Abstract

Coding technique has long been investigated as a solution to improve the signal-to-noise ratio (SNR) without sacrificing spatial resolution in optical time domain reflectometry (OTDR) systems. The past researches have been focusing at the construction of new codes, the combination of coding and other techniques, and the application of coding technique to versatile distributed optical fiber sensing systems such as Raman OTDR and Brillouin optical time domain analyzer, where the results are fruitful. Here, we reveal that oversampling after photodetection opens up a new dimension for coded OTDR other than code length and code type. We demonstrate that the coding gain can be further improved by harnessing the oversampling. Furthermore, the photodetector’s bandwidth-limited feature can also be used to select the optimal sampling rate in order to obtain additional SNR enhancement. We believe this principle could be applied to any practical correlation-coded OTDR-based distributed fiber sensing systems with sufficient SNR enhancement. Our findings can serve to update existing instruments based on correlation-coded OTDR in a straightforward manner and at a relatively low cost.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  13. M. A. Soto, M. Taki, G. Bolognini, and F. D. Pasquale, “Simplex-Coded BOTDA Sensor Over 120-Km SMF with 1-m Spatial Resolution Assisted by Optimized Bidirectional Raman Amplification,” IEEE Photonics Technol. Lett. 20(24), 1823–1826 (2012).
    [Crossref]
  14. M. A. Soto, X. Angulo-Vinuesa, S. Martin-Lopez, S. Chin, J. D. Ania-Castañon, P. Corredera, E. Rochat, M. Gonzalez-Herraez, and L. Thévenaz, “Extending the Real Remoteness of Long-Range Brillouin Optical Time-Domain Fiber Analyzers,” J. Lightwave Technol. 32(1), 152–162 (2014).
    [Crossref]
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    [Crossref]
  16. A. Denisov, M. A. Soto, and L. Thévenaz, “Going beyond 1000000 resolved points in a Brillouin distributed fiber sensor: theoretical analysis and experimental demonstration,” Light Sci. Appl. 5(5), e16074 (2016).
    [Crossref] [PubMed]
  17. M. A. Soto, T. Nannipieri, A. Signorini, A. Lazzeri, F. Baronti, R. Roncella, G. Bolognini, and F. Di Pasquale, “Raman-based distributed temperature sensor with 1 m spatial resolution over 26 km SMF using low-repetition-rate cyclic pulse coding,” Opt. Lett. 36(13), 2557–2559 (2011).
    [Crossref] [PubMed]
  18. M. Taki, Y. Muanenda, C. J. Oton, T. Nannipieri, A. Signorini, and F. Di Pasquale, “Cyclic pulse coding for fast BOTDA fiber sensors,” Opt. Lett. 38(15), 2877–2880 (2013).
    [Crossref] [PubMed]
  19. P. K. Sahu, S. C. Gowre, and S. Mahapatra, “Optical time-domain reflectometer performance improvement using complementary correlated Prometheus orthonormal sequence,” IET Optoelectron. 2(3), 128–133 (2008).
    [Crossref]
  20. M. A. Soto, S. Le Floch, and L. Thévenaz, “Bipolar optical pulse coding for performance enhancement in BOTDA sensors,” Opt. Express 21(14), 16390–16397 (2013).
    [Crossref] [PubMed]
  21. Z. Yang, M. A. Soto, and L. Thévenaz, “Increasing robustness of bipolar pulse coding in Brillouin distributed fiber sensors,” Opt. Express 24(1), 586–597 (2016).
    [Crossref] [PubMed]
  22. Z. Li, Z. Yang, L. Yan, M. A. Soto, and L. Thévenaz, “Hybrid Golay-coded Brillouin optical time-domain analysis based on differential pulses,” Opt. Lett. 43(19), 4574–4577 (2018).
    [Crossref] [PubMed]

2018 (1)

2017 (1)

2016 (2)

Z. Yang, M. A. Soto, and L. Thévenaz, “Increasing robustness of bipolar pulse coding in Brillouin distributed fiber sensors,” Opt. Express 24(1), 586–597 (2016).
[Crossref] [PubMed]

A. Denisov, M. A. Soto, and L. Thévenaz, “Going beyond 1000000 resolved points in a Brillouin distributed fiber sensor: theoretical analysis and experimental demonstration,” Light Sci. Appl. 5(5), e16074 (2016).
[Crossref] [PubMed]

2014 (2)

2013 (2)

2012 (1)

M. A. Soto, M. Taki, G. Bolognini, and F. D. Pasquale, “Simplex-Coded BOTDA Sensor Over 120-Km SMF with 1-m Spatial Resolution Assisted by Optimized Bidirectional Raman Amplification,” IEEE Photonics Technol. Lett. 20(24), 1823–1826 (2012).
[Crossref]

2011 (3)

2010 (2)

2008 (2)

P. K. Sahu, S. C. Gowre, and S. Mahapatra, “Optical time-domain reflectometer performance improvement using complementary correlated Prometheus orthonormal sequence,” IET Optoelectron. 2(3), 128–133 (2008).
[Crossref]

M. A. Soto, P. K. Sahu, G. Bolognini, and F. Di Pasquale, “Brillouin-Based Distributed Temperature Sensor Employing Pulse Coding,” IEEE Sens. J. 8(3), 225–226 (2008).
[Crossref]

2006 (2)

D. Lee, H. Yoon, P. Kim, J. Park, and N. Park, “Optimization of SNR Improvement in the Noncoherent OTDR Based on Simplex Codes,” J. Lightwave Technol. 24(1), 322–328 (2006).
[Crossref]

J. Park, G. Bolognini, D. Lee, P. Kim, P. Cho, F. Di Pasquale, and N. Park, “Raman-based distributed temperature sensor with simplex coding and link optimization,” IEEE Photonics Technol. Lett. 18(17), 1879–1881 (2006).
[Crossref]

1993 (1)

M. D. Jones, “Using simplex codes to improve OTDR sensitivity,” IEEE Photonics Technol. Lett. 5(7), 822–824 (1993).
[Crossref]

1989 (1)

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[Crossref]

1980 (1)

K. Okada, K. Hashimoto, T. Shibata, and Y. Nagaki, “Optical cable fault location using correlation technique,” Electron. Lett. 16(16), 629–630 (1980).
[Crossref]

Angulo-Vinuesa, X.

Ania-Castañon, J. D.

Bao, X.

Baronti, F.

Bolognini, G.

M. A. Soto, M. Taki, G. Bolognini, and F. D. Pasquale, “Simplex-Coded BOTDA Sensor Over 120-Km SMF with 1-m Spatial Resolution Assisted by Optimized Bidirectional Raman Amplification,” IEEE Photonics Technol. Lett. 20(24), 1823–1826 (2012).
[Crossref]

M. A. Soto, T. Nannipieri, A. Signorini, A. Lazzeri, F. Baronti, R. Roncella, G. Bolognini, and F. Di Pasquale, “Raman-based distributed temperature sensor with 1 m spatial resolution over 26 km SMF using low-repetition-rate cyclic pulse coding,” Opt. Lett. 36(13), 2557–2559 (2011).
[Crossref] [PubMed]

M. A. Soto, G. Bolognini, F. Di Pasquale, and L. Thévenaz, “Simplex-coded BOTDA fiber sensor with 1 m spatial resolution over a 50 km range,” Opt. Lett. 35(2), 259–261 (2010).
[Crossref] [PubMed]

M. A. Soto, P. K. Sahu, G. Bolognini, and F. Di Pasquale, “Brillouin-Based Distributed Temperature Sensor Employing Pulse Coding,” IEEE Sens. J. 8(3), 225–226 (2008).
[Crossref]

J. Park, G. Bolognini, D. Lee, P. Kim, P. Cho, F. Di Pasquale, and N. Park, “Raman-based distributed temperature sensor with simplex coding and link optimization,” IEEE Photonics Technol. Lett. 18(17), 1879–1881 (2006).
[Crossref]

Cao, C.

Chang, L.

X. Jia, Y. Rao, K. Deng, Z. Yang, L. Chang, C. Zhang, and Z. Ran, “Experimental Demonstration on 2.5-m Spatial Resolution and 1 °C Temperature Uncertainty Over Long-Distance BOTDA With Combined Raman Amplification and Optical Pulse Coding,” IEEE Photonics Technol. Lett. 23(7), 435–437 (2011).
[Crossref]

Chen, L.

Chin, S.

Cho, P.

J. Park, G. Bolognini, D. Lee, P. Kim, P. Cho, F. Di Pasquale, and N. Park, “Raman-based distributed temperature sensor with simplex coding and link optimization,” IEEE Photonics Technol. Lett. 18(17), 1879–1881 (2006).
[Crossref]

Cobo, A.

Corredera, P.

Deng, K.

X. Jia, Y. Rao, K. Deng, Z. Yang, L. Chang, C. Zhang, and Z. Ran, “Experimental Demonstration on 2.5-m Spatial Resolution and 1 °C Temperature Uncertainty Over Long-Distance BOTDA With Combined Raman Amplification and Optical Pulse Coding,” IEEE Photonics Technol. Lett. 23(7), 435–437 (2011).
[Crossref]

Denisov, A.

A. Denisov, M. A. Soto, and L. Thévenaz, “Going beyond 1000000 resolved points in a Brillouin distributed fiber sensor: theoretical analysis and experimental demonstration,” Light Sci. Appl. 5(5), e16074 (2016).
[Crossref] [PubMed]

Di Pasquale, F.

Foster, S.

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[Crossref]

Giffard, R. P.

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[Crossref]

Gonzalez-Herraez, M.

Gowre, S. C.

P. K. Sahu, S. C. Gowre, and S. Mahapatra, “Optical time-domain reflectometer performance improvement using complementary correlated Prometheus orthonormal sequence,” IET Optoelectron. 2(3), 128–133 (2008).
[Crossref]

Hashimoto, K.

K. Okada, K. Hashimoto, T. Shibata, and Y. Nagaki, “Optical cable fault location using correlation technique,” Electron. Lett. 16(16), 629–630 (1980).
[Crossref]

Jia, X.

X. Jia, Y. Rao, K. Deng, Z. Yang, L. Chang, C. Zhang, and Z. Ran, “Experimental Demonstration on 2.5-m Spatial Resolution and 1 °C Temperature Uncertainty Over Long-Distance BOTDA With Combined Raman Amplification and Optical Pulse Coding,” IEEE Photonics Technol. Lett. 23(7), 435–437 (2011).
[Crossref]

Jia, X. H.

Jones, M. D.

M. D. Jones, “Using simplex codes to improve OTDR sensitivity,” IEEE Photonics Technol. Lett. 5(7), 822–824 (1993).
[Crossref]

Kim, P.

J. Park, G. Bolognini, D. Lee, P. Kim, P. Cho, F. Di Pasquale, and N. Park, “Raman-based distributed temperature sensor with simplex coding and link optimization,” IEEE Photonics Technol. Lett. 18(17), 1879–1881 (2006).
[Crossref]

D. Lee, H. Yoon, P. Kim, J. Park, and N. Park, “Optimization of SNR Improvement in the Noncoherent OTDR Based on Simplex Codes,” J. Lightwave Technol. 24(1), 322–328 (2006).
[Crossref]

Lazzeri, A.

Le Floch, S.

Lee, D.

D. Lee, H. Yoon, P. Kim, J. Park, and N. Park, “Optimization of SNR Improvement in the Noncoherent OTDR Based on Simplex Codes,” J. Lightwave Technol. 24(1), 322–328 (2006).
[Crossref]

J. Park, G. Bolognini, D. Lee, P. Kim, P. Cho, F. Di Pasquale, and N. Park, “Raman-based distributed temperature sensor with simplex coding and link optimization,” IEEE Photonics Technol. Lett. 18(17), 1879–1881 (2006).
[Crossref]

Li, Z.

Lopez-Higuera, J. M.

Lu, Y.

Mahapatra, S.

P. K. Sahu, S. C. Gowre, and S. Mahapatra, “Optical time-domain reflectometer performance improvement using complementary correlated Prometheus orthonormal sequence,” IET Optoelectron. 2(3), 128–133 (2008).
[Crossref]

Martin-Lopez, S.

Moberly, D. S.

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[Crossref]

Muanenda, Y.

Nagaki, Y.

K. Okada, K. Hashimoto, T. Shibata, and Y. Nagaki, “Optical cable fault location using correlation technique,” Electron. Lett. 16(16), 629–630 (1980).
[Crossref]

Nannipieri, T.

Nazarathy, M.

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[Crossref]

Newton, S. A.

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[Crossref]

Okada, K.

K. Okada, K. Hashimoto, T. Shibata, and Y. Nagaki, “Optical cable fault location using correlation technique,” Electron. Lett. 16(16), 629–630 (1980).
[Crossref]

Oton, C. J.

Park, J.

D. Lee, H. Yoon, P. Kim, J. Park, and N. Park, “Optimization of SNR Improvement in the Noncoherent OTDR Based on Simplex Codes,” J. Lightwave Technol. 24(1), 322–328 (2006).
[Crossref]

J. Park, G. Bolognini, D. Lee, P. Kim, P. Cho, F. Di Pasquale, and N. Park, “Raman-based distributed temperature sensor with simplex coding and link optimization,” IEEE Photonics Technol. Lett. 18(17), 1879–1881 (2006).
[Crossref]

Park, N.

J. Park, G. Bolognini, D. Lee, P. Kim, P. Cho, F. Di Pasquale, and N. Park, “Raman-based distributed temperature sensor with simplex coding and link optimization,” IEEE Photonics Technol. Lett. 18(17), 1879–1881 (2006).
[Crossref]

D. Lee, H. Yoon, P. Kim, J. Park, and N. Park, “Optimization of SNR Improvement in the Noncoherent OTDR Based on Simplex Codes,” J. Lightwave Technol. 24(1), 322–328 (2006).
[Crossref]

Pasquale, F. D.

M. A. Soto, M. Taki, G. Bolognini, and F. D. Pasquale, “Simplex-Coded BOTDA Sensor Over 120-Km SMF with 1-m Spatial Resolution Assisted by Optimized Bidirectional Raman Amplification,” IEEE Photonics Technol. Lett. 20(24), 1823–1826 (2012).
[Crossref]

Peng, F.

Peng, Z. P.

Quintela Incera, A.

Ran, Z.

X. Jia, Y. Rao, K. Deng, Z. Yang, L. Chang, C. Zhang, and Z. Ran, “Experimental Demonstration on 2.5-m Spatial Resolution and 1 °C Temperature Uncertainty Over Long-Distance BOTDA With Combined Raman Amplification and Optical Pulse Coding,” IEEE Photonics Technol. Lett. 23(7), 435–437 (2011).
[Crossref]

Rao, Y.

X. Jia, Y. Rao, K. Deng, Z. Yang, L. Chang, C. Zhang, and Z. Ran, “Experimental Demonstration on 2.5-m Spatial Resolution and 1 °C Temperature Uncertainty Over Long-Distance BOTDA With Combined Raman Amplification and Optical Pulse Coding,” IEEE Photonics Technol. Lett. 23(7), 435–437 (2011).
[Crossref]

Rao, Y. J.

Rochat, E.

Rodriguez Cobo, L.

Roncella, R.

Sahu, P. K.

P. K. Sahu, S. C. Gowre, and S. Mahapatra, “Optical time-domain reflectometer performance improvement using complementary correlated Prometheus orthonormal sequence,” IET Optoelectron. 2(3), 128–133 (2008).
[Crossref]

M. A. Soto, P. K. Sahu, G. Bolognini, and F. Di Pasquale, “Brillouin-Based Distributed Temperature Sensor Employing Pulse Coding,” IEEE Sens. J. 8(3), 225–226 (2008).
[Crossref]

Shibata, T.

K. Okada, K. Hashimoto, T. Shibata, and Y. Nagaki, “Optical cable fault location using correlation technique,” Electron. Lett. 16(16), 629–630 (1980).
[Crossref]

Signorini, A.

Sischka, F.

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[Crossref]

Soto, M. A.

Z. Li, Z. Yang, L. Yan, M. A. Soto, and L. Thévenaz, “Hybrid Golay-coded Brillouin optical time-domain analysis based on differential pulses,” Opt. Lett. 43(19), 4574–4577 (2018).
[Crossref] [PubMed]

Z. Yang, M. A. Soto, and L. Thévenaz, “Increasing robustness of bipolar pulse coding in Brillouin distributed fiber sensors,” Opt. Express 24(1), 586–597 (2016).
[Crossref] [PubMed]

A. Denisov, M. A. Soto, and L. Thévenaz, “Going beyond 1000000 resolved points in a Brillouin distributed fiber sensor: theoretical analysis and experimental demonstration,” Light Sci. Appl. 5(5), e16074 (2016).
[Crossref] [PubMed]

M. A. Soto, X. Angulo-Vinuesa, S. Martin-Lopez, S. Chin, J. D. Ania-Castañon, P. Corredera, E. Rochat, M. Gonzalez-Herraez, and L. Thévenaz, “Extending the Real Remoteness of Long-Range Brillouin Optical Time-Domain Fiber Analyzers,” J. Lightwave Technol. 32(1), 152–162 (2014).
[Crossref]

M. A. Soto, S. Le Floch, and L. Thévenaz, “Bipolar optical pulse coding for performance enhancement in BOTDA sensors,” Opt. Express 21(14), 16390–16397 (2013).
[Crossref] [PubMed]

M. A. Soto, M. Taki, G. Bolognini, and F. D. Pasquale, “Simplex-Coded BOTDA Sensor Over 120-Km SMF with 1-m Spatial Resolution Assisted by Optimized Bidirectional Raman Amplification,” IEEE Photonics Technol. Lett. 20(24), 1823–1826 (2012).
[Crossref]

M. A. Soto, T. Nannipieri, A. Signorini, A. Lazzeri, F. Baronti, R. Roncella, G. Bolognini, and F. Di Pasquale, “Raman-based distributed temperature sensor with 1 m spatial resolution over 26 km SMF using low-repetition-rate cyclic pulse coding,” Opt. Lett. 36(13), 2557–2559 (2011).
[Crossref] [PubMed]

M. A. Soto, G. Bolognini, F. Di Pasquale, and L. Thévenaz, “Simplex-coded BOTDA fiber sensor with 1 m spatial resolution over a 50 km range,” Opt. Lett. 35(2), 259–261 (2010).
[Crossref] [PubMed]

M. A. Soto, P. K. Sahu, G. Bolognini, and F. Di Pasquale, “Brillouin-Based Distributed Temperature Sensor Employing Pulse Coding,” IEEE Sens. J. 8(3), 225–226 (2008).
[Crossref]

Taki, M.

M. Taki, Y. Muanenda, C. J. Oton, T. Nannipieri, A. Signorini, and F. Di Pasquale, “Cyclic pulse coding for fast BOTDA fiber sensors,” Opt. Lett. 38(15), 2877–2880 (2013).
[Crossref] [PubMed]

M. A. Soto, M. Taki, G. Bolognini, and F. D. Pasquale, “Simplex-Coded BOTDA Sensor Over 120-Km SMF with 1-m Spatial Resolution Assisted by Optimized Bidirectional Raman Amplification,” IEEE Photonics Technol. Lett. 20(24), 1823–1826 (2012).
[Crossref]

Thévenaz, L.

Trutna, W. R.

M. Nazarathy, S. A. Newton, R. P. Giffard, D. S. Moberly, F. Sischka, W. R. Trutna, and S. Foster, “Real-time long range complementary correlation optical time domain reflectometer,” J. Lightwave Technol. 7(1), 24–38 (1989).
[Crossref]

Wang, F.

Wang, Z. N.

Wu, H.

Yan, L.

Yang, Z.

Z. Li, Z. Yang, L. Yan, M. A. Soto, and L. Thévenaz, “Hybrid Golay-coded Brillouin optical time-domain analysis based on differential pulses,” Opt. Lett. 43(19), 4574–4577 (2018).
[Crossref] [PubMed]

Z. Yang, M. A. Soto, and L. Thévenaz, “Increasing robustness of bipolar pulse coding in Brillouin distributed fiber sensors,” Opt. Express 24(1), 586–597 (2016).
[Crossref] [PubMed]

X. Jia, Y. Rao, K. Deng, Z. Yang, L. Chang, C. Zhang, and Z. Ran, “Experimental Demonstration on 2.5-m Spatial Resolution and 1 °C Temperature Uncertainty Over Long-Distance BOTDA With Combined Raman Amplification and Optical Pulse Coding,” IEEE Photonics Technol. Lett. 23(7), 435–437 (2011).
[Crossref]

Yoon, H.

Zhang, C.

X. Jia, Y. Rao, K. Deng, Z. Yang, L. Chang, C. Zhang, and Z. Ran, “Experimental Demonstration on 2.5-m Spatial Resolution and 1 °C Temperature Uncertainty Over Long-Distance BOTDA With Combined Raman Amplification and Optical Pulse Coding,” IEEE Photonics Technol. Lett. 23(7), 435–437 (2011).
[Crossref]

Zhang, X.

Zhu, C.

Zhu, T.

Electron. Lett. (1)

K. Okada, K. Hashimoto, T. Shibata, and Y. Nagaki, “Optical cable fault location using correlation technique,” Electron. Lett. 16(16), 629–630 (1980).
[Crossref]

IEEE Photonics Technol. Lett. (4)

M. D. Jones, “Using simplex codes to improve OTDR sensitivity,” IEEE Photonics Technol. Lett. 5(7), 822–824 (1993).
[Crossref]

J. Park, G. Bolognini, D. Lee, P. Kim, P. Cho, F. Di Pasquale, and N. Park, “Raman-based distributed temperature sensor with simplex coding and link optimization,” IEEE Photonics Technol. Lett. 18(17), 1879–1881 (2006).
[Crossref]

X. Jia, Y. Rao, K. Deng, Z. Yang, L. Chang, C. Zhang, and Z. Ran, “Experimental Demonstration on 2.5-m Spatial Resolution and 1 °C Temperature Uncertainty Over Long-Distance BOTDA With Combined Raman Amplification and Optical Pulse Coding,” IEEE Photonics Technol. Lett. 23(7), 435–437 (2011).
[Crossref]

M. A. Soto, M. Taki, G. Bolognini, and F. D. Pasquale, “Simplex-Coded BOTDA Sensor Over 120-Km SMF with 1-m Spatial Resolution Assisted by Optimized Bidirectional Raman Amplification,” IEEE Photonics Technol. Lett. 20(24), 1823–1826 (2012).
[Crossref]

IEEE Sens. J. (1)

M. A. Soto, P. K. Sahu, G. Bolognini, and F. Di Pasquale, “Brillouin-Based Distributed Temperature Sensor Employing Pulse Coding,” IEEE Sens. J. 8(3), 225–226 (2008).
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P. K. Sahu, S. C. Gowre, and S. Mahapatra, “Optical time-domain reflectometer performance improvement using complementary correlated Prometheus orthonormal sequence,” IET Optoelectron. 2(3), 128–133 (2008).
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A. Denisov, M. A. Soto, and L. Thévenaz, “Going beyond 1000000 resolved points in a Brillouin distributed fiber sensor: theoretical analysis and experimental demonstration,” Light Sci. Appl. 5(5), e16074 (2016).
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D. Tan, X. Tian, W. Sun, Y. Zhou, L. Liu, Y. Ma, J. Meng, and H. Zhang, “An oil and gas pipeline pre-warning system based on Φ-OTDR,” in Proceedings of the 23rd International Conference on Optical Fiber Sensors. OSA: Santander, Spain, 2014, pp91578W.

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Figures (7)

Fig. 1
Fig. 1 The input and output relationship for oversampling.
Fig. 2
Fig. 2 (a) Code word of a Golay pair when the code length is 2 and m = 2. (b) Comparison between a single rectangular pulse (blue) and the equivalent triangular pulse (red).
Fig. 3
Fig. 3 (a) Autocorrelation function of noise. (b) Unit triangular function. (c) Their product. The points p1, p2, and p3 are the first three zero-crossings. (d) The sampling of qm(k)RN(k). The sampling rate is equal to 1/τ.
Fig. 4
Fig. 4 Experimental setup for coded OTDR.
Fig. 5
Fig. 5 Comparison between the intensities of the Golay-coded OTDR (blue) and Simplex-coded OTDR (red) response signals.
Fig. 6
Fig. 6 (a) Comparison between the intensities of the single-pulse OTDR (blue) and 2048 bit Golay-coded OTDR (red & yellow, for two different oversampling ratios) response signals. The single pulse results were averaged, while the coded results were not. (b) Measured coding gain versus code length for different sampling rates. The curves represent theoretical values, while the crosses correspond to the experimental results.
Fig. 7
Fig. 7 (a) Autocorrelation function of the 150 MHz PD noise and (b) the corresponding measured coding gain versus sampling rate; (c) Autocorrelation function of another 300 MHz PD noise and (d) the corresponding measured coding gain versus sampling rate. The curves represent theoretical values, while the crosses correspond to the experimental results.

Equations (28)

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A ( k ) A ( k ) + B ( k ) B ( k ) = 2 L δ ( k )
A ( k ) A ( k ) + B ( k ) B ( k ) = 2 L m q m ( k )
q m ( k ) = { 1 | k | / m , m k m 0 , otherwise
coding gain = σ 2 σ 2 + 2 k = 1 m 1 q m ( k ) R N ( k ) L m 2
coding gain = S c / N c S p / N p = N p N c ,
y ( k ) = c ( k ) f ( k )
A ( k ) A ( k ) + B ( k ) B ( k ) = 2 L δ ( k )
{ y A ( k ) = A ( k ) f ( k ) y B ( k ) = B ( k ) f ( k )
z ( k ) = A ( k ) y A ( k ) + B ( k ) y B ( k ) = ( A ( k ) A ( k ) + B ( k ) B ( k ) ) f ( k ) = 2 L f ( k ) .
{ u A ( k ) = ( 1 + A ( k ) ) / 2 u ¯ A ( k ) = ( 1 A ( k ) ) / 2 u B ( k ) = ( 1 + B ( k ) ) / 2 u ¯ B ( k ) = ( 1 B ( k ) ) / 2 .
{ u A ( k ) f ( k ) u ¯ A ( k ) f ( k ) = A ( k ) f ( k ) = y A ( k ) u B ( k ) f ( k ) u ¯ B ( k ) f ( k ) = B ( k ) f ( k ) = y B ( k ) .
A ( k ) A ( k ) + B ( k ) B ( k ) = 2 L m q m ( k ) ,
z ( k ) = 2 L m q m ( k ) f ( k ) = 2 L m f t r i ( k ) .
q m ( k ) = { 1 | k | / m , m k m 0 , otherwise
{ ( u A ( k ) f ( k ) + N 1 ( k ) ) ( u ¯ A ( k ) f ( k ) + N 2 ( k ) ) = y A ( k ) + N 1 ( k ) N 2 ( k ) ( u B ( k ) f ( k ) + N 3 ( k ) ) ( u ¯ B ( k ) f ( k ) + N 4 ( k ) ) = y B ( k ) + N 3 ( k ) N 4 ( k )
z ( k ) = 2 L m f t r i ( k ) + A ( k ) ( N 1 ( k ) N 2 ( k ) ) + B n ( N 3 ( k ) N 4 ( k ) ) .
N t o t a l ( k ) = A ( k ) ( N 1 ( k ) N 2 ( k ) ) + B n ( N 3 ( k ) N 4 ( k ) ) = j = 1 L m { A ( j ) ( ( N 1 ( j + k ) N 2 ( j + k ) ) ) + B ( j ) ( N 3 ( j + k ) N 4 ( j + k ) ) } .
σ t o t a l = D ( N t o t a l ( k ) ) = L m × { ( σ 2 + σ 2 ) + ( σ 2 + σ 2 ) } = 2 L m σ ,
S N R c = 2 L m f t r i ( k ) σ t o t a l = L m f t r i ( k ) σ .
S N R p = 2 f ( k ) σ .
coding gain = S N R c S N R p = L m 2 .
E { N a ( k ) } = 0 ; E { N a ( k ) N b ( k + j ) } = 0 ; E { N a ( k ) N a ( k + j ) } = R N ( j ) ; E { ( N a ( k ) ) 2 } = R N ( 0 ) = σ 2 ; ( a , b = 1 , 2 , 3 , 4 ; a b ) ,
D { j = 1 L m A ( j ) N 1 ( j + k ) } = E { ( j = 1 L m A ( j ) N 1 ( j + k ) ) 2 } = j = 1 L m i = 1 L m A ( i ) A ( j ) E { N 1 ( i + k ) N 1 ( j + k ) } = j = 1 L m i = 1 L m A ( i ) A ( j ) R N ( j i ) .
D { j = 1 L m A ( j ) N 1 ( j + k ) } = k = ( L m 1 ) L m 1 i = 1 L m A ( i ) A ( i + k ) R N ( k ) = k = ( L m 1 ) L m 1 R A ( k ) R N ( k ) ,
σ n ( t o t a l ) = 2 k = ( L m 1 ) L m 1 ( R A ( k ) + R B ( k ) ) R N ( k ) = 4 L m k = ( m 1 ) m 1 q m ( k ) R N ( k ) = 4 L m ( σ 2 + 2 k = 1 m 1 q m ( k ) R N ( k ) ) .
R = 2 L m σ 4 L m ( σ 2 + 2 k = 1 m 1 q m ( k ) R N ( k ) ) = σ 2 σ 2 + 2 k = 1 m 1 q m ( k ) R N ( k )
k = ( m 1 ) m 1 q m ( k ) R N ( k ) = m T ( k = ( m 1 ) m 1 q m ( k ) R N ( k ) T m ) = m C T .
coding gain = 2 L m f t r i ( k ) / 4 L m 2 C / T 2 f ( k ) / σ = σ 2 L T C .

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