Abstract

Ghost imaging allows image reconstruction by correlation measurements between a light beam that interacts with the object without spatially resolved detection and a spatially resolved light beam that never interacts with the object. The two light beams are copies of each other. Its computational version removes the requirement of a spatially resolved detector when the light intensity pattern is pre-known. Here, we exploit the temporal analogue of computational ghost imaging, and demonstrate a computational distributed fiber-optic sensing technique. Temporal images containing spatially distributed scattering information used for sensing purposes are retrieved through correlating the “integrated” backscattered light and the pre-known binary patterns. The sampling rate required for our technique is inversely proportional to the total time duration of a binary sequence, so that it can be significantly reduced compared to that of the traditional methods. Our experiments demonstrate a 3 orders of magnitude reduction in the sampling rate, offering great simplification and cost reduction in the distributed fiber-optic sensors.

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

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References

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    [Crossref]
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    [Crossref] [PubMed]
  3. X. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors (Basel) 12(7), 8601–8639 (2012).
    [Crossref] [PubMed]
  4. A. Motil, A. Bergman, and M. Tur, “State of the art of Brillouin fiber-optic distributed sensing,” Opt. Laser Technol. 78, 81–103 (2016).
    [Crossref]
  5. K.-I. Aoyama, K. Nakagawa, and T. Itoh, “Optical time domain reflectometry in a single-mode fiber,” IEEE J. Quantum Electron. 17(6), 862–868 (1981).
    [Crossref]
  6. E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
    [Crossref]
  7. M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
    [Crossref]
  8. J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A, 78, 061802 (2008).
  9. Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
    [Crossref]
  10. B. Sun, S. S. Welsh, M. P. Edgar, J. H. Shapiro, and M. J. Padgett, “Normalized ghost imaging,” Opt. Express 20(15), 16892–16901 (2012).
    [Crossref]
  11. T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
    [Crossref] [PubMed]
  12. J. H. Shapiro and R. W. Boyd, “The physics of ghost imaging,” Quantum Inform. Process. 11(4), 949–993 (2012).
    [Crossref]
  13. R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92(3), 033601 (2004).
    [Crossref] [PubMed]
  14. B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photonics 2(4), 405–450 (2010).
    [Crossref]
  15. R. Salem, M. A. Foster, and A. L. Gaeta, “Application of space-time duality to ultrahigh-speed optical signal processing,” Adv. Opt. Photonics 5(3), 274–317 (2013).
    [Crossref]
  16. T. Shirai, T. Setälä, and A. T. Friberg, “Temporal ghost imaging with classical non-stationary pulsed light,” J. Opt. Soc. Am. B 27(12), 2549–2555 (2010).
    [Crossref]
  17. T. Setälä, T. Shirai, and A. T. Friberg, “Fractional Fourier transform in temporal ghost imaging with classical light,” Phys. Rev. A 82(4), 043813 (2010).
    [Crossref]
  18. Z. Chen, H. Li, Y. Li, J. Shi, and G. Zeng, “Temporal ghost imaging with a chaotic laser,” Opt. Eng. 52(7), 076103 (2013).
    [Crossref]
  19. K. Cho and J. Noh, “Temporal ghost imaging of a time object, dispersion cancelation, and nonlocal time lens with bi-photon state,” Opt. Commun. 285(6), 1275–1282 (2012).
    [Crossref]
  20. P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nat. Photonics 10(3), 167–170 (2016).
    [Crossref]
  21. D. Faccio, “Temporal ghost imaging,” Nat. Photonics 10(3), 150–152 (2016).
    [Crossref]
  22. X. Yao, W. Zhang, H. Li, L. You, Z. Wang, and Y. Huang, “Long-distance thermal temporal ghost imaging over optical fibers,” Opt. Lett. 43(4), 759–762 (2018).
    [Crossref] [PubMed]
  23. F. Devaux, P.-A. Moreau, S. Denis, and E. Lantz, “Computational temporal ghost imaging,” Optica 3(7), 698–701 (2016).
    [Crossref]
  24. Y.-K. Xu, S.-H. Sun, W.-T. Liu, G.-Z. Tang, J.-Y. Liu, and P.-X. Chen, “Detecting fast signals beyond bandwidth of detectors based on computational temporal ghost imaging,” Opt. Express 26(1), 99–107 (2018).
    [Crossref] [PubMed]
  25. M. A. Soto and L. Thévenaz, “Modeling and evaluating the performance of Brillouin distributed optical fiber sensors,” Opt. Express 21(25), 31347–31366 (2013).
    [Crossref] [PubMed]
  26. F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104(25), 253603 (2010).
    [Crossref] [PubMed]
  27. Y. O-oka and S. Fukatsu, “Differential ghost imaging in time domain,” Appl. Phys. Lett. 111(6), 061106 (2017).
    [Crossref]
  28. K. Shibuya, K. Nakae, Y. Mizutani, and T. Iwata, “Comparison of reconstructed images between ghost imaging and Hadamard transform imaging,” Opt. Rev. 22(6), 897–902 (2015).
    [Crossref]
  29. Y. A. Geadah and M. J. G. Corinthios, “Natural, dyadic, and sequency order algorithms and processors for the Walsh-Hadamard transform,” IEEE Trans. Comput. C-26(5), 435–442 (1977).
    [Crossref]
  30. O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
    [Crossref]
  31. 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]

2018 (2)

2017 (1)

Y. O-oka and S. Fukatsu, “Differential ghost imaging in time domain,” Appl. Phys. Lett. 111(6), 061106 (2017).
[Crossref]

2016 (5)

F. Devaux, P.-A. Moreau, S. Denis, and E. Lantz, “Computational temporal ghost imaging,” Optica 3(7), 698–701 (2016).
[Crossref]

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nat. Photonics 10(3), 167–170 (2016).
[Crossref]

D. Faccio, “Temporal ghost imaging,” Nat. Photonics 10(3), 150–152 (2016).
[Crossref]

M. A. Soto, J. A. Ramírez, and L. Thévenaz, “Intensifying the response of distributed optical fibre sensors using 2D and 3D image restoration,” Nat. Commun. 7(1), 10870 (2016).
[Crossref] [PubMed]

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

2015 (1)

K. Shibuya, K. Nakae, Y. Mizutani, and T. Iwata, “Comparison of reconstructed images between ghost imaging and Hadamard transform imaging,” Opt. Rev. 22(6), 897–902 (2015).
[Crossref]

2013 (3)

M. A. Soto and L. Thévenaz, “Modeling and evaluating the performance of Brillouin distributed optical fiber sensors,” Opt. Express 21(25), 31347–31366 (2013).
[Crossref] [PubMed]

R. Salem, M. A. Foster, and A. L. Gaeta, “Application of space-time duality to ultrahigh-speed optical signal processing,” Adv. Opt. Photonics 5(3), 274–317 (2013).
[Crossref]

Z. Chen, H. Li, Y. Li, J. Shi, and G. Zeng, “Temporal ghost imaging with a chaotic laser,” Opt. Eng. 52(7), 076103 (2013).
[Crossref]

2012 (4)

K. Cho and J. Noh, “Temporal ghost imaging of a time object, dispersion cancelation, and nonlocal time lens with bi-photon state,” Opt. Commun. 285(6), 1275–1282 (2012).
[Crossref]

B. Sun, S. S. Welsh, M. P. Edgar, J. H. Shapiro, and M. J. Padgett, “Normalized ghost imaging,” Opt. Express 20(15), 16892–16901 (2012).
[Crossref]

J. H. Shapiro and R. W. Boyd, “The physics of ghost imaging,” Quantum Inform. Process. 11(4), 949–993 (2012).
[Crossref]

X. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors (Basel) 12(7), 8601–8639 (2012).
[Crossref] [PubMed]

2010 (4)

T. Shirai, T. Setälä, and A. T. Friberg, “Temporal ghost imaging with classical non-stationary pulsed light,” J. Opt. Soc. Am. B 27(12), 2549–2555 (2010).
[Crossref]

T. Setälä, T. Shirai, and A. T. Friberg, “Fractional Fourier transform in temporal ghost imaging with classical light,” Phys. Rev. A 82(4), 043813 (2010).
[Crossref]

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104(25), 253603 (2010).
[Crossref] [PubMed]

B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photonics 2(4), 405–450 (2010).
[Crossref]

2009 (2)

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[Crossref]

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

2008 (4)

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A, 78, 061802 (2008).

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]

2004 (1)

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92(3), 033601 (2004).
[Crossref] [PubMed]

1999 (1)

A. Rogers, “Distributed optical-fibre sensing,” Meas. Sci. Technol. 10(8), R75–R99 (1999).
[Crossref]

1995 (1)

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref] [PubMed]

1981 (1)

K.-I. Aoyama, K. Nakagawa, and T. Itoh, “Optical time domain reflectometry in a single-mode fiber,” IEEE J. Quantum Electron. 17(6), 862–868 (1981).
[Crossref]

1977 (1)

Y. A. Geadah and M. J. G. Corinthios, “Natural, dyadic, and sequency order algorithms and processors for the Walsh-Hadamard transform,” IEEE Trans. Comput. C-26(5), 435–442 (1977).
[Crossref]

Aoyama, K.-I.

K.-I. Aoyama, K. Nakagawa, and T. Itoh, “Optical time domain reflectometry in a single-mode fiber,” IEEE J. Quantum Electron. 17(6), 862–868 (1981).
[Crossref]

Bao, X.

Baraniuk, R. G.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

Barbier, M.

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nat. Photonics 10(3), 167–170 (2016).
[Crossref]

Bennink, R. S.

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92(3), 033601 (2004).
[Crossref] [PubMed]

Bentley, S. J.

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92(3), 033601 (2004).
[Crossref] [PubMed]

Bergman, A.

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

Boyd, R. W.

J. H. Shapiro and R. W. Boyd, “The physics of ghost imaging,” Quantum Inform. Process. 11(4), 949–993 (2012).
[Crossref]

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92(3), 033601 (2004).
[Crossref] [PubMed]

Bromberg, Y.

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[Crossref]

Candès, E. J.

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

Chen, L.

Chen, P.-X.

Chen, Z.

Z. Chen, H. Li, Y. Li, J. Shi, and G. Zeng, “Temporal ghost imaging with a chaotic laser,” Opt. Eng. 52(7), 076103 (2013).
[Crossref]

Cho, K.

K. Cho and J. Noh, “Temporal ghost imaging of a time object, dispersion cancelation, and nonlocal time lens with bi-photon state,” Opt. Commun. 285(6), 1275–1282 (2012).
[Crossref]

Corinthios, M. J. G.

Y. A. Geadah and M. J. G. Corinthios, “Natural, dyadic, and sequency order algorithms and processors for the Walsh-Hadamard transform,” IEEE Trans. Comput. C-26(5), 435–442 (1977).
[Crossref]

Davenport, M. A.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

Denis, S.

Devaux, F.

Duarte, M. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

Dudley, J. M.

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nat. Photonics 10(3), 167–170 (2016).
[Crossref]

Edgar, M. P.

Erkmen, B. I.

B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photonics 2(4), 405–450 (2010).
[Crossref]

Faccio, D.

D. Faccio, “Temporal ghost imaging,” Nat. Photonics 10(3), 150–152 (2016).
[Crossref]

Ferri, F.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104(25), 253603 (2010).
[Crossref] [PubMed]

Foster, M. A.

R. Salem, M. A. Foster, and A. L. Gaeta, “Application of space-time duality to ultrahigh-speed optical signal processing,” Adv. Opt. Photonics 5(3), 274–317 (2013).
[Crossref]

Friberg, A. T.

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nat. Photonics 10(3), 167–170 (2016).
[Crossref]

T. Setälä, T. Shirai, and A. T. Friberg, “Fractional Fourier transform in temporal ghost imaging with classical light,” Phys. Rev. A 82(4), 043813 (2010).
[Crossref]

T. Shirai, T. Setälä, and A. T. Friberg, “Temporal ghost imaging with classical non-stationary pulsed light,” J. Opt. Soc. Am. B 27(12), 2549–2555 (2010).
[Crossref]

Fukatsu, S.

Y. O-oka and S. Fukatsu, “Differential ghost imaging in time domain,” Appl. Phys. Lett. 111(6), 061106 (2017).
[Crossref]

Gaeta, A. L.

R. Salem, M. A. Foster, and A. L. Gaeta, “Application of space-time duality to ultrahigh-speed optical signal processing,” Adv. Opt. Photonics 5(3), 274–317 (2013).
[Crossref]

Gatti, A.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104(25), 253603 (2010).
[Crossref] [PubMed]

Geadah, Y. A.

Y. A. Geadah and M. J. G. Corinthios, “Natural, dyadic, and sequency order algorithms and processors for the Walsh-Hadamard transform,” IEEE Trans. Comput. C-26(5), 435–442 (1977).
[Crossref]

Genty, G.

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nat. Photonics 10(3), 167–170 (2016).
[Crossref]

Howell, J. C.

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92(3), 033601 (2004).
[Crossref] [PubMed]

Huang, Y.

Itoh, T.

K.-I. Aoyama, K. Nakagawa, and T. Itoh, “Optical time domain reflectometry in a single-mode fiber,” IEEE J. Quantum Electron. 17(6), 862–868 (1981).
[Crossref]

Iwata, T.

K. Shibuya, K. Nakae, Y. Mizutani, and T. Iwata, “Comparison of reconstructed images between ghost imaging and Hadamard transform imaging,” Opt. Rev. 22(6), 897–902 (2015).
[Crossref]

Katz, O.

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[Crossref]

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

Kelly, K. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

Lantz, E.

Laska, J. N.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

Li, H.

X. Yao, W. Zhang, H. Li, L. You, Z. Wang, and Y. Huang, “Long-distance thermal temporal ghost imaging over optical fibers,” Opt. Lett. 43(4), 759–762 (2018).
[Crossref] [PubMed]

Z. Chen, H. Li, Y. Li, J. Shi, and G. Zeng, “Temporal ghost imaging with a chaotic laser,” Opt. Eng. 52(7), 076103 (2013).
[Crossref]

Li, W.

Li, Y.

Z. Chen, H. Li, Y. Li, J. Shi, and G. Zeng, “Temporal ghost imaging with a chaotic laser,” Opt. Eng. 52(7), 076103 (2013).
[Crossref]

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]

Liu, J.-Y.

Liu, W.-T.

Lugiato, L. A.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104(25), 253603 (2010).
[Crossref] [PubMed]

Magatti, D.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104(25), 253603 (2010).
[Crossref] [PubMed]

Mizutani, Y.

K. Shibuya, K. Nakae, Y. Mizutani, and T. Iwata, “Comparison of reconstructed images between ghost imaging and Hadamard transform imaging,” Opt. Rev. 22(6), 897–902 (2015).
[Crossref]

Moreau, P.-A.

Motil, A.

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

Nakae, K.

K. Shibuya, K. Nakae, Y. Mizutani, and T. Iwata, “Comparison of reconstructed images between ghost imaging and Hadamard transform imaging,” Opt. Rev. 22(6), 897–902 (2015).
[Crossref]

Nakagawa, K.

K.-I. Aoyama, K. Nakagawa, and T. Itoh, “Optical time domain reflectometry in a single-mode fiber,” IEEE J. Quantum Electron. 17(6), 862–868 (1981).
[Crossref]

Noh, J.

K. Cho and J. Noh, “Temporal ghost imaging of a time object, dispersion cancelation, and nonlocal time lens with bi-photon state,” Opt. Commun. 285(6), 1275–1282 (2012).
[Crossref]

O-oka, Y.

Y. O-oka and S. Fukatsu, “Differential ghost imaging in time domain,” Appl. Phys. Lett. 111(6), 061106 (2017).
[Crossref]

Padgett, M. J.

Pittman, T. B.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref] [PubMed]

Ramírez, J. A.

M. A. Soto, J. A. Ramírez, and L. Thévenaz, “Intensifying the response of distributed optical fibre sensors using 2D and 3D image restoration,” Nat. Commun. 7(1), 10870 (2016).
[Crossref] [PubMed]

Rogers, A.

A. Rogers, “Distributed optical-fibre sensing,” Meas. Sci. Technol. 10(8), R75–R99 (1999).
[Crossref]

Ryczkowski, P.

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nat. Photonics 10(3), 167–170 (2016).
[Crossref]

Salem, R.

R. Salem, M. A. Foster, and A. L. Gaeta, “Application of space-time duality to ultrahigh-speed optical signal processing,” Adv. Opt. Photonics 5(3), 274–317 (2013).
[Crossref]

Sergienko, A. V.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref] [PubMed]

Setälä, T.

T. Setälä, T. Shirai, and A. T. Friberg, “Fractional Fourier transform in temporal ghost imaging with classical light,” Phys. Rev. A 82(4), 043813 (2010).
[Crossref]

T. Shirai, T. Setälä, and A. T. Friberg, “Temporal ghost imaging with classical non-stationary pulsed light,” J. Opt. Soc. Am. B 27(12), 2549–2555 (2010).
[Crossref]

Shapiro, J. H.

B. Sun, S. S. Welsh, M. P. Edgar, J. H. Shapiro, and M. J. Padgett, “Normalized ghost imaging,” Opt. Express 20(15), 16892–16901 (2012).
[Crossref]

J. H. Shapiro and R. W. Boyd, “The physics of ghost imaging,” Quantum Inform. Process. 11(4), 949–993 (2012).
[Crossref]

B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photonics 2(4), 405–450 (2010).
[Crossref]

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A, 78, 061802 (2008).

Shi, J.

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Supplementary Material (4)

NameDescription
» Visualization 1       Related to Fig. 2(a).
» Visualization 2       Related to Fig. 2(b).
» Visualization 3       Related to Fig. 4(a).
» Visualization 4       Related to Fig. 4(b).

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Figures (5)

Fig. 1
Fig. 1 Schematic of the proposed computational distributed fiber-optic sensing system. (a) Binary pulse pattern sequences are sent into an optical fiber, and the backscattered integrated signals are received by a photodetector followed by a digitizer. Each pulse sequence has a total duration of T, so that the sampling rate of the digitizer is 1/T. Correlation calculations are performed between the pre-known pulse pattern and the acquired integrated signal retrieving the temporal image containing scattering information. (b) Experiment setup utilizing stimulated Brillouin scattering to demonstrate the proposed sensing technique. (c) Illustration of trigger delaying method to increase the read-out spatial samples. The reconstruction process is repeated by 5 times, and each time the trigger is delayed by Δt/5 with Δt being bit duration of the binary pulse sequence, so that each time the reconstructed temporal image is shifted by Δt/5. After interleaving the 5 images, one can obtain the entire temporal image with more detailed location information.
Fig. 2
Fig. 2 Reconstructed temporal images at several different frequencies for 1 km fiber. (a) and (b) show the results at frequencies of 10860 MHz and 10790 MHz, respectively. The spatial distance between two neighboring points is 5 m determined by the bit period of 50 ns. The WHGI reconstructed images are also compared with the time-domain traces obtained by RSGI, IWHT and the conventional method using a single 25 ns pulse with 5 m read-out resolution. (c) and (d) show the results at frequencies of 10900 MHz and 10750 MHz, respectively. The spatial distance between two neighboring points is 1 m by interleaving 5 reconstructed temporal images of 5 m read-out resolution. The WHGI reconstructed images are also compared with the time-domain traces obtained by conventional method using a single 25 ns pulse with 1 m read-out resolution. The insets show enlarged view of the 20 m fiber confirming the 2.5 m spatial resolution.
Fig. 3
Fig. 3 Comparison of the results obtained by conventional method and the proposed WHGI method for the 1 km fiber. Brillouin spectra obtained by (a) conventional method using a single 25 ns pulse and (b) the proposed WHGI method. The read-out resolution for both (a) and (b) is 1 m, and the frequency is scanned from 10500 MHz to 11200 MHz with 1 MHz increment. (c) the distributed Brillouin frequency (BF) using the two methods along the 1 km fiber by Lorentzian fitting of the Brillouin spectra in (a) and (b).
Fig. 4
Fig. 4 Reconstructed temporal images at two different frequencies for 51 km fiber. (a) and (b) show the results at frequencies of 10860 MHz and 10790 MHz, respectively. The spatial distance between two neighboring points is 2 m by interleaving 5 reconstructed temporal images of 10 m read-out resolution. The WHGI reconstructed images are also compared with the time-domain traces obtained by conventional method using a single 50 ns pulse with 2 m read-out resolution. The insets show enlarged view of the 20 m fiber confirming the 5 m spatial resolution.
Fig. 5
Fig. 5 Comparison of the results obtained by conventional method and the proposed WHGI method for the 51 km fiber. Brillouin spectra obtained by (a) conventional method using a single 50 ns pulse, and (b) the proposed WHGI method. The read-out resolution for both (a) and (b) is 2 m, and the frequency is scanned from 10600 MHz to 11200 MHz with 1 MHz increment. (c) the distributed Brillouin frequency (BF) using the two methods along the 51 km fiber by Lorentzian fitting of the Brillouin spectra in (a) and (b).

Equations (10)

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H 2 k =[ H 2 k1 H 2 k1 H 2 k1 H 2 k1 ],
H 2 1 =[ 1 1 1 1 ].
  D i =γ 0 T I i ( t )S( t )dt,
  D ˜ i =γ 0 T I ˜ i ( t )S( t )dt,
S( t )=S( z ) g( z ) A eff P P ( z ) P s ( z )Δz,
 S( t )=S( z )α( z ) P P ( z )Δz
 γS( t )= D R + 1 I( t ) 2 [ DI( t ) D R RI( t ) ],
R i = 0 T I i ( t )dt,
R ˜ i = 0 T I ˜ i ( t )dt,
γ[ S( t 1 ) S( t 2 ) S( t 2 k ) ]= H 2 k 1 D= 1 2 k H 2 k D= 1 2 k [ I 1 ( t 1 ) I ˜ 1 ( t 1 ) I 1 ( t 2 ) I ˜ 1 ( t 2 ) I 1 ( t 2 k ) I ˜ 1 ( t 2 k ) I 2 ( t 1 ) I ˜ 2 ( t 1 ) I 2 ( t 2 ) I ˜ 2 ( t 2 ) I 2 ( t 2 k ) I ˜ 2 ( t 2 k ) I 2 k ( t 1 ) I ˜ 2 k ( t 1 ) I 2 k ( t 2 ) I ˜ 2 k ( t 2 ) I 2 k ( t 2 k ) I ˜ 2 k ( t 2 k ) ][ D 1 D ˜ 1 D 2 D ˜ 2 D 2 k D ˜ 2 k ],

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