Abstract

A new technology for Brillouin optical correlation domain analysis (BOCDA) based on true random codes has been proposed, theoretically simulated, and experimentally demonstrated with high spatial resolution. The spatial resolution of 3.9 cm over a 1.1 km single mode fiber is experimentally achieved by using true random codes with 3Gbit/s rate. The numerical simulation shows that the higher spatial resolution of 1 cm can be further obtained by utilizing true random codes with a higher code rate of 10Gbit/s. Additionally, the maximum uncertainty of the local Brillouin frequency shift is ± 1.1 MHz and the temperature coefficient is 1.15 MHz/℃.

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

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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]
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    [Crossref]
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    [Crossref]
  13. K. Hotate and T. Hasegawa, “Measurement of brillouin gain spectrum distribution along an optical fiber using a correlation-based technique-proposal, experiment and simulation,” IEICE Trans. Electron. E83-C(3), 405–412 (2000).
  14. K. Y. Song and K. Hotate, “Enlargement of measurement range in a brillouin optical correlation domain analysis system using double lock-in amplifiers and a single-sideband modulator,” IEEE Photonics Technol. Lett. 18(3), 499–501 (2006).
    [Crossref]
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    [Crossref]
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  22. M. Ghil, I. Zaliapin, and B. Coluzzi, “Boolean delay equations: a simple way of looking at complex systems,” Phys. D. 237(23), 2967–2986 (2008).
    [Crossref]
  23. K. Y. Song, W. W. Zou, Z. Y. He, and K. Hotate, “All-optical dynamic grating generation based on brillouin scattering in polarizationmaintaining fiber,” Opt. Lett. 33(9), 926–928 (2008).
    [Crossref]
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    [Crossref]
  25. J. Zhang, C. Feng, M. Zhang, Y. Liu, C. Wu, and Y. Wang, “Brillouin optical correlation domain analysis based on chaotic laser with suppressed time delay signature,” Opt. Express 26(6), 6962–6972 (2018).
    [Crossref]

2018 (3)

2017 (1)

2016 (4)

2014 (1)

2013 (3)

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

S. L. Floch, F. Sauser, M. Llera, M. A. Soto, and L. Thévenaz, “Colour Simplex coding for Brillouin distributed sensors,” Proc. SPIE 8794, 879437 (2013).
[Crossref]

D. P. Rosin, D. Rontani, and D. J. Gauthier, “Ultra-fast physical generation of random numbers using hybrid boolean networks,” Phys. Rev. E 87(4), 040902 (2013).
[Crossref]

2012 (4)

S. L. Floch, F. Sauser, M. A. Soto, and L. Thévenaz, “Time/frequency coding for Brillouin distributed sensors,” Proc. SPIE 8421, 84211J (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]

M. S. D. B. Zan and T. Horiguchi, “A dual golay complementary pair of sequences for improving the performance of phase-shift pulse BOTDA fiber sensor,” J. Lightwave Technol. 30(21), 3338–3356 (2012).
[Crossref]

A. Zadok, Y. Antman, N. Primerov, A. Denisov, J. Sancho, and L. Thévenaz, “Random-access distributed fiber sensing,” Laser Photonics Rev. 6(5), L1–L5 (2012).
[Crossref]

2010 (2)

2008 (3)

S. Diaz, S. Foaleng Mafang, M. Lopez-Amo, and L. Thévenaz, “A high-performance optical time-domain brillouin distributed fiber sensor,” IEEE Sens. J. 8(7), 1268–1272 (2008).
[Crossref]

M. Ghil, I. Zaliapin, and B. Coluzzi, “Boolean delay equations: a simple way of looking at complex systems,” Phys. D. 237(23), 2967–2986 (2008).
[Crossref]

K. Y. Song, W. W. Zou, Z. Y. He, and K. Hotate, “All-optical dynamic grating generation based on brillouin scattering in polarizationmaintaining fiber,” Opt. Lett. 33(9), 926–928 (2008).
[Crossref]

2006 (1)

K. Y. Song and K. Hotate, “Enlargement of measurement range in a brillouin optical correlation domain analysis system using double lock-in amplifiers and a single-sideband modulator,” IEEE Photonics Technol. Lett. 18(3), 499–501 (2006).
[Crossref]

2005 (1)

A. Minardo, R. Bernini, L. Zeni, L. Thevenaz, and F. Briffod, “A reconstruction technique for long-range stimulated Brillouin scattering distributed fibre-optic sensors: experimental results,” Meas. Sci. Technol. 16(4), 900–908 (2005).
[Crossref]

2000 (1)

K. Hotate and T. Hasegawa, “Measurement of brillouin gain spectrum distribution along an optical fiber using a correlation-based technique-proposal, experiment and simulation,” IEICE Trans. Electron. E83-C(3), 405–412 (2000).

1990 (1)

Antman, Y.

Ba, D.

D. Zhou, Y. k. Dong, B. Wang, C. Pang, D. Ba, H. Zhang, Z. Lu, H. Li, and X. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

O. Shlomi, E. Preter, D. Ba, Y. London, Y. Antman, and A. Zadok, “Double-pulse pair brillouin optical correlationdomain analysis,” Opt. Express 24(23), 26867–26876 (2016).
[Crossref]

Bao, X.

D. Zhou, Y. k. Dong, B. Wang, C. Pang, D. Ba, H. Zhang, Z. Lu, H. Li, and X. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

H. Liang, W. Li, N. Linze, L. Chen, and X. Bao, “High-resolution DPP-BOTDA over 50 km LEAF using return-to-zero coded pulses,” Opt. Lett. 35(10), 1503–1505 (2010).
[Crossref]

Bernini, R.

A. Minardo, R. Bernini, L. Zeni, L. Thevenaz, and F. Briffod, “A reconstruction technique for long-range stimulated Brillouin scattering distributed fibre-optic sensors: experimental results,” Meas. Sci. Technol. 16(4), 900–908 (2005).
[Crossref]

Bolognini, G.

Briffod, F.

A. Minardo, R. Bernini, L. Zeni, L. Thevenaz, and F. Briffod, “A reconstruction technique for long-range stimulated Brillouin scattering distributed fibre-optic sensors: experimental results,” Meas. Sci. Technol. 16(4), 900–908 (2005).
[Crossref]

Chen, L.

Coluzzi, B.

M. Ghil, I. Zaliapin, and B. Coluzzi, “Boolean delay equations: a simple way of looking at complex systems,” Phys. D. 237(23), 2967–2986 (2008).
[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]

A. Zadok, Y. Antman, N. Primerov, A. Denisov, J. Sancho, and L. Thévenaz, “Random-access distributed fiber sensing,” Laser Photonics Rev. 6(5), L1–L5 (2012).
[Crossref]

Diaz, S.

S. Diaz, S. Foaleng Mafang, M. Lopez-Amo, and L. Thévenaz, “A high-performance optical time-domain brillouin distributed fiber sensor,” IEEE Sens. J. 8(7), 1268–1272 (2008).
[Crossref]

Dong, Y. k.

D. Zhou, Y. k. Dong, B. Wang, C. Pang, D. Ba, H. Zhang, Z. Lu, H. Li, and X. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

Elooz, D.

Feng, C.

Floch, S. L.

S. L. Floch, F. Sauser, M. Llera, M. A. Soto, and L. Thévenaz, “Colour Simplex coding for Brillouin distributed sensors,” Proc. SPIE 8794, 879437 (2013).
[Crossref]

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

S. L. Floch, F. Sauser, M. A. Soto, and L. Thévenaz, “Time/frequency coding for Brillouin distributed sensors,” Proc. SPIE 8421, 84211J (2012).
[Crossref]

Foaleng Mafang, S.

S. Diaz, S. Foaleng Mafang, M. Lopez-Amo, and L. Thévenaz, “A high-performance optical time-domain brillouin distributed fiber sensor,” IEEE Sens. J. 8(7), 1268–1272 (2008).
[Crossref]

Gauthier, D. J.

D. P. Rosin, D. Rontani, and D. J. Gauthier, “Ultra-fast physical generation of random numbers using hybrid boolean networks,” Phys. Rev. E 87(4), 040902 (2013).
[Crossref]

Ghil, M.

M. Ghil, I. Zaliapin, and B. Coluzzi, “Boolean delay equations: a simple way of looking at complex systems,” Phys. D. 237(23), 2967–2986 (2008).
[Crossref]

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]

Hasegawa, T.

K. Hotate and T. Hasegawa, “Measurement of brillouin gain spectrum distribution along an optical fiber using a correlation-based technique-proposal, experiment and simulation,” IEICE Trans. Electron. E83-C(3), 405–412 (2000).

He, Z. Y.

Horiguchi, T.

Hotate, K.

K. Y. Song, W. W. Zou, Z. Y. He, and K. Hotate, “All-optical dynamic grating generation based on brillouin scattering in polarizationmaintaining fiber,” Opt. Lett. 33(9), 926–928 (2008).
[Crossref]

K. Y. Song and K. Hotate, “Enlargement of measurement range in a brillouin optical correlation domain analysis system using double lock-in amplifiers and a single-sideband modulator,” IEEE Photonics Technol. Lett. 18(3), 499–501 (2006).
[Crossref]

K. Hotate and T. Hasegawa, “Measurement of brillouin gain spectrum distribution along an optical fiber using a correlation-based technique-proposal, experiment and simulation,” IEICE Trans. Electron. E83-C(3), 405–412 (2000).

Kurashima, T.

Levanon, N.

Li, H.

D. Zhou, Y. k. Dong, B. Wang, C. Pang, D. Ba, H. Zhang, Z. Lu, H. Li, and X. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

Li, W.

Liang, H.

Linze, N.

Liu, Y.

Llera, M.

S. L. Floch, F. Sauser, M. Llera, M. A. Soto, and L. Thévenaz, “Colour Simplex coding for Brillouin distributed sensors,” Proc. SPIE 8794, 879437 (2013).
[Crossref]

London, Y.

Lopez-Amo, M.

S. Diaz, S. Foaleng Mafang, M. Lopez-Amo, and L. Thévenaz, “A high-performance optical time-domain brillouin distributed fiber sensor,” IEEE Sens. J. 8(7), 1268–1272 (2008).
[Crossref]

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, Z.

D. Zhou, Y. k. Dong, B. Wang, C. Pang, D. Ba, H. Zhang, Z. Lu, H. Li, and X. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

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]

Martin-Lopez, S.

Minardo, A.

A. Minardo, R. Bernini, L. Zeni, L. Thevenaz, and F. Briffod, “A reconstruction technique for long-range stimulated Brillouin scattering distributed fibre-optic sensors: experimental results,” Meas. Sci. Technol. 16(4), 900–908 (2005).
[Crossref]

Pang, C.

D. Zhou, Y. k. Dong, B. Wang, C. Pang, D. Ba, H. Zhang, Z. Lu, H. Li, and X. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

Pasquale, F. D.

Preter, E.

Primerov, N.

A. Zadok, Y. Antman, N. Primerov, A. Denisov, J. Sancho, and L. Thévenaz, “Random-access distributed fiber sensing,” Laser Photonics Rev. 6(5), L1–L5 (2012).
[Crossref]

Rontani, D.

D. P. Rosin, D. Rontani, and D. J. Gauthier, “Ultra-fast physical generation of random numbers using hybrid boolean networks,” Phys. Rev. E 87(4), 040902 (2013).
[Crossref]

Rosin, D. P.

D. P. Rosin, D. Rontani, and D. J. Gauthier, “Ultra-fast physical generation of random numbers using hybrid boolean networks,” Phys. Rev. E 87(4), 040902 (2013).
[Crossref]

Sancho, J.

A. Zadok, Y. Antman, N. Primerov, A. Denisov, J. Sancho, and L. Thévenaz, “Random-access distributed fiber sensing,” Laser Photonics Rev. 6(5), L1–L5 (2012).
[Crossref]

Sauser, F.

S. L. Floch, F. Sauser, M. Llera, M. A. Soto, and L. Thévenaz, “Colour Simplex coding for Brillouin distributed sensors,” Proc. SPIE 8794, 879437 (2013).
[Crossref]

S. L. Floch, F. Sauser, M. A. Soto, and L. Thévenaz, “Time/frequency coding for Brillouin distributed sensors,” Proc. SPIE 8421, 84211J (2012).
[Crossref]

Shlomi, O.

Song, K. Y.

K. Y. Song, W. W. Zou, Z. Y. He, and K. Hotate, “All-optical dynamic grating generation based on brillouin scattering in polarizationmaintaining fiber,” Opt. Lett. 33(9), 926–928 (2008).
[Crossref]

K. Y. Song and K. Hotate, “Enlargement of measurement range in a brillouin optical correlation domain analysis system using double lock-in amplifiers and a single-sideband modulator,” IEEE Photonics Technol. Lett. 18(3), 499–501 (2006).
[Crossref]

Soto, M. 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]

Soto, M. A.

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]

Tateda, M.

Thevenaz, L.

A. Minardo, R. Bernini, L. Zeni, L. Thevenaz, and F. Briffod, “A reconstruction technique for long-range stimulated Brillouin scattering distributed fibre-optic sensors: experimental results,” Meas. Sci. Technol. 16(4), 900–908 (2005).
[Crossref]

Thévenaz, L.

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]

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]

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

S. L. Floch, F. Sauser, M. Llera, M. A. Soto, and L. Thévenaz, “Colour Simplex coding for Brillouin distributed sensors,” Proc. SPIE 8794, 879437 (2013).
[Crossref]

S. L. Floch, F. Sauser, M. A. Soto, and L. Thévenaz, “Time/frequency coding for Brillouin distributed sensors,” Proc. SPIE 8421, 84211J (2012).
[Crossref]

A. Zadok, Y. Antman, N. Primerov, A. Denisov, J. Sancho, and L. Thévenaz, “Random-access distributed fiber sensing,” Laser Photonics Rev. 6(5), L1–L5 (2012).
[Crossref]

M. A. Soto, G. Bolognini, F. D. 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]

S. Diaz, S. Foaleng Mafang, M. Lopez-Amo, and L. Thévenaz, “A high-performance optical time-domain brillouin distributed fiber sensor,” IEEE Sens. J. 8(7), 1268–1272 (2008).
[Crossref]

Wang, B.

D. Zhou, Y. k. Dong, B. Wang, C. Pang, D. Ba, H. Zhang, Z. Lu, H. Li, and X. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

Wang, Y.

Wu, C.

Yang, Z.

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]

Zadok, A.

Zaliapin, I.

M. Ghil, I. Zaliapin, and B. Coluzzi, “Boolean delay equations: a simple way of looking at complex systems,” Phys. D. 237(23), 2967–2986 (2008).
[Crossref]

Zan, M. S. D. B.

Zeni, L.

A. Minardo, R. Bernini, L. Zeni, L. Thevenaz, and F. Briffod, “A reconstruction technique for long-range stimulated Brillouin scattering distributed fibre-optic sensors: experimental results,” Meas. Sci. Technol. 16(4), 900–908 (2005).
[Crossref]

Zhang, H.

D. Zhou, Y. k. Dong, B. Wang, C. Pang, D. Ba, H. Zhang, Z. Lu, H. Li, and X. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

Zhang, J.

Zhang, M.

Zhou, D.

D. Zhou, Y. k. Dong, B. Wang, C. Pang, D. Ba, H. Zhang, Z. Lu, H. Li, and X. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

Zou, W. W.

IEEE Photonics J. (1)

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]

IEEE Photonics Technol. Lett. (1)

K. Y. Song and K. Hotate, “Enlargement of measurement range in a brillouin optical correlation domain analysis system using double lock-in amplifiers and a single-sideband modulator,” IEEE Photonics Technol. Lett. 18(3), 499–501 (2006).
[Crossref]

IEEE Sens. J. (1)

S. Diaz, S. Foaleng Mafang, M. Lopez-Amo, and L. Thévenaz, “A high-performance optical time-domain brillouin distributed fiber sensor,” IEEE Sens. J. 8(7), 1268–1272 (2008).
[Crossref]

IEICE Trans. Electron. (1)

K. Hotate and T. Hasegawa, “Measurement of brillouin gain spectrum distribution along an optical fiber using a correlation-based technique-proposal, experiment and simulation,” IEICE Trans. Electron. E83-C(3), 405–412 (2000).

J. Lightwave Technol. (2)

Laser Photonics Rev. (1)

A. Zadok, Y. Antman, N. Primerov, A. Denisov, J. Sancho, and L. Thévenaz, “Random-access distributed fiber sensing,” Laser Photonics Rev. 6(5), L1–L5 (2012).
[Crossref]

Light Sci. Appl. (1)

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]

Light: Sci. Appl. (1)

D. Zhou, Y. k. Dong, B. Wang, C. Pang, D. Ba, H. Zhang, Z. Lu, H. Li, and X. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

Meas. Sci. Technol. (1)

A. Minardo, R. Bernini, L. Zeni, L. Thevenaz, and F. Briffod, “A reconstruction technique for long-range stimulated Brillouin scattering distributed fibre-optic sensors: experimental results,” Meas. Sci. Technol. 16(4), 900–908 (2005).
[Crossref]

Opt. Express (5)

Opt. Lett. (6)

Phys. D. (1)

M. Ghil, I. Zaliapin, and B. Coluzzi, “Boolean delay equations: a simple way of looking at complex systems,” Phys. D. 237(23), 2967–2986 (2008).
[Crossref]

Phys. Rev. E (1)

D. P. Rosin, D. Rontani, and D. J. Gauthier, “Ultra-fast physical generation of random numbers using hybrid boolean networks,” Phys. Rev. E 87(4), 040902 (2013).
[Crossref]

Proc. SPIE (2)

S. L. Floch, F. Sauser, M. Llera, M. A. Soto, and L. Thévenaz, “Colour Simplex coding for Brillouin distributed sensors,” Proc. SPIE 8794, 879437 (2013).
[Crossref]

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[Crossref]

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Figures (8)

Fig. 1.
Fig. 1. Schematic diagram of true random code generation using the autonomous Boolean network oscillator.
Fig. 2.
Fig. 2. The spatio-temporal two-dimensional distribution of the acoustic wave field Q (t, z).
Fig. 3.
Fig. 3. Experimental setup of BOCDA system based on true random codes. TRNG, True Random Number Generator; ISO1, ISO2, isolator; PC1, PC2, polarization controller; EDFA1, EDFA2, erbium-doped optical fiber amplifier; OC, optical circulator; EOM, electro-optic modulator; PODG, programmable optical delay generator; PS, polarization scrambler; FUT, fiber under test; OPM, optical power meter; RF, radio frequency.
Fig. 4.
Fig. 4. True random codes from the autonomous Boolean network oscillator. (a) Time series; (b) Auto-correlation curve.
Fig. 5.
Fig. 5. The relationship of the BGS with temperature. (a) Temperature-dependence of the BGS along the FUT; (b) temperature coefficient: that of the BFS along the FUT.
Fig. 6.
Fig. 6. Measured distribution of the BGS along the FUT.
Fig. 7.
Fig. 7. Measured distributions of the BFS along the FUT. The rise and fall time equivalent length are 3.8 cm and 4 cm, respectively. It is an enlarged illustration that shows the rising edge of 1 m long heated fiber.
Fig. 8.
Fig. 8. (a) The BGS along the FUT. The blue and red lines represent the correlation peaks located at 500 m of the FUT with the ambient temperature of 25℃ and at the middle of the 1-m heated fiber with the temperature of 55℃, respectively; (b) the relationship curve between SBR and EXT at different locations.

Equations (7)

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x n ( t ) = f n [ t , x 1 ( t τ n 1 ) , x 2 ( t τ n 2 ) , , x n ( t τ n n ) ]
s n ( t ) = { 0 ,   i f   x n ( t ) C 1 ,   i f   x n ( t ) C
H ( X ) = x n = { 0.1 } p X ( x n ) log 2 p X ( x n )
Q ( t , z ) = 1 2 τ B 0 t exp ( t 1 t 2 τ B ) A p u m p ( t 1 z ν g ) A p r o b e [ t 1 z ν g + θ ( z ) ] d t 1
Q ( t , z ) ¯ = 1 2 τ B 0 t exp ( t 1 t 2 τ B ) A p u m p ( t 1 z ν g ) A p r o b e [ t 1 z ν g + θ ( z ) ] ¯ d t 1 = c ( θ ( z ) )
δ f = i = 1 n ( f i f ¯ ) n ( n 1 )
f ¯ = i = 1 n f i n

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