “Analysis of SNR penalty in Brillouin optical time-domain analysis sensors induced by laser source phase noise,” J. Opt. 18(2), 025601 (2016).
[Crossref]

A. Minardo, A. Coscetta, R. Bernini, and L. Zeni, “Heterodyne slope-assisted Brillouin optical time-domain analysis for dynamic strain measurements,” J. Opt. 18(2), 025606 (2016).
[Crossref]

Z. Li, L. Yan, L. Shao, W. Pan, B. Luo, J. Liang, and H. He, “Coherent BOTDA Sensor With Single-Sideband Modulated Probe Light,” IEEE Photonics J. 8(1), 1–8 (2016).

D. Ba, B. Wang, D. Zhou, M. Yin, Y. Dong, H. Li, Z. Lu, and Z. Fan, “Distributed measurement of dynamic strain based on multi-slope assisted fast BOTDA,” Opt. Express 24(9), 9781–9793 (2016).
[Crossref] [PubMed]

A. Lopez-Gil, M. A. Soto, X. Angulo-Vinuesa, A. Dominguez-Lopez, S. Martin-Lopez, L. Thévenaz, and M. Gonzalez-Herraez, “Evaluation of the accuracy of BOTDA systems based on the phase spectral response,” Opt. Express 24(15), 17200–17214 (2016).
[Crossref] [PubMed]

2015 (6)

2014 (9)

N. Hayashi, Y. Mizuno, and K. Nakamura, “Simplified Configuration of Brillouin Optical Correlation-Domain Reflectometry,” IEEE Photonics J. 6(5), 1–7 (2014).
[Crossref]

N. Hayashi, Y. Mizuno, and K. Nakamura, “Alternative Implementation of Simplified Brillouin Optical Correlation-Domain Reflectometry,” IEEE Photonics J. 6(6), 1–8 (2014).
[Crossref]

A. Minardo, A. Coscetta, L. Zeni, and R. Bernini, “High-Spatial Resolution DPP-BOTDA by Real-Time Balanced Detection,” IEEE Photonics Technol. Lett. 26(12), 1251–1254 (2014).
[Crossref]

A. Motil, O. Danon, Y. Peled, and M. Tur, “Pump-Power-Independent Double Slope-Assisted Distributed and Fast Brillouin Fiber-Optic Sensor,” IEEE Photonics Technol. Lett. 26(8), 797–800 (2014).
[Crossref]

X. Tu, Q. Sun, W. Chen, M. Chen, and Z. Meng, “Vector Brillouin Optical Time-Domain Analysis With Heterodyne Detection and IQ Demodulation Algorithm,” IEEE Photonics J. 6(2), 1–8 (2014).
[Crossref]

J. Urricelqui, M. Sagues, and A. Loayssa, “Phasorial differential pulse-width pair technique for long-range Brillouin optical time-domain analysis sensors,” Opt. Express 22(14), 17403–17408 (2014).
[Crossref] [PubMed]

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. 39(15), 4313–4316 (2014).
[Crossref] [PubMed]

M. Pagani, D. Marpaung, and B. J. Eggleton, “Ultra-wideband microwave photonic phase shifter with configurable amplitude response,” Opt. Lett. 39(20), 5854–5857 (2014).
[Crossref] [PubMed]

Y. Dong, P. Xu, H. Zhang, Z. Lu, L. Chen, and X. Bao, “Characterization of evolution of mode coupling in a graded-index polymer optical fiber by using Brillouin optical time-domain analysis,” Opt. Express 22(22), 26510–26516 (2014).
[Crossref] [PubMed]

2013 (5)

L. Thévenaz, S. F. Mafang, and J. Lin, “Effect of pulse depletion in a Brillouin optical time-domain analysis system,” Opt. Express 21(12), 14017–14035 (2013).
[Crossref] [PubMed]

J. Urricelqui, M. Sagues, and A. Loayssa, “BOTDA measurements tolerant to non-local effects by using a phase-modulated probe wave and RF demodulation,” Opt. Express 21(14), 17186–17194 (2013).
[Crossref] [PubMed]

Y. Dong, D. Ba, T. Jiang, D. Zhou, H. Zhang, C. Zhu, Z. Lu, H. Li, L. Chen, and X. Bao, “High-Spatial-Resolution Fast BOTDA for Dynamic Strain Measurement Based on Differential Double-Pulse and Second-Order Sideband of Modulation,” IEEE Photonics J. 5(3), 2600407 (2013).
[Crossref]

Y. Lu, Z. Qin, P. Lu, D. Zhou, L. Chen, and X. Bao, “Distributed Strain and Temperature Measurement by Brillouin Beat Spectrum,” IEEE Photonics Technol. Lett. 25(11), 1050–1053 (2013).
[Crossref]

K. Hotate, “Fiber distributed Brillouin sensing with optical correlation domain techniques,” Opt. Fiber Technol. 19(66, Part B), 700–719 (2013).
[Crossref]

2012 (8)

R. Bernini, A. Minardo, and L. Zeni, “Distributed Sensing at Centimeter-Scale Spatial Resolution by BOFDA: Measurements and Signal Processing,” IEEE Photonics J. 4(1), 48–56 (2012).
[Crossref]

Y. Mao, N. Guo, K. L. Yu, H. Y. Tam, and C. Lu, “1-cm-Spatial-Resolution Brillouin Optical Time-Domain Analysis Based on Bright Pulse Brillouin Gain and Complementary Code,” IEEE Photonics J. 4(6), 2243–2248 (2012).
[Crossref]

Y. Dong, H. Zhang, L. Chen, and X. Bao, “2 cm spatial-resolution and 2 km range Brillouin optical fiber sensor using a transient differential pulse pair,” Appl. Opt. 51(9), 1229–1235 (2012).
[Crossref] [PubMed]

Y. Peled, A. Motil, and M. Tur, “Fast Brillouin optical time domain analysis for dynamic sensing,” Opt. Express 20(8), 8584–8591 (2012).
[Crossref] [PubMed]

A. Zornoza, M. Sagues, and A. Loayssa, “Self-Heterodyne Detection for SNR Improvement and Distributed Phase-Shift Measurements in BOTDA,” J. Lightwave Technol. 30(8), 1066–1072 (2012).
[Crossref]

Y. Dong, L. Chen, and X. Bao, “Extending the Sensing Range of Brillouin Optical Time-Domain Analysis Combining Frequency-Division Multiplexing and In-Line EDFAs,” J. Lightwave Technol. 30(8), 1161–1167 (2012).
[Crossref]

X. Angulo-Vinuesa, S. Martin-Lopez, P. Corredera, and M. Gonzalez-Herraez, “Raman-assisted Brillouin optical time-domain analysis with sub-meter resolution over 100 km,” Opt. Express 20(11), 12147–12154 (2012).
[Crossref] [PubMed]

J. Urricelqui, A. Zornoza, M. Sagues, and A. Loayssa, “Dynamic BOTDA measurements based on Brillouin phase-shift and RF demodulation,” Opt. Express 20(24), 26942–26949 (2012).
[Crossref] [PubMed]

2011 (3)

Y. Peled, A. Motil, L. Yaron, and M. Tur, “Slope-assisted fast distributed sensing in optical fibers with arbitrary Brillouin profile,” Opt. Express 19(21), 19845–19854 (2011).
[Crossref] [PubMed]

Q. Cui, S. Pamukcu, W. Xiao, and M. Pervizpour, “Truly Distributed Fiber Vibration Sensor Using Pulse Base BOTDA With Wide Dynamic Range,” IEEE Photonics Technol. Lett. 23(24), 1887–1889 (2011).
[Crossref]

X. Bao and L. Chen, “Recent Progress in Brillouin Scattering Based Fiber Sensors,” Sensors (Basel) 11(12), 4152–4187 (2011).
[Crossref] [PubMed]

2010 (2)

L. Thévenaz, “Brillouin distributed time-domain sensing in optical fibers: state of the art and perspectives,” Front. Optoelectron. China 3(1), 13–21 (2010).
[Crossref]

M. A. Soto, G. Bolognini, F. Di Pasquale, and L. Thévenaz, “Long-range Brillouin optical time-domain analysis sensor employing pulse coding techniques,” Meas. Sci. Technol. 21(9), 094024 (2010).
[Crossref]

2009 (1)

2008 (1)

2007 (2)

A. W. Brown, B. G. Colpitts, and K. Brown, “Dark-Pulse Brillouin Optical Time-Domain Sensor With 20-mm Spatial Resolution,” J. Lightwave Technol. 25(1), 381–386 (2007).
[Crossref]

Y. Koyamada, Y. Sakairi, N. Takeuchi, and S. Adachi, “Novel Technique to Improve Spatial Resolution in Brillouin Optical Time-Domain Reflectometry,” IEEE Photonics Technol. Lett. 19(23), 1910–1912 (2007).
[Crossref]

2006 (1)

2005 (1)

2002 (1)

K. Hotate and M. Tanaka, “Distributed fiber Brillouin strain sensing with 1-cm spatial resolution by correlation-based continuous-wave technique,” IEEE Photonics Technol. Lett. 14(2), 179–181 (2002).
[Crossref]

1997 (1)

D. Garcus, T. Gogolla, K. Krebber, and F. Schliep, “Brillouin optical-fiber frequency-domain analysis for distributed temperature and strain measurements,” J. Lightwave Technol. 15(4), 654–662 (1997).
[Crossref]

1996 (1)

Adachi, S.

Y. Koyamada, Y. Sakairi, N. Takeuchi, and S. Adachi, “Novel Technique to Improve Spatial Resolution in Brillouin Optical Time-Domain Reflectometry,” IEEE Photonics Technol. Lett. 19(23), 1910–1912 (2007).
[Crossref]

Angulo-Vinuesa, X.

Ba, D.

D. Ba, B. Wang, D. Zhou, M. Yin, Y. Dong, H. Li, Z. Lu, and Z. Fan, “Distributed measurement of dynamic strain based on multi-slope assisted fast BOTDA,” Opt. Express 24(9), 9781–9793 (2016).
[Crossref] [PubMed]

Y. Dong, D. Ba, T. Jiang, D. Zhou, H. Zhang, C. Zhu, Z. Lu, H. Li, L. Chen, and X. Bao, “High-Spatial-Resolution Fast BOTDA for Dynamic Strain Measurement Based on Differential Double-Pulse and Second-Order Sideband of Modulation,” IEEE Photonics J. 5(3), 2600407 (2013).
[Crossref]

Bao, X.

Z. Ma, M. Zhang, Y. Liu, X. Bao, H. Liu, Y. Zhang, and Y. Wang, “Incoherent Brillouin Optical Time-Domain Reflectometry With Random State Correlated Brillouin Spectrum,” IEEE Photonics J. 7(4), 1–7 (2015).
[Crossref]

P. Xu, Y. Dong, J. Zhang, D. Zhou, T. Jiang, J. Xu, H. Zhang, T. Zhu, Z. Lu, L. Chen, and X. Bao, “Bend-insensitive distributed sensing in singlemode-multimode-singlemode optical fiber structure by using Brillouin optical time-domain analysis,” Opt. Express 23(17), 22714–22722 (2015).
[Crossref] [PubMed]

Y. Dong, P. Xu, H. Zhang, Z. Lu, L. Chen, and X. Bao, “Characterization of evolution of mode coupling in a graded-index polymer optical fiber by using Brillouin optical time-domain analysis,” Opt. Express 22(22), 26510–26516 (2014).
[Crossref] [PubMed]

Y. Dong, D. Ba, T. Jiang, D. Zhou, H. Zhang, C. Zhu, Z. Lu, H. Li, L. Chen, and X. Bao, “High-Spatial-Resolution Fast BOTDA for Dynamic Strain Measurement Based on Differential Double-Pulse and Second-Order Sideband of Modulation,” IEEE Photonics J. 5(3), 2600407 (2013).
[Crossref]

Y. Lu, Z. Qin, P. Lu, D. Zhou, L. Chen, and X. Bao, “Distributed Strain and Temperature Measurement by Brillouin Beat Spectrum,” IEEE Photonics Technol. Lett. 25(11), 1050–1053 (2013).
[Crossref]

Y. Dong, L. Chen, and X. Bao, “Extending the Sensing Range of Brillouin Optical Time-Domain Analysis Combining Frequency-Division Multiplexing and In-Line EDFAs,” J. Lightwave Technol. 30(8), 1161–1167 (2012).
[Crossref]

Y. Dong, H. Zhang, L. Chen, and X. Bao, “2 cm spatial-resolution and 2 km range Brillouin optical fiber sensor using a transient differential pulse pair,” Appl. Opt. 51(9), 1229–1235 (2012).
[Crossref] [PubMed]

X. Bao and L. Chen, “Recent Progress in Brillouin Scattering Based Fiber Sensors,” Sensors (Basel) 11(12), 4152–4187 (2011).
[Crossref] [PubMed]

W. Li, X. Bao, Y. Li, and L. Chen, “Differential pulse-width pair BOTDA for high spatial resolution sensing,” Opt. Express 16(26), 21616–21625 (2008).
[Crossref] [PubMed]

Bernini, R.

A. Minardo, R. Bernini, and L. Zeni, “Analysis of SNR penalty in Brillouin optical time-domain analysis sensors induced by laser source phase noise,” J. Opt. 18(2), 025601 (2016).
[Crossref]

A. Minardo, A. Coscetta, R. Bernini, and L. Zeni, “Heterodyne slope-assisted Brillouin optical time-domain analysis for dynamic strain measurements,” J. Opt. 18(2), 025606 (2016).
[Crossref]

A. Minardo, A. Coscetta, L. Zeni, and R. Bernini, “High-Spatial Resolution DPP-BOTDA by Real-Time Balanced Detection,” IEEE Photonics Technol. Lett. 26(12), 1251–1254 (2014).
[Crossref]

R. Bernini, A. Minardo, and L. Zeni, “Distributed Sensing at Centimeter-Scale Spatial Resolution by BOFDA: Measurements and Signal Processing,” IEEE Photonics J. 4(1), 48–56 (2012).
[Crossref]

R. Bernini, A. Minardo, and L. Zeni, “Dynamic strain measurement in optical fibers by stimulated Brillouin scattering,” Opt. Lett. 34(17), 2613–2615 (2009).
[Crossref] [PubMed]

Bolognini, G.

M. A. Soto, G. Bolognini, F. Di Pasquale, and L. Thévenaz, “Long-range Brillouin optical time-domain analysis sensor employing pulse coding techniques,” Meas. Sci. Technol. 21(9), 094024 (2010).
[Crossref]

Boyd, R. W.

Brown, A. W.

Brown, K.

Chen, L.

P. Xu, Y. Dong, J. Zhang, D. Zhou, T. Jiang, J. Xu, H. Zhang, T. Zhu, Z. Lu, L. Chen, and X. Bao, “Bend-insensitive distributed sensing in singlemode-multimode-singlemode optical fiber structure by using Brillouin optical time-domain analysis,” Opt. Express 23(17), 22714–22722 (2015).
[Crossref] [PubMed]

Y. Dong, P. Xu, H. Zhang, Z. Lu, L. Chen, and X. Bao, “Characterization of evolution of mode coupling in a graded-index polymer optical fiber by using Brillouin optical time-domain analysis,” Opt. Express 22(22), 26510–26516 (2014).
[Crossref] [PubMed]

Y. Lu, Z. Qin, P. Lu, D. Zhou, L. Chen, and X. Bao, “Distributed Strain and Temperature Measurement by Brillouin Beat Spectrum,” IEEE Photonics Technol. Lett. 25(11), 1050–1053 (2013).
[Crossref]

Y. Dong, D. Ba, T. Jiang, D. Zhou, H. Zhang, C. Zhu, Z. Lu, H. Li, L. Chen, and X. Bao, “High-Spatial-Resolution Fast BOTDA for Dynamic Strain Measurement Based on Differential Double-Pulse and Second-Order Sideband of Modulation,” IEEE Photonics J. 5(3), 2600407 (2013).
[Crossref]

Y. Dong, H. Zhang, L. Chen, and X. Bao, “2 cm spatial-resolution and 2 km range Brillouin optical fiber sensor using a transient differential pulse pair,” Appl. Opt. 51(9), 1229–1235 (2012).
[Crossref] [PubMed]

Y. Dong, L. Chen, and X. Bao, “Extending the Sensing Range of Brillouin Optical Time-Domain Analysis Combining Frequency-Division Multiplexing and In-Line EDFAs,” J. Lightwave Technol. 30(8), 1161–1167 (2012).
[Crossref]

X. Bao and L. Chen, “Recent Progress in Brillouin Scattering Based Fiber Sensors,” Sensors (Basel) 11(12), 4152–4187 (2011).
[Crossref] [PubMed]

W. Li, X. Bao, Y. Li, and L. Chen, “Differential pulse-width pair BOTDA for high spatial resolution sensing,” Opt. Express 16(26), 21616–21625 (2008).
[Crossref] [PubMed]

Chen, M.

X. Tu, Q. Sun, W. Chen, M. Chen, and Z. Meng, “Vector Brillouin Optical Time-Domain Analysis With Heterodyne Detection and IQ Demodulation Algorithm,” IEEE Photonics J. 6(2), 1–8 (2014).
[Crossref]

Chen, W.

X. Tu, Q. Sun, W. Chen, M. Chen, and Z. Meng, “Vector Brillouin Optical Time-Domain Analysis With Heterodyne Detection and IQ Demodulation Algorithm,” IEEE Photonics J. 6(2), 1–8 (2014).
[Crossref]

Colpitts, B. G.

Corredera, P.

Coscetta, A.

A. Minardo, A. Coscetta, R. Bernini, and L. Zeni, “Heterodyne slope-assisted Brillouin optical time-domain analysis for dynamic strain measurements,” J. Opt. 18(2), 025606 (2016).
[Crossref]

A. Minardo, A. Coscetta, L. Zeni, and R. Bernini, “High-Spatial Resolution DPP-BOTDA by Real-Time Balanced Detection,” IEEE Photonics Technol. Lett. 26(12), 1251–1254 (2014).
[Crossref]

Cui, Q.

Q. Cui, S. Pamukcu, W. Xiao, and M. Pervizpour, “Truly Distributed Fiber Vibration Sensor Using Pulse Base BOTDA With Wide Dynamic Range,” IEEE Photonics Technol. Lett. 23(24), 1887–1889 (2011).
[Crossref]

Danon, O.

A. Motil, O. Danon, Y. Peled, and M. Tur, “Pump-Power-Independent Double Slope-Assisted Distributed and Fast Brillouin Fiber-Optic Sensor,” IEEE Photonics Technol. Lett. 26(8), 797–800 (2014).
[Crossref]

Di Pasquale, F.

M. A. Soto, G. Bolognini, F. Di Pasquale, and L. Thévenaz, “Long-range Brillouin optical time-domain analysis sensor employing pulse coding techniques,” Meas. Sci. Technol. 21(9), 094024 (2010).
[Crossref]

Dominguez-Lopez, A.

Dong, Y.

D. Ba, B. Wang, D. Zhou, M. Yin, Y. Dong, H. Li, Z. Lu, and Z. Fan, “Distributed measurement of dynamic strain based on multi-slope assisted fast BOTDA,” Opt. Express 24(9), 9781–9793 (2016).
[Crossref] [PubMed]

P. Xu, Y. Dong, J. Zhang, D. Zhou, T. Jiang, J. Xu, H. Zhang, T. Zhu, Z. Lu, L. Chen, and X. Bao, “Bend-insensitive distributed sensing in singlemode-multimode-singlemode optical fiber structure by using Brillouin optical time-domain analysis,” Opt. Express 23(17), 22714–22722 (2015).
[Crossref] [PubMed]

Y. Dong, P. Xu, H. Zhang, Z. Lu, L. Chen, and X. Bao, “Characterization of evolution of mode coupling in a graded-index polymer optical fiber by using Brillouin optical time-domain analysis,” Opt. Express 22(22), 26510–26516 (2014).
[Crossref] [PubMed]

Y. Dong, D. Ba, T. Jiang, D. Zhou, H. Zhang, C. Zhu, Z. Lu, H. Li, L. Chen, and X. Bao, “High-Spatial-Resolution Fast BOTDA for Dynamic Strain Measurement Based on Differential Double-Pulse and Second-Order Sideband of Modulation,” IEEE Photonics J. 5(3), 2600407 (2013).
[Crossref]

Y. Dong, L. Chen, and X. Bao, “Extending the Sensing Range of Brillouin Optical Time-Domain Analysis Combining Frequency-Division Multiplexing and In-Line EDFAs,” J. Lightwave Technol. 30(8), 1161–1167 (2012).
[Crossref]

Y. Dong, H. Zhang, L. Chen, and X. Bao, “2 cm spatial-resolution and 2 km range Brillouin optical fiber sensor using a transient differential pulse pair,” Appl. Opt. 51(9), 1229–1235 (2012).
[Crossref] [PubMed]

Eggleton, B. J.

Fan, M. Q.

Fan, Z.

Gaeta, A. L.

Garcus, D.

D. Garcus, T. Gogolla, K. Krebber, and F. Schliep, “Brillouin optical-fiber frequency-domain analysis for distributed temperature and strain measurements,” J. Lightwave Technol. 15(4), 654–662 (1997).
[Crossref]

Garus, D.

Gauthier, D. J.

Gogolla, T.

D. Garcus, T. Gogolla, K. Krebber, and F. Schliep, “Brillouin optical-fiber frequency-domain analysis for distributed temperature and strain measurements,” J. Lightwave Technol. 15(4), 654–662 (1997).
[Crossref]

D. Garus, T. Gogolla, K. Krebber, and F. Schliep, “Distributed sensing technique based on Brillouin optical-fiber frequency-domain analysis,” Opt. Lett. 21(17), 1402–1404 (1996).
[Crossref] [PubMed]

Gonzalez-Herraez, M.

Guo, N.

Y. Mao, N. Guo, K. L. Yu, H. Y. Tam, and C. Lu, “1-cm-Spatial-Resolution Brillouin Optical Time-Domain Analysis Based on Bright Pulse Brillouin Gain and Complementary Code,” IEEE Photonics J. 4(6), 2243–2248 (2012).
[Crossref]

Hayashi, N.

N. Hayashi, Y. Mizuno, and K. Nakamura, “Simplified Brillouin Optical Correlation-Domain Reflectometry Using Polymer Optical Fiber,” IEEE Photonics J. 7(1), 1–7 (2015).
[Crossref]

N. Hayashi, Y. Mizuno, and K. Nakamura, “Alternative Implementation of Simplified Brillouin Optical Correlation-Domain Reflectometry,” IEEE Photonics J. 6(6), 1–8 (2014).
[Crossref]

N. Hayashi, Y. Mizuno, and K. Nakamura, “Simplified Configuration of Brillouin Optical Correlation-Domain Reflectometry,” IEEE Photonics J. 6(5), 1–7 (2014).
[Crossref]

He, H.

Z. Li, L. Yan, L. Shao, W. Pan, B. Luo, J. Liang, and H. He, “Coherent BOTDA Sensor With Single-Sideband Modulated Probe Light,” IEEE Photonics J. 8(1), 1–8 (2016).

He, Z.

Hotate, K.

K. Hotate, “Fiber distributed Brillouin sensing with optical correlation domain techniques,” Opt. Fiber Technol. 19(66, Part B), 700–719 (2013).
[Crossref]

K. Y. Song, Z. He, and K. Hotate, “Distributed strain measurement with millimeter-order spatial resolution based on Brillouin optical correlation domain analysis,” Opt. Lett. 31(17), 2526–2528 (2006).
[Crossref] [PubMed]

K. Hotate and M. Tanaka, “Distributed fiber Brillouin strain sensing with 1-cm spatial resolution by correlation-based continuous-wave technique,” IEEE Photonics Technol. Lett. 14(2), 179–181 (2002).
[Crossref]

Ip, E.

Jiang, T.

P. Xu, Y. Dong, J. Zhang, D. Zhou, T. Jiang, J. Xu, H. Zhang, T. Zhu, Z. Lu, L. Chen, and X. Bao, “Bend-insensitive distributed sensing in singlemode-multimode-singlemode optical fiber structure by using Brillouin optical time-domain analysis,” Opt. Express 23(17), 22714–22722 (2015).
[Crossref] [PubMed]

Y. Dong, D. Ba, T. Jiang, D. Zhou, H. Zhang, C. Zhu, Z. Lu, H. Li, L. Chen, and X. Bao, “High-Spatial-Resolution Fast BOTDA for Dynamic Strain Measurement Based on Differential Double-Pulse and Second-Order Sideband of Modulation,” IEEE Photonics J. 5(3), 2600407 (2013).
[Crossref]

Koyamada, Y.

Y. Koyamada, Y. Sakairi, N. Takeuchi, and S. Adachi, “Novel Technique to Improve Spatial Resolution in Brillouin Optical Time-Domain Reflectometry,” IEEE Photonics Technol. Lett. 19(23), 1910–1912 (2007).
[Crossref]

Krebber, K.

D. Garcus, T. Gogolla, K. Krebber, and F. Schliep, “Brillouin optical-fiber frequency-domain analysis for distributed temperature and strain measurements,” J. Lightwave Technol. 15(4), 654–662 (1997).
[Crossref]

D. Garus, T. Gogolla, K. Krebber, and F. Schliep, “Distributed sensing technique based on Brillouin optical-fiber frequency-domain analysis,” Opt. Lett. 21(17), 1402–1404 (1996).
[Crossref] [PubMed]

Li, H.

D. Ba, B. Wang, D. Zhou, M. Yin, Y. Dong, H. Li, Z. Lu, and Z. Fan, “Distributed measurement of dynamic strain based on multi-slope assisted fast BOTDA,” Opt. Express 24(9), 9781–9793 (2016).
[Crossref] [PubMed]

Y. Dong, D. Ba, T. Jiang, D. Zhou, H. Zhang, C. Zhu, Z. Lu, H. Li, L. Chen, and X. Bao, “High-Spatial-Resolution Fast BOTDA for Dynamic Strain Measurement Based on Differential Double-Pulse and Second-Order Sideband of Modulation,” IEEE Photonics J. 5(3), 2600407 (2013).
[Crossref]

Li, J.

Li, W.

Li, Y.

Li, Z.

Z. Li, L. Yan, L. Shao, W. Pan, B. Luo, J. Liang, and H. He, “Coherent BOTDA Sensor With Single-Sideband Modulated Probe Light,” IEEE Photonics J. 8(1), 1–8 (2016).

Z. Li, L. Yan, L. Shao, W. Pan, and B. Luo, “Coherent BOTDA sensor with intensity modulated local light and IQ demodulation,” Opt. Express 23(12), 16407–16415 (2015).
[Crossref] [PubMed]

Liang, J.

Z. Li, L. Yan, L. Shao, W. Pan, B. Luo, J. Liang, and H. He, “Coherent BOTDA Sensor With Single-Sideband Modulated Probe Light,” IEEE Photonics J. 8(1), 1–8 (2016).

Lin, J.

Liu, H.

Z. Ma, M. Zhang, Y. Liu, X. Bao, H. Liu, Y. Zhang, and Y. Wang, “Incoherent Brillouin Optical Time-Domain Reflectometry With Random State Correlated Brillouin Spectrum,” IEEE Photonics J. 7(4), 1–7 (2015).
[Crossref]

Liu, Y.

Z. Ma, M. Zhang, Y. Liu, X. Bao, H. Liu, Y. Zhang, and Y. Wang, “Incoherent Brillouin Optical Time-Domain Reflectometry With Random State Correlated Brillouin Spectrum,” IEEE Photonics J. 7(4), 1–7 (2015).
[Crossref]

Loayssa, A.

Lopez-Gil, A.

Lu, C.

Y. Mao, N. Guo, K. L. Yu, H. Y. Tam, and C. Lu, “1-cm-Spatial-Resolution Brillouin Optical Time-Domain Analysis Based on Bright Pulse Brillouin Gain and Complementary Code,” IEEE Photonics J. 4(6), 2243–2248 (2012).
[Crossref]

Lu, P.

Y. Lu, Z. Qin, P. Lu, D. Zhou, L. Chen, and X. Bao, “Distributed Strain and Temperature Measurement by Brillouin Beat Spectrum,” IEEE Photonics Technol. Lett. 25(11), 1050–1053 (2013).
[Crossref]

Lu, Y.

Y. Lu, Z. Qin, P. Lu, D. Zhou, L. Chen, and X. Bao, “Distributed Strain and Temperature Measurement by Brillouin Beat Spectrum,” IEEE Photonics Technol. Lett. 25(11), 1050–1053 (2013).
[Crossref]

Lu, Z.

Luo, B.

Z. Li, L. Yan, L. Shao, W. Pan, B. Luo, J. Liang, and H. He, “Coherent BOTDA Sensor With Single-Sideband Modulated Probe Light,” IEEE Photonics J. 8(1), 1–8 (2016).

Z. Li, L. Yan, L. Shao, W. Pan, and B. Luo, “Coherent BOTDA sensor with intensity modulated local light and IQ demodulation,” Opt. Express 23(12), 16407–16415 (2015).
[Crossref] [PubMed]

Ma, Z.

Z. Ma, M. Zhang, Y. Liu, X. Bao, H. Liu, Y. Zhang, and Y. Wang, “Incoherent Brillouin Optical Time-Domain Reflectometry With Random State Correlated Brillouin Spectrum,” IEEE Photonics J. 7(4), 1–7 (2015).
[Crossref]

Mafang, S. F.

Mao, Y.

Y. Mao, N. Guo, K. L. Yu, H. Y. Tam, and C. Lu, “1-cm-Spatial-Resolution Brillouin Optical Time-Domain Analysis Based on Bright Pulse Brillouin Gain and Complementary Code,” IEEE Photonics J. 4(6), 2243–2248 (2012).
[Crossref]

Marpaung, D.

Martin-Lopez, S.

Meng, Z.

X. Tu, Q. Sun, W. Chen, M. Chen, and Z. Meng, “Vector Brillouin Optical Time-Domain Analysis With Heterodyne Detection and IQ Demodulation Algorithm,” IEEE Photonics J. 6(2), 1–8 (2014).
[Crossref]

Minardo, A.

A. Minardo, R. Bernini, and L. Zeni, “Analysis of SNR penalty in Brillouin optical time-domain analysis sensors induced by laser source phase noise,” J. Opt. 18(2), 025601 (2016).
[Crossref]

A. Minardo, A. Coscetta, R. Bernini, and L. Zeni, “Heterodyne slope-assisted Brillouin optical time-domain analysis for dynamic strain measurements,” J. Opt. 18(2), 025606 (2016).
[Crossref]

A. Minardo, A. Coscetta, L. Zeni, and R. Bernini, “High-Spatial Resolution DPP-BOTDA by Real-Time Balanced Detection,” IEEE Photonics Technol. Lett. 26(12), 1251–1254 (2014).
[Crossref]

R. Bernini, A. Minardo, and L. Zeni, “Distributed Sensing at Centimeter-Scale Spatial Resolution by BOFDA: Measurements and Signal Processing,” IEEE Photonics J. 4(1), 48–56 (2012).
[Crossref]

R. Bernini, A. Minardo, and L. Zeni, “Dynamic strain measurement in optical fibers by stimulated Brillouin scattering,” Opt. Lett. 34(17), 2613–2615 (2009).
[Crossref] [PubMed]

Mizuno, Y.

N. Hayashi, Y. Mizuno, and K. Nakamura, “Simplified Brillouin Optical Correlation-Domain Reflectometry Using Polymer Optical Fiber,” IEEE Photonics J. 7(1), 1–7 (2015).
[Crossref]

N. Hayashi, Y. Mizuno, and K. Nakamura, “Alternative Implementation of Simplified Brillouin Optical Correlation-Domain Reflectometry,” IEEE Photonics J. 6(6), 1–8 (2014).
[Crossref]

N. Hayashi, Y. Mizuno, and K. Nakamura, “Simplified Configuration of Brillouin Optical Correlation-Domain Reflectometry,” IEEE Photonics J. 6(5), 1–7 (2014).
[Crossref]

Motil, A.

Nakamura, K.

N. Hayashi, Y. Mizuno, and K. Nakamura, “Simplified Brillouin Optical Correlation-Domain Reflectometry Using Polymer Optical Fiber,” IEEE Photonics J. 7(1), 1–7 (2015).
[Crossref]

N. Hayashi, Y. Mizuno, and K. Nakamura, “Alternative Implementation of Simplified Brillouin Optical Correlation-Domain Reflectometry,” IEEE Photonics J. 6(6), 1–8 (2014).
[Crossref]

N. Hayashi, Y. Mizuno, and K. Nakamura, “Simplified Configuration of Brillouin Optical Correlation-Domain Reflectometry,” IEEE Photonics J. 6(5), 1–7 (2014).
[Crossref]

Okawachi, Y.

Pagani, M.

Pamukcu, S.

Q. Cui, S. Pamukcu, W. Xiao, and M. Pervizpour, “Truly Distributed Fiber Vibration Sensor Using Pulse Base BOTDA With Wide Dynamic Range,” IEEE Photonics Technol. Lett. 23(24), 1887–1889 (2011).
[Crossref]

Pan, W.

Z. Li, L. Yan, L. Shao, W. Pan, B. Luo, J. Liang, and H. He, “Coherent BOTDA Sensor With Single-Sideband Modulated Probe Light,” IEEE Photonics J. 8(1), 1–8 (2016).

Z. Li, L. Yan, L. Shao, W. Pan, and B. Luo, “Coherent BOTDA sensor with intensity modulated local light and IQ demodulation,” Opt. Express 23(12), 16407–16415 (2015).
[Crossref] [PubMed]

Pan, Z.

Peled, Y.

Peng, F.

Pervizpour, M.

Q. Cui, S. Pamukcu, W. Xiao, and M. Pervizpour, “Truly Distributed Fiber Vibration Sensor Using Pulse Base BOTDA With Wide Dynamic Range,” IEEE Photonics Technol. Lett. 23(24), 1887–1889 (2011).
[Crossref]

Qin, Z.

Y. Lu, Z. Qin, P. Lu, D. Zhou, L. Chen, and X. Bao, “Distributed Strain and Temperature Measurement by Brillouin Beat Spectrum,” IEEE Photonics Technol. Lett. 25(11), 1050–1053 (2013).
[Crossref]

Rao, Y. J.

Sagues, M.

Sakairi, Y.

Y. Koyamada, Y. Sakairi, N. Takeuchi, and S. Adachi, “Novel Technique to Improve Spatial Resolution in Brillouin Optical Time-Domain Reflectometry,” IEEE Photonics Technol. Lett. 19(23), 1910–1912 (2007).
[Crossref]

Schliep, F.

D. Garcus, T. Gogolla, K. Krebber, and F. Schliep, “Brillouin optical-fiber frequency-domain analysis for distributed temperature and strain measurements,” J. Lightwave Technol. 15(4), 654–662 (1997).
[Crossref]

D. Garus, T. Gogolla, K. Krebber, and F. Schliep, “Distributed sensing technique based on Brillouin optical-fiber frequency-domain analysis,” Opt. Lett. 21(17), 1402–1404 (1996).
[Crossref] [PubMed]

Shao, L.

Z. Li, L. Yan, L. Shao, W. Pan, B. Luo, J. Liang, and H. He, “Coherent BOTDA Sensor With Single-Sideband Modulated Probe Light,” IEEE Photonics J. 8(1), 1–8 (2016).

Z. Li, L. Yan, L. Shao, W. Pan, and B. Luo, “Coherent BOTDA sensor with intensity modulated local light and IQ demodulation,” Opt. Express 23(12), 16407–16415 (2015).
[Crossref] [PubMed]

Sharping, J. E.

Song, K. Y.

Soto, M. A.

A. Lopez-Gil, M. A. Soto, X. Angulo-Vinuesa, A. Dominguez-Lopez, S. Martin-Lopez, L. Thévenaz, and M. Gonzalez-Herraez, “Evaluation of the accuracy of BOTDA systems based on the phase spectral response,” Opt. Express 24(15), 17200–17214 (2016).
[Crossref] [PubMed]

M. A. Soto, G. Bolognini, F. Di Pasquale, and L. Thévenaz, “Long-range Brillouin optical time-domain analysis sensor employing pulse coding techniques,” Meas. Sci. Technol. 21(9), 094024 (2010).
[Crossref]

Sun, Q.

X. Tu, Q. Sun, W. Chen, M. Chen, and Z. Meng, “Vector Brillouin Optical Time-Domain Analysis With Heterodyne Detection and IQ Demodulation Algorithm,” IEEE Photonics J. 6(2), 1–8 (2014).
[Crossref]

Takeuchi, N.

Y. Koyamada, Y. Sakairi, N. Takeuchi, and S. Adachi, “Novel Technique to Improve Spatial Resolution in Brillouin Optical Time-Domain Reflectometry,” IEEE Photonics Technol. Lett. 19(23), 1910–1912 (2007).
[Crossref]

Tam, H. Y.

Y. Mao, N. Guo, K. L. Yu, H. Y. Tam, and C. Lu, “1-cm-Spatial-Resolution Brillouin Optical Time-Domain Analysis Based on Bright Pulse Brillouin Gain and Complementary Code,” IEEE Photonics J. 4(6), 2243–2248 (2012).
[Crossref]

Tanaka, M.

K. Hotate and M. Tanaka, “Distributed fiber Brillouin strain sensing with 1-cm spatial resolution by correlation-based continuous-wave technique,” IEEE Photonics Technol. Lett. 14(2), 179–181 (2002).
[Crossref]

Thévenaz, L.

A. Lopez-Gil, M. A. Soto, X. Angulo-Vinuesa, A. Dominguez-Lopez, S. Martin-Lopez, L. Thévenaz, and M. Gonzalez-Herraez, “Evaluation of the accuracy of BOTDA systems based on the phase spectral response,” Opt. Express 24(15), 17200–17214 (2016).
[Crossref] [PubMed]

L. Thévenaz, S. F. Mafang, and J. Lin, “Effect of pulse depletion in a Brillouin optical time-domain analysis system,” Opt. Express 21(12), 14017–14035 (2013).
[Crossref] [PubMed]

L. Thévenaz, “Brillouin distributed time-domain sensing in optical fibers: state of the art and perspectives,” Front. Optoelectron. China 3(1), 13–21 (2010).
[Crossref]

M. A. Soto, G. Bolognini, F. Di Pasquale, and L. Thévenaz, “Long-range Brillouin optical time-domain analysis sensor employing pulse coding techniques,” Meas. Sci. Technol. 21(9), 094024 (2010).
[Crossref]

Tu, X.

X. Tu, Q. Sun, W. Chen, M. Chen, and Z. Meng, “Vector Brillouin Optical Time-Domain Analysis With Heterodyne Detection and IQ Demodulation Algorithm,” IEEE Photonics J. 6(2), 1–8 (2014).
[Crossref]

Tur, M.

Urricelqui, J.

Wang, B.

Wang, T.

Wang, Y.

Z. Ma, M. Zhang, Y. Liu, X. Bao, H. Liu, Y. Zhang, and Y. Wang, “Incoherent Brillouin Optical Time-Domain Reflectometry With Random State Correlated Brillouin Spectrum,” IEEE Photonics J. 7(4), 1–7 (2015).
[Crossref]

Wang, Z. N.

Weng, Y.

Willner, A. E.

Wu, H.

Xiao, W.

Q. Cui, S. Pamukcu, W. Xiao, and M. Pervizpour, “Truly Distributed Fiber Vibration Sensor Using Pulse Base BOTDA With Wide Dynamic Range,” IEEE Photonics Technol. Lett. 23(24), 1887–1889 (2011).
[Crossref]

Xu, J.

Xu, P.

Yan, L.

Z. Li, L. Yan, L. Shao, W. Pan, B. Luo, J. Liang, and H. He, “Coherent BOTDA Sensor With Single-Sideband Modulated Probe Light,” IEEE Photonics J. 8(1), 1–8 (2016).

Z. Li, L. Yan, L. Shao, W. Pan, and B. Luo, “Coherent BOTDA sensor with intensity modulated local light and IQ demodulation,” Opt. Express 23(12), 16407–16415 (2015).
[Crossref] [PubMed]

Yaron, L.

Yin, M.

Yu, K. L.

Y. Mao, N. Guo, K. L. Yu, H. Y. Tam, and C. Lu, “1-cm-Spatial-Resolution Brillouin Optical Time-Domain Analysis Based on Bright Pulse Brillouin Gain and Complementary Code,” IEEE Photonics J. 4(6), 2243–2248 (2012).
[Crossref]

Zeng, J. J.

Zeni, L.

A. Minardo, R. Bernini, and L. Zeni, “Analysis of SNR penalty in Brillouin optical time-domain analysis sensors induced by laser source phase noise,” J. Opt. 18(2), 025601 (2016).
[Crossref]

A. Minardo, A. Coscetta, R. Bernini, and L. Zeni, “Heterodyne slope-assisted Brillouin optical time-domain analysis for dynamic strain measurements,” J. Opt. 18(2), 025606 (2016).
[Crossref]

A. Minardo, A. Coscetta, L. Zeni, and R. Bernini, “High-Spatial Resolution DPP-BOTDA by Real-Time Balanced Detection,” IEEE Photonics Technol. Lett. 26(12), 1251–1254 (2014).
[Crossref]

R. Bernini, A. Minardo, and L. Zeni, “Distributed Sensing at Centimeter-Scale Spatial Resolution by BOFDA: Measurements and Signal Processing,” IEEE Photonics J. 4(1), 48–56 (2012).
[Crossref]

R. Bernini, A. Minardo, and L. Zeni, “Dynamic strain measurement in optical fibers by stimulated Brillouin scattering,” Opt. Lett. 34(17), 2613–2615 (2009).
[Crossref] [PubMed]

Zhang, H.

Zhang, J.

Zhang, L.

Zhang, M.

Z. Ma, M. Zhang, Y. Liu, X. Bao, H. Liu, Y. Zhang, and Y. Wang, “Incoherent Brillouin Optical Time-Domain Reflectometry With Random State Correlated Brillouin Spectrum,” IEEE Photonics J. 7(4), 1–7 (2015).
[Crossref]

Zhang, Y.

Z. Ma, M. Zhang, Y. Liu, X. Bao, H. Liu, Y. Zhang, and Y. Wang, “Incoherent Brillouin Optical Time-Domain Reflectometry With Random State Correlated Brillouin Spectrum,” IEEE Photonics J. 7(4), 1–7 (2015).
[Crossref]

Zhou, D.

D. Ba, B. Wang, D. Zhou, M. Yin, Y. Dong, H. Li, Z. Lu, and Z. Fan, “Distributed measurement of dynamic strain based on multi-slope assisted fast BOTDA,” Opt. Express 24(9), 9781–9793 (2016).
[Crossref] [PubMed]

P. Xu, Y. Dong, J. Zhang, D. Zhou, T. Jiang, J. Xu, H. Zhang, T. Zhu, Z. Lu, L. Chen, and X. Bao, “Bend-insensitive distributed sensing in singlemode-multimode-singlemode optical fiber structure by using Brillouin optical time-domain analysis,” Opt. Express 23(17), 22714–22722 (2015).
[Crossref] [PubMed]

Y. Dong, D. Ba, T. Jiang, D. Zhou, H. Zhang, C. Zhu, Z. Lu, H. Li, L. Chen, and X. Bao, “High-Spatial-Resolution Fast BOTDA for Dynamic Strain Measurement Based on Differential Double-Pulse and Second-Order Sideband of Modulation,” IEEE Photonics J. 5(3), 2600407 (2013).
[Crossref]

Y. Lu, Z. Qin, P. Lu, D. Zhou, L. Chen, and X. Bao, “Distributed Strain and Temperature Measurement by Brillouin Beat Spectrum,” IEEE Photonics Technol. Lett. 25(11), 1050–1053 (2013).
[Crossref]

Zhou, Y.

Zhu, C.

Y. Dong, D. Ba, T. Jiang, D. Zhou, H. Zhang, C. Zhu, Z. Lu, H. Li, L. Chen, and X. Bao, “High-Spatial-Resolution Fast BOTDA for Dynamic Strain Measurement Based on Differential Double-Pulse and Second-Order Sideband of Modulation,” IEEE Photonics J. 5(3), 2600407 (2013).
[Crossref]

Zhu, T.

Zhu, Z.

Zornoza, A.

Appl. Opt. (1)

Front. Optoelectron. China (1)

L. Thévenaz, “Brillouin distributed time-domain sensing in optical fibers: state of the art and perspectives,” Front. Optoelectron. China 3(1), 13–21 (2010).
[Crossref]

IEEE Photonics J. (9)

N. Hayashi, Y. Mizuno, and K. Nakamura, “Simplified Configuration of Brillouin Optical Correlation-Domain Reflectometry,” IEEE Photonics J. 6(5), 1–7 (2014).
[Crossref]

N. Hayashi, Y. Mizuno, and K. Nakamura, “Alternative Implementation of Simplified Brillouin Optical Correlation-Domain Reflectometry,” IEEE Photonics J. 6(6), 1–8 (2014).
[Crossref]

N. Hayashi, Y. Mizuno, and K. Nakamura, “Simplified Brillouin Optical Correlation-Domain Reflectometry Using Polymer Optical Fiber,” IEEE Photonics J. 7(1), 1–7 (2015).
[Crossref]

R. Bernini, A. Minardo, and L. Zeni, “Distributed Sensing at Centimeter-Scale Spatial Resolution by BOFDA: Measurements and Signal Processing,” IEEE Photonics J. 4(1), 48–56 (2012).
[Crossref]

Z. Ma, M. Zhang, Y. Liu, X. Bao, H. Liu, Y. Zhang, and Y. Wang, “Incoherent Brillouin Optical Time-Domain Reflectometry With Random State Correlated Brillouin Spectrum,” IEEE Photonics J. 7(4), 1–7 (2015).
[Crossref]

Y. Mao, N. Guo, K. L. Yu, H. Y. Tam, and C. Lu, “1-cm-Spatial-Resolution Brillouin Optical Time-Domain Analysis Based on Bright Pulse Brillouin Gain and Complementary Code,” IEEE Photonics J. 4(6), 2243–2248 (2012).
[Crossref]

Y. Dong, D. Ba, T. Jiang, D. Zhou, H. Zhang, C. Zhu, Z. Lu, H. Li, L. Chen, and X. Bao, “High-Spatial-Resolution Fast BOTDA for Dynamic Strain Measurement Based on Differential Double-Pulse and Second-Order Sideband of Modulation,” IEEE Photonics J. 5(3), 2600407 (2013).
[Crossref]

X. Tu, Q. Sun, W. Chen, M. Chen, and Z. Meng, “Vector Brillouin Optical Time-Domain Analysis With Heterodyne Detection and IQ Demodulation Algorithm,” IEEE Photonics J. 6(2), 1–8 (2014).
[Crossref]

Z. Li, L. Yan, L. Shao, W. Pan, B. Luo, J. Liang, and H. He, “Coherent BOTDA Sensor With Single-Sideband Modulated Probe Light,” IEEE Photonics J. 8(1), 1–8 (2016).

IEEE Photonics Technol. Lett. (6)

Y. Lu, Z. Qin, P. Lu, D. Zhou, L. Chen, and X. Bao, “Distributed Strain and Temperature Measurement by Brillouin Beat Spectrum,” IEEE Photonics Technol. Lett. 25(11), 1050–1053 (2013).
[Crossref]

Q. Cui, S. Pamukcu, W. Xiao, and M. Pervizpour, “Truly Distributed Fiber Vibration Sensor Using Pulse Base BOTDA With Wide Dynamic Range,” IEEE Photonics Technol. Lett. 23(24), 1887–1889 (2011).
[Crossref]

A. Motil, O. Danon, Y. Peled, and M. Tur, “Pump-Power-Independent Double Slope-Assisted Distributed and Fast Brillouin Fiber-Optic Sensor,” IEEE Photonics Technol. Lett. 26(8), 797–800 (2014).
[Crossref]

A. Minardo, A. Coscetta, L. Zeni, and R. Bernini, “High-Spatial Resolution DPP-BOTDA by Real-Time Balanced Detection,” IEEE Photonics Technol. Lett. 26(12), 1251–1254 (2014).
[Crossref]

Y. Koyamada, Y. Sakairi, N. Takeuchi, and S. Adachi, “Novel Technique to Improve Spatial Resolution in Brillouin Optical Time-Domain Reflectometry,” IEEE Photonics Technol. Lett. 19(23), 1910–1912 (2007).
[Crossref]

K. Hotate and M. Tanaka, “Distributed fiber Brillouin strain sensing with 1-cm spatial resolution by correlation-based continuous-wave technique,” IEEE Photonics Technol. Lett. 14(2), 179–181 (2002).
[Crossref]

J. Lightwave Technol. (4)

J. Opt. (2)

A. Minardo, A. Coscetta, R. Bernini, and L. Zeni, “Heterodyne slope-assisted Brillouin optical time-domain analysis for dynamic strain measurements,” J. Opt. 18(2), 025606 (2016).
[Crossref]

A. Minardo, R. Bernini, and L. Zeni, “Analysis of SNR penalty in Brillouin optical time-domain analysis sensors induced by laser source phase noise,” J. Opt. 18(2), 025601 (2016).
[Crossref]

J. Opt. Soc. Am. B (1)

Meas. Sci. Technol. (1)

M. A. Soto, G. Bolognini, F. Di Pasquale, and L. Thévenaz, “Long-range Brillouin optical time-domain analysis sensor employing pulse coding techniques,” Meas. Sci. Technol. 21(9), 094024 (2010).
[Crossref]

Opt. Express (15)

X. Angulo-Vinuesa, S. Martin-Lopez, P. Corredera, and M. Gonzalez-Herraez, “Raman-assisted Brillouin optical time-domain analysis with sub-meter resolution over 100 km,” Opt. Express 20(11), 12147–12154 (2012).
[Crossref] [PubMed]

Z. Li, L. Yan, L. Shao, W. Pan, and B. Luo, “Coherent BOTDA sensor with intensity modulated local light and IQ demodulation,” Opt. Express 23(12), 16407–16415 (2015).
[Crossref] [PubMed]

W. Li, X. Bao, Y. Li, and L. Chen, “Differential pulse-width pair BOTDA for high spatial resolution sensing,” Opt. Express 16(26), 21616–21625 (2008).
[Crossref] [PubMed]

Y. Dong, P. Xu, H. Zhang, Z. Lu, L. Chen, and X. Bao, “Characterization of evolution of mode coupling in a graded-index polymer optical fiber by using Brillouin optical time-domain analysis,” Opt. Express 22(22), 26510–26516 (2014).
[Crossref] [PubMed]

P. Xu, Y. Dong, J. Zhang, D. Zhou, T. Jiang, J. Xu, H. Zhang, T. Zhu, Z. Lu, L. Chen, and X. Bao, “Bend-insensitive distributed sensing in singlemode-multimode-singlemode optical fiber structure by using Brillouin optical time-domain analysis,” Opt. Express 23(17), 22714–22722 (2015).
[Crossref] [PubMed]

D. Ba, B. Wang, D. Zhou, M. Yin, Y. Dong, H. Li, Z. Lu, and Z. Fan, “Distributed measurement of dynamic strain based on multi-slope assisted fast BOTDA,” Opt. Express 24(9), 9781–9793 (2016).
[Crossref] [PubMed]

Y. Peled, A. Motil, and M. Tur, “Fast Brillouin optical time domain analysis for dynamic sensing,” Opt. Express 20(8), 8584–8591 (2012).
[Crossref] [PubMed]

Y. Peled, A. Motil, L. Yaron, and M. Tur, “Slope-assisted fast distributed sensing in optical fibers with arbitrary Brillouin profile,” Opt. Express 19(21), 19845–19854 (2011).
[Crossref] [PubMed]

A. Dominguez-Lopez, X. Angulo-Vinuesa, A. Lopez-Gil, S. Martin-Lopez, and M. Gonzalez-Herraez, “Non-local effects in dual-probe-sideband Brillouin optical time domain analysis,” Opt. Express 23(8), 10341–10352 (2015).
[Crossref] [PubMed]

J. Urricelqui, M. Sagues, and A. Loayssa, “Phasorial differential pulse-width pair technique for long-range Brillouin optical time-domain analysis sensors,” Opt. Express 22(14), 17403–17408 (2014).
[Crossref] [PubMed]

L. Thévenaz, S. F. Mafang, and J. Lin, “Effect of pulse depletion in a Brillouin optical time-domain analysis system,” Opt. Express 21(12), 14017–14035 (2013).
[Crossref] [PubMed]

Y. Weng, E. Ip, Z. Pan, and T. Wang, “Single-end simultaneous temperature and strain sensing techniques based on Brillouin optical time domain reflectometry in few-mode fibers,” Opt. Express 23(7), 9024–9039 (2015).
[Crossref] [PubMed]

A. Lopez-Gil, M. A. Soto, X. Angulo-Vinuesa, A. Dominguez-Lopez, S. Martin-Lopez, L. Thévenaz, and M. Gonzalez-Herraez, “Evaluation of the accuracy of BOTDA systems based on the phase spectral response,” Opt. Express 24(15), 17200–17214 (2016).
[Crossref] [PubMed]

J. Urricelqui, M. Sagues, and A. Loayssa, “BOTDA measurements tolerant to non-local effects by using a phase-modulated probe wave and RF demodulation,” Opt. Express 21(14), 17186–17194 (2013).
[Crossref] [PubMed]

J. Urricelqui, A. Zornoza, M. Sagues, and A. Loayssa, “Dynamic BOTDA measurements based on Brillouin phase-shift and RF demodulation,” Opt. Express 20(24), 26942–26949 (2012).
[Crossref] [PubMed]

Opt. Fiber Technol. (1)

K. Hotate, “Fiber distributed Brillouin sensing with optical correlation domain techniques,” Opt. Fiber Technol. 19(66, Part B), 700–719 (2013).
[Crossref]

Opt. Lett. (5)

Sensors (Basel) (1)

X. Bao and L. Chen, “Recent Progress in Brillouin Scattering Based Fiber Sensors,” Sensors (Basel) 11(12), 4152–4187 (2011).
[Crossref] [PubMed]

Other (2)

R. W. Boyd, Nonlinear Optics (Academic) 3rd edition, Chap. 9.

A. Minardo, R. Bernini, and L. Zeni, “Brillouin optical frequency domain analysis in polymer optical fiber,” (2014), pp. 91576V–91576V–91574.

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Figures (10)

Fig. 1
Fig. 1 Principle of the SBS process for probe wave.

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Fig. 2
Fig. 2 Simulation of (a) BGS, (b) BPSS and (c) the coefficient K spectrum for different pump pulses.

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Fig. 3
Fig. 3 Principle of the heterodyne detection and IQ demodulation.

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Fig. 4
Fig. 4 Sketch map of the frequency relationship of (a) the single-slope and (b) the multi-slope assisted BOTDA based on vector SBS and FAT. (c) Multi-slope assisted BOTDA: the pump pulse train is frequency-modulated using FAT and injected into the sensing fiber with the counter-propagating probe and Ref-wave.

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Fig. 5
Fig. 5 Experimental setup of the slope-assisted BOTDA based on vector SBS and FAT. SSBM: single sideband modulator; MWG: microwave generator; MWS: microwave splitter; FPI: Fabry–Pérot interferometer; OI: optical isolator; C: circulator; EOM: electro-optic modulator; EDFA: erbium doped fiber amplifier; AWG, Arbitrary-waveform generator; UFM: up-converter module; FBG: fiber Bragg grating.

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Fig. 6
Fig. 6 The top-views of the measured 3-D (a) BGS and (b) BPSS for 10ns-pump pulse over a 50m sensing fiber. The top-views of the measured 3-D KS correspond to the pump pulse width of (c) 10ns, (e) 20ns and (g) 30ns, respectively. The BGS, BPSS and KS at z = 13.6m correspond to the pump pulse width of (d) 10ns, (f) 20ns and (h) 30ns, respectively.

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Fig. 7
Fig. 7 The strain dependences of BFS measured by the BGS, the BPSS and the KS. Symbolic points denote the experimental data, while the solid lines are the linear fitting curves.

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Fig. 8
Fig. 8 (a) The dynamic strain measurements of the single-slope-assisted BOTDA and (b) its power spectrum analysis.

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Fig. 9
Fig. 9 The top-views of the measured 3-D (a) BGS, (b) BPSS and (c) KS over 512ms.

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Fig. 10
Fig. 10 The dynamic strain measurements of the multi-slope assisted BOTDA. The comparison between the reference time traces and the demodulated time traces in case of the frequency intervals (a) Δ f = 80 MHz , (b) Δ f = 120 MHz , (c) Δ f = 160 MHz and (d) Δ f = 180 MHz . (e) A zoon on view of the time traces within the red blocks. (f) The power spectra of the reference time traces (black and blue lines) and the time trace corresponding to the frequency interval Δ f = 160 MHz .

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Equations (13)

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

g S B S ( v S , z ) = g 0 Δ v B 2 4 Δ v 2 + Δ v B 2 ⊗ P P ( v P , z )
φ S B S ( v S , z ) = g 0 2 Δ v B Δ v 4 Δ v 2 + Δ v B 2 ⊗ P P ( v P , z )
K ( v S , z ) = φ S B S ( v S , z ) g S B S ( v S , z )
P P ( v P , z ) = P 0 [ sin π ( ν p − ν 0 ) τ P π ( ν p − ν 0 ) ] 2
K ( v S , z ) = 2 Δ v Δ v B
E ( ν S , z ) = E S exp ( g ( ν S , z ) ) exp ( j 2 π ν S t + j φ B ( ν S , z ) ) + E R exp ( j 2 π ( ν S + f 0 ) t )
I ( f 0 ) = 2 R D E S E R ( 1 + g ( ν S , z ) ) cos ( 2 π f 0 t − φ B ( ν S , z ) )
I ( ν S , z ) = 2 2 R D E S E R E 0 ( 1 + g ( ν S , z ) ) cos ( φ B ( ν S , z ) )
Q ( ν S , z ) = 2 2 R D E S E R E 0 ( 1 + g ( ν S , z ) ) s i n ( φ B ( ν S , z ) )
A ( ν S , z ) = I 2 ( ν S , z ) + Q 2 ( ν S , z ) = 2 2 R D E S E R E 0 ( 1 + g ( ν S , z ) )
P ( ν S , z ) = arc tan ( Q ( ν S , z ) I ( ν S , z ) ) = φ B ( ν S , z )
g ( ν S , z ) = A ( ν S , z ) A ( ν S , 0 ) − 1
f multi = 1 2 1 N ⋅ Δ T min

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