Abstract

Ghost imaging is an unconventional optical imaging technique that reconstructs the shape of an object by combining the measurement of two signals: one that interacted with the object, but without any spatial information; the other containing spatial information, but that never interacted with the object. Here we demonstrate that ghost imaging can be performed without ever knowing the patterns that illuminate the object, by instead using patterns correlated with them, no matter how weakly. As an experimental proof, we reconstruct the image of an object hidden behind a scattering layer using only the reflected light, which never interacts with the object.

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References

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  1. P. Sen, B. Chen, G. Garg, S. R. Marschner, M. Horowitz, M. Levoy, and H. P. A. Lensch, “Dual photography,” ACM Trans. Graph. 24, 745 (2005).
    [Crossref]
  2. 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, 83–91 (2008).
    [Crossref]
  3. 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, R3429–R3432 (1995).
    [Crossref]
  4. R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Two-photon coincidence imaging with a classical source,” Phys. Rev. Lett. 89, 113601 (2002).
    [Crossref]
  5. F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
    [Crossref]
  6. R. S. Aspden, D. S. Tasca, R. W. Boyd, and M. J. Padgett, “EPR-based ghost imaging using a single-photon-sensitive camera,” New J. Phys. 15, 073032 (2013).
    [Crossref]
  7. P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nat. Photonics 10, 167–170 (2016).
    [Crossref]
  8. D. Shrekenhamer, C. M. Watts, and W. J. Padilla, “Terahertz single pixel imaging with an optically controlled dynamic spatial light modulator,” Opt. Express 21, 12507–12518 (2013).
    [Crossref]
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    [Crossref]
  10. D. B. Phillips, M.-J. Sun, J. M. Taylor, M. P. Edgar, S. M. Barnett, G. M. Gibson, and M. J. Padgett, “Adaptive foveated single-pixel imaging with dynamic supersampling,” Sci. Adv. 3, e1601782 (2017).
    [Crossref]
  11. O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).
    [Crossref]
  12. P. Zerom, Z. Shi, M. N. O’Sullivan, K. W. C. Chan, M. Krogstad, J. H. Shapiro, and R. W. Boyd, “Thermal ghost imaging with averaged speckle patterns,” Phys. Rev. A 86, 063817 (2012).
    [Crossref]
  13. N. Fayard, A. Cazé, R. Pierrat, and R. Carminati, “Intensity correlations between reflected and transmitted speckle patterns,” Phys. Rev. A 92, 033827 (2015).
    [Crossref]
  14. I. Starshynov, A. M. Paniagua-Diaz, N. Fayard, A. Goetschy, R. Pierrat, R. Carminati, and J. Bertolotti, “Non-Gaussian correlations between reflected and transmitted intensity patterns emerging from opaque disordered media,” Phys. Rev. X 8, 021041 (2018).
    [Crossref]
  15. N. Fayard, A. Goetschy, R. Pierrat, and R. Carminati, “Mutual information between reflected and transmitted speckle images,” Phys. Rev. Lett. 120, 073901 (2018).
    [Crossref]
  16. N. D. Hardy and J. H. Shapiro, “Reflective ghost imaging through turbulence,” Phys. Rev. A 84, 063824 (2011).
    [Crossref]
  17. M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110, 083901 (2013).
    [Crossref]
  18. S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
    [Crossref]
  19. M. J. Stephen and G. Cwilich, “Intensity correlation functions and fluctuations in light scattered from a random medium,” Phys. Rev. Lett. 59, 285–287 (1987).
    [Crossref]
  20. M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
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    [Crossref]
  23. M. van Albada, J. De Boer, and A. Lagendijk, “Observation of long-range intensity correlation in the transport of coherent light through a random medium,” Phys. Rev. Lett. 64, 2787–2790 (1990).
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    [Crossref]
  25. J. F. de Boer, M. P. van Albada, and A. Lagendijk, “Transmission and intensity correlations in wave propagation through random media,” Phys. Rev. B 45, 658–666 (1992).
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  26. D. B. Rogozkin and M. Y. Cherkasov, “Long-range intensity correlations in wave reflection from a disordered medium,” Phys. Rev. B 51, 12256–12267 (1995).
    [Crossref]
  27. L. Froufe-Perez, A. Garcia-Martin, G. Cwilich, and J. Sáenz, “Fluctuations and correlations in wave transport through complex media,” Physica A 386, 625–632 (2007).
    [Crossref]
  28. T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
    [Crossref]
  29. J. Bertolotti, E. van Putten, C. Blum, A. Lagendijk, W. Vos, and A. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
    [Crossref]
  30. O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
    [Crossref]
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2018 (2)

I. Starshynov, A. M. Paniagua-Diaz, N. Fayard, A. Goetschy, R. Pierrat, R. Carminati, and J. Bertolotti, “Non-Gaussian correlations between reflected and transmitted intensity patterns emerging from opaque disordered media,” Phys. Rev. X 8, 021041 (2018).
[Crossref]

N. Fayard, A. Goetschy, R. Pierrat, and R. Carminati, “Mutual information between reflected and transmitted speckle images,” Phys. Rev. Lett. 120, 073901 (2018).
[Crossref]

2017 (2)

M. J. Padgett and R. W. Boyd, “An introduction to ghost imaging: quantum and classical,” Philos. Trans. R. Soc. A 375, 20160233 (2017).
[Crossref]

D. B. Phillips, M.-J. Sun, J. M. Taylor, M. P. Edgar, S. M. Barnett, G. M. Gibson, and M. J. Padgett, “Adaptive foveated single-pixel imaging with dynamic supersampling,” Sci. Adv. 3, e1601782 (2017).
[Crossref]

2016 (1)

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

2015 (1)

N. Fayard, A. Cazé, R. Pierrat, and R. Carminati, “Intensity correlations between reflected and transmitted speckle patterns,” Phys. Rev. A 92, 033827 (2015).
[Crossref]

2014 (1)

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
[Crossref]

2013 (3)

D. Shrekenhamer, C. M. Watts, and W. J. Padilla, “Terahertz single pixel imaging with an optically controlled dynamic spatial light modulator,” Opt. Express 21, 12507–12518 (2013).
[Crossref]

R. S. Aspden, D. S. Tasca, R. W. Boyd, and M. J. Padgett, “EPR-based ghost imaging using a single-photon-sensitive camera,” New J. Phys. 15, 073032 (2013).
[Crossref]

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110, 083901 (2013).
[Crossref]

2012 (2)

P. Zerom, Z. Shi, M. N. O’Sullivan, K. W. C. Chan, M. Krogstad, J. H. Shapiro, and R. W. Boyd, “Thermal ghost imaging with averaged speckle patterns,” Phys. Rev. A 86, 063817 (2012).
[Crossref]

J. Bertolotti, E. van Putten, C. Blum, A. Lagendijk, W. Vos, and A. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

2011 (1)

N. D. Hardy and J. H. Shapiro, “Reflective ghost imaging through turbulence,” Phys. Rev. A 84, 063824 (2011).
[Crossref]

2010 (1)

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
[Crossref]

2009 (1)

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

2008 (1)

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, 83–91 (2008).
[Crossref]

2007 (1)

L. Froufe-Perez, A. Garcia-Martin, G. Cwilich, and J. Sáenz, “Fluctuations and correlations in wave transport through complex media,” Physica A 386, 625–632 (2007).
[Crossref]

2005 (2)

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[Crossref]

P. Sen, B. Chen, G. Garg, S. R. Marschner, M. Horowitz, M. Levoy, and H. P. A. Lensch, “Dual photography,” ACM Trans. Graph. 24, 745 (2005).
[Crossref]

2002 (1)

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Two-photon coincidence imaging with a classical source,” Phys. Rev. Lett. 89, 113601 (2002).
[Crossref]

1999 (1)

M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
[Crossref]

1995 (2)

D. B. Rogozkin and M. Y. Cherkasov, “Long-range intensity correlations in wave reflection from a disordered medium,” Phys. Rev. B 51, 12256–12267 (1995).
[Crossref]

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, R3429–R3432 (1995).
[Crossref]

1992 (1)

J. F. de Boer, M. P. van Albada, and A. Lagendijk, “Transmission and intensity correlations in wave propagation through random media,” Phys. Rev. B 45, 658–666 (1992).
[Crossref]

1990 (2)

M. van Albada, J. De Boer, and A. Lagendijk, “Observation of long-range intensity correlation in the transport of coherent light through a random medium,” Phys. Rev. Lett. 64, 2787–2790 (1990).
[Crossref]

A. Z. Genack, N. Garcia, and W. Polkosnik, “Long-range intensity correlation in random media,” Phys. Rev. Lett. 65, 2129–2132 (1990).
[Crossref]

1989 (1)

R. Pnini and B. Shapiro, “Fluctuations in transmission of waves through disordered slabs,” Phys. Rev. B 39, 6986–6994 (1989).
[Crossref]

1988 (1)

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[Crossref]

1987 (2)

M. J. Stephen and G. Cwilich, “Intensity correlation functions and fluctuations in light scattered from a random medium,” Phys. Rev. Lett. 59, 285–287 (1987).
[Crossref]

A. U. Zyuzin and B. Z. Spivak, “Langevin description of mesoscopic fluctuations in disordered media,” JETP Lett. 66, 560–566 (1987).

Aspden, R. S.

R. S. Aspden, D. S. Tasca, R. W. Boyd, and M. J. Padgett, “EPR-based ghost imaging using a single-photon-sensitive camera,” New J. Phys. 15, 073032 (2013).
[Crossref]

Bache, M.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[Crossref]

Baker, W. B.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
[Crossref]

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, 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, 167–170 (2016).
[Crossref]

Barnett, S. M.

D. B. Phillips, M.-J. Sun, J. M. Taylor, M. P. Edgar, S. M. Barnett, G. M. Gibson, and M. J. Padgett, “Adaptive foveated single-pixel imaging with dynamic supersampling,” Sci. Adv. 3, e1601782 (2017).
[Crossref]

Bennink, R. S.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Two-photon coincidence imaging with a classical source,” Phys. Rev. Lett. 89, 113601 (2002).
[Crossref]

Bentley, S. J.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Two-photon coincidence imaging with a classical source,” Phys. Rev. Lett. 89, 113601 (2002).
[Crossref]

Bertolotti, J.

I. Starshynov, A. M. Paniagua-Diaz, N. Fayard, A. Goetschy, R. Pierrat, R. Carminati, and J. Bertolotti, “Non-Gaussian correlations between reflected and transmitted intensity patterns emerging from opaque disordered media,” Phys. Rev. X 8, 021041 (2018).
[Crossref]

J. Bertolotti, E. van Putten, C. Blum, A. Lagendijk, W. Vos, and A. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

Bina, M.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110, 083901 (2013).
[Crossref]

Blum, C.

J. Bertolotti, E. van Putten, C. Blum, A. Lagendijk, W. Vos, and A. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

Boyd, R. W.

M. J. Padgett and R. W. Boyd, “An introduction to ghost imaging: quantum and classical,” Philos. Trans. R. Soc. A 375, 20160233 (2017).
[Crossref]

R. S. Aspden, D. S. Tasca, R. W. Boyd, and M. J. Padgett, “EPR-based ghost imaging using a single-photon-sensitive camera,” New J. Phys. 15, 073032 (2013).
[Crossref]

P. Zerom, Z. Shi, M. N. O’Sullivan, K. W. C. Chan, M. Krogstad, J. H. Shapiro, and R. W. Boyd, “Thermal ghost imaging with averaged speckle patterns,” Phys. Rev. A 86, 063817 (2012).
[Crossref]

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Two-photon coincidence imaging with a classical source,” Phys. Rev. Lett. 89, 113601 (2002).
[Crossref]

Brambilla, E.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[Crossref]

Bromberg, Y.

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

Carminati, R.

N. Fayard, A. Goetschy, R. Pierrat, and R. Carminati, “Mutual information between reflected and transmitted speckle images,” Phys. Rev. Lett. 120, 073901 (2018).
[Crossref]

I. Starshynov, A. M. Paniagua-Diaz, N. Fayard, A. Goetschy, R. Pierrat, R. Carminati, and J. Bertolotti, “Non-Gaussian correlations between reflected and transmitted intensity patterns emerging from opaque disordered media,” Phys. Rev. X 8, 021041 (2018).
[Crossref]

N. Fayard, A. Cazé, R. Pierrat, and R. Carminati, “Intensity correlations between reflected and transmitted speckle patterns,” Phys. Rev. A 92, 033827 (2015).
[Crossref]

Cazé, A.

N. Fayard, A. Cazé, R. Pierrat, and R. Carminati, “Intensity correlations between reflected and transmitted speckle patterns,” Phys. Rev. A 92, 033827 (2015).
[Crossref]

Chan, K. W. C.

P. Zerom, Z. Shi, M. N. O’Sullivan, K. W. C. Chan, M. Krogstad, J. H. Shapiro, and R. W. Boyd, “Thermal ghost imaging with averaged speckle patterns,” Phys. Rev. A 86, 063817 (2012).
[Crossref]

Chen, B.

P. Sen, B. Chen, G. Garg, S. R. Marschner, M. Horowitz, M. Levoy, and H. P. A. Lensch, “Dual photography,” ACM Trans. Graph. 24, 745 (2005).
[Crossref]

Cherkasov, M. Y.

D. B. Rogozkin and M. Y. Cherkasov, “Long-range intensity correlations in wave reflection from a disordered medium,” Phys. Rev. B 51, 12256–12267 (1995).
[Crossref]

Choe, R.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
[Crossref]

Cwilich, G.

L. Froufe-Perez, A. Garcia-Martin, G. Cwilich, and J. Sáenz, “Fluctuations and correlations in wave transport through complex media,” Physica A 386, 625–632 (2007).
[Crossref]

M. J. Stephen and G. Cwilich, “Intensity correlation functions and fluctuations in light scattered from a random medium,” Phys. Rev. Lett. 59, 285–287 (1987).
[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, 83–91 (2008).
[Crossref]

De Boer, J.

M. van Albada, J. De Boer, and A. Lagendijk, “Observation of long-range intensity correlation in the transport of coherent light through a random medium,” Phys. Rev. Lett. 64, 2787–2790 (1990).
[Crossref]

de Boer, J. F.

J. F. de Boer, M. P. van Albada, and A. Lagendijk, “Transmission and intensity correlations in wave propagation through random media,” Phys. Rev. B 45, 658–666 (1992).
[Crossref]

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, 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, 167–170 (2016).
[Crossref]

Durduran, T.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
[Crossref]

Edgar, M. P.

D. B. Phillips, M.-J. Sun, J. M. Taylor, M. P. Edgar, S. M. Barnett, G. M. Gibson, and M. J. Padgett, “Adaptive foveated single-pixel imaging with dynamic supersampling,” Sci. Adv. 3, e1601782 (2017).
[Crossref]

Fayard, N.

I. Starshynov, A. M. Paniagua-Diaz, N. Fayard, A. Goetschy, R. Pierrat, R. Carminati, and J. Bertolotti, “Non-Gaussian correlations between reflected and transmitted intensity patterns emerging from opaque disordered media,” Phys. Rev. X 8, 021041 (2018).
[Crossref]

N. Fayard, A. Goetschy, R. Pierrat, and R. Carminati, “Mutual information between reflected and transmitted speckle images,” Phys. Rev. Lett. 120, 073901 (2018).
[Crossref]

N. Fayard, A. Cazé, R. Pierrat, and R. Carminati, “Intensity correlations between reflected and transmitted speckle patterns,” Phys. Rev. A 92, 033827 (2015).
[Crossref]

Feng, S.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[Crossref]

Ferri, F.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110, 083901 (2013).
[Crossref]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[Crossref]

Fink, M.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
[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, 167–170 (2016).
[Crossref]

Froufe-Perez, L.

L. Froufe-Perez, A. Garcia-Martin, G. Cwilich, and J. Sáenz, “Fluctuations and correlations in wave transport through complex media,” Physica A 386, 625–632 (2007).
[Crossref]

Garcia, N.

A. Z. Genack, N. Garcia, and W. Polkosnik, “Long-range intensity correlation in random media,” Phys. Rev. Lett. 65, 2129–2132 (1990).
[Crossref]

Garcia-Martin, A.

L. Froufe-Perez, A. Garcia-Martin, G. Cwilich, and J. Sáenz, “Fluctuations and correlations in wave transport through complex media,” Physica A 386, 625–632 (2007).
[Crossref]

Garg, G.

P. Sen, B. Chen, G. Garg, S. R. Marschner, M. Horowitz, M. Levoy, and H. P. A. Lensch, “Dual photography,” ACM Trans. Graph. 24, 745 (2005).
[Crossref]

Gatti, A.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110, 083901 (2013).
[Crossref]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[Crossref]

Genack, A. Z.

A. Z. Genack, N. Garcia, and W. Polkosnik, “Long-range intensity correlation in random media,” Phys. Rev. Lett. 65, 2129–2132 (1990).
[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, 167–170 (2016).
[Crossref]

Gibson, G. M.

D. B. Phillips, M.-J. Sun, J. M. Taylor, M. P. Edgar, S. M. Barnett, G. M. Gibson, and M. J. Padgett, “Adaptive foveated single-pixel imaging with dynamic supersampling,” Sci. Adv. 3, e1601782 (2017).
[Crossref]

Gigan, S.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
[Crossref]

Goetschy, A.

N. Fayard, A. Goetschy, R. Pierrat, and R. Carminati, “Mutual information between reflected and transmitted speckle images,” Phys. Rev. Lett. 120, 073901 (2018).
[Crossref]

I. Starshynov, A. M. Paniagua-Diaz, N. Fayard, A. Goetschy, R. Pierrat, R. Carminati, and J. Bertolotti, “Non-Gaussian correlations between reflected and transmitted intensity patterns emerging from opaque disordered media,” Phys. Rev. X 8, 021041 (2018).
[Crossref]

Hardy, N. D.

N. D. Hardy and J. H. Shapiro, “Reflective ghost imaging through turbulence,” Phys. Rev. A 84, 063824 (2011).
[Crossref]

Heidmann, P.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
[Crossref]

Horowitz, M.

P. Sen, B. Chen, G. Garg, S. R. Marschner, M. Horowitz, M. Levoy, and H. P. A. Lensch, “Dual photography,” ACM Trans. Graph. 24, 745 (2005).
[Crossref]

Kane, C.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[Crossref]

Katz, O.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
[Crossref]

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (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, 83–91 (2008).
[Crossref]

Krogstad, M.

P. Zerom, Z. Shi, M. N. O’Sullivan, K. W. C. Chan, M. Krogstad, J. H. Shapiro, and R. W. Boyd, “Thermal ghost imaging with averaged speckle patterns,” Phys. Rev. A 86, 063817 (2012).
[Crossref]

Lagendijk, A.

J. Bertolotti, E. van Putten, C. Blum, A. Lagendijk, W. Vos, and A. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

J. F. de Boer, M. P. van Albada, and A. Lagendijk, “Transmission and intensity correlations in wave propagation through random media,” Phys. Rev. B 45, 658–666 (1992).
[Crossref]

M. van Albada, J. De Boer, and A. Lagendijk, “Observation of long-range intensity correlation in the transport of coherent light through a random medium,” Phys. Rev. Lett. 64, 2787–2790 (1990).
[Crossref]

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, 83–91 (2008).
[Crossref]

Lee, P. A.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[Crossref]

Lensch, H. P. A.

P. Sen, B. Chen, G. Garg, S. R. Marschner, M. Horowitz, M. Levoy, and H. P. A. Lensch, “Dual photography,” ACM Trans. Graph. 24, 745 (2005).
[Crossref]

Levoy, M.

P. Sen, B. Chen, G. Garg, S. R. Marschner, M. Horowitz, M. Levoy, and H. P. A. Lensch, “Dual photography,” ACM Trans. Graph. 24, 745 (2005).
[Crossref]

Lugiato, L. A.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110, 083901 (2013).
[Crossref]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[Crossref]

Magatti, D.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110, 083901 (2013).
[Crossref]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[Crossref]

Marschner, S. R.

P. Sen, B. Chen, G. Garg, S. R. Marschner, M. Horowitz, M. Levoy, and H. P. A. Lensch, “Dual photography,” ACM Trans. Graph. 24, 745 (2005).
[Crossref]

Molteni, M.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110, 083901 (2013).
[Crossref]

Mosk, A.

J. Bertolotti, E. van Putten, C. Blum, A. Lagendijk, W. Vos, and A. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

Nieuwenhuizen, T. M.

M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
[Crossref]

O’Sullivan, M. N.

P. Zerom, Z. Shi, M. N. O’Sullivan, K. W. C. Chan, M. Krogstad, J. H. Shapiro, and R. W. Boyd, “Thermal ghost imaging with averaged speckle patterns,” Phys. Rev. A 86, 063817 (2012).
[Crossref]

Padgett, M. J.

D. B. Phillips, M.-J. Sun, J. M. Taylor, M. P. Edgar, S. M. Barnett, G. M. Gibson, and M. J. Padgett, “Adaptive foveated single-pixel imaging with dynamic supersampling,” Sci. Adv. 3, e1601782 (2017).
[Crossref]

M. J. Padgett and R. W. Boyd, “An introduction to ghost imaging: quantum and classical,” Philos. Trans. R. Soc. A 375, 20160233 (2017).
[Crossref]

R. S. Aspden, D. S. Tasca, R. W. Boyd, and M. J. Padgett, “EPR-based ghost imaging using a single-photon-sensitive camera,” New J. Phys. 15, 073032 (2013).
[Crossref]

Padilla, W. J.

Paniagua-Diaz, A. M.

I. Starshynov, A. M. Paniagua-Diaz, N. Fayard, A. Goetschy, R. Pierrat, R. Carminati, and J. Bertolotti, “Non-Gaussian correlations between reflected and transmitted intensity patterns emerging from opaque disordered media,” Phys. Rev. X 8, 021041 (2018).
[Crossref]

Phillips, D. B.

D. B. Phillips, M.-J. Sun, J. M. Taylor, M. P. Edgar, S. M. Barnett, G. M. Gibson, and M. J. Padgett, “Adaptive foveated single-pixel imaging with dynamic supersampling,” Sci. Adv. 3, e1601782 (2017).
[Crossref]

Pierrat, R.

I. Starshynov, A. M. Paniagua-Diaz, N. Fayard, A. Goetschy, R. Pierrat, R. Carminati, and J. Bertolotti, “Non-Gaussian correlations between reflected and transmitted intensity patterns emerging from opaque disordered media,” Phys. Rev. X 8, 021041 (2018).
[Crossref]

N. Fayard, A. Goetschy, R. Pierrat, and R. Carminati, “Mutual information between reflected and transmitted speckle images,” Phys. Rev. Lett. 120, 073901 (2018).
[Crossref]

N. Fayard, A. Cazé, R. Pierrat, and R. Carminati, “Intensity correlations between reflected and transmitted speckle patterns,” Phys. Rev. A 92, 033827 (2015).
[Crossref]

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, R3429–R3432 (1995).
[Crossref]

Pnini, R.

R. Pnini and B. Shapiro, “Fluctuations in transmission of waves through disordered slabs,” Phys. Rev. B 39, 6986–6994 (1989).
[Crossref]

Polkosnik, W.

A. Z. Genack, N. Garcia, and W. Polkosnik, “Long-range intensity correlation in random media,” Phys. Rev. Lett. 65, 2129–2132 (1990).
[Crossref]

Rogozkin, D. B.

D. B. Rogozkin and M. Y. Cherkasov, “Long-range intensity correlations in wave reflection from a disordered medium,” Phys. Rev. B 51, 12256–12267 (1995).
[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, 167–170 (2016).
[Crossref]

Sáenz, J.

L. Froufe-Perez, A. Garcia-Martin, G. Cwilich, and J. Sáenz, “Fluctuations and correlations in wave transport through complex media,” Physica A 386, 625–632 (2007).
[Crossref]

Sen, P.

P. Sen, B. Chen, G. Garg, S. R. Marschner, M. Horowitz, M. Levoy, and H. P. A. Lensch, “Dual photography,” ACM Trans. Graph. 24, 745 (2005).
[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, R3429–R3432 (1995).
[Crossref]

Shapiro, B.

R. Pnini and B. Shapiro, “Fluctuations in transmission of waves through disordered slabs,” Phys. Rev. B 39, 6986–6994 (1989).
[Crossref]

Shapiro, J. H.

P. Zerom, Z. Shi, M. N. O’Sullivan, K. W. C. Chan, M. Krogstad, J. H. Shapiro, and R. W. Boyd, “Thermal ghost imaging with averaged speckle patterns,” Phys. Rev. A 86, 063817 (2012).
[Crossref]

N. D. Hardy and J. H. Shapiro, “Reflective ghost imaging through turbulence,” Phys. Rev. A 84, 063824 (2011).
[Crossref]

Shi, Z.

P. Zerom, Z. Shi, M. N. O’Sullivan, K. W. C. Chan, M. Krogstad, J. H. Shapiro, and R. W. Boyd, “Thermal ghost imaging with averaged speckle patterns,” Phys. Rev. A 86, 063817 (2012).
[Crossref]

Shih, Y. H.

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, R3429–R3432 (1995).
[Crossref]

Shrekenhamer, D.

Silberberg, Y.

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

Spivak, B. Z.

A. U. Zyuzin and B. Z. Spivak, “Langevin description of mesoscopic fluctuations in disordered media,” JETP Lett. 66, 560–566 (1987).

Starshynov, I.

I. Starshynov, A. M. Paniagua-Diaz, N. Fayard, A. Goetschy, R. Pierrat, R. Carminati, and J. Bertolotti, “Non-Gaussian correlations between reflected and transmitted intensity patterns emerging from opaque disordered media,” Phys. Rev. X 8, 021041 (2018).
[Crossref]

Stephen, M. J.

M. J. Stephen and G. Cwilich, “Intensity correlation functions and fluctuations in light scattered from a random medium,” Phys. Rev. Lett. 59, 285–287 (1987).
[Crossref]

Stone, A. D.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[Crossref]

Strekalov, D. 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, R3429–R3432 (1995).
[Crossref]

Sun, M.-J.

D. B. Phillips, M.-J. Sun, J. M. Taylor, M. P. Edgar, S. M. Barnett, G. M. Gibson, and M. J. Padgett, “Adaptive foveated single-pixel imaging with dynamic supersampling,” Sci. Adv. 3, e1601782 (2017).
[Crossref]

Sun, T.

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, 83–91 (2008).
[Crossref]

Takhar, D.

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, 83–91 (2008).
[Crossref]

Tasca, D. S.

R. S. Aspden, D. S. Tasca, R. W. Boyd, and M. J. Padgett, “EPR-based ghost imaging using a single-photon-sensitive camera,” New J. Phys. 15, 073032 (2013).
[Crossref]

Taylor, J. M.

D. B. Phillips, M.-J. Sun, J. M. Taylor, M. P. Edgar, S. M. Barnett, G. M. Gibson, and M. J. Padgett, “Adaptive foveated single-pixel imaging with dynamic supersampling,” Sci. Adv. 3, e1601782 (2017).
[Crossref]

van Albada, M.

M. van Albada, J. De Boer, and A. Lagendijk, “Observation of long-range intensity correlation in the transport of coherent light through a random medium,” Phys. Rev. Lett. 64, 2787–2790 (1990).
[Crossref]

van Albada, M. P.

J. F. de Boer, M. P. van Albada, and A. Lagendijk, “Transmission and intensity correlations in wave propagation through random media,” Phys. Rev. B 45, 658–666 (1992).
[Crossref]

van Putten, E.

J. Bertolotti, E. van Putten, C. Blum, A. Lagendijk, W. Vos, and A. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

van Rossum, M. C. W.

M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
[Crossref]

Vos, W.

J. Bertolotti, E. van Putten, C. Blum, A. Lagendijk, W. Vos, and A. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

Watts, C. M.

Yodh, A. G.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
[Crossref]

Zerom, P.

P. Zerom, Z. Shi, M. N. O’Sullivan, K. W. C. Chan, M. Krogstad, J. H. Shapiro, and R. W. Boyd, “Thermal ghost imaging with averaged speckle patterns,” Phys. Rev. A 86, 063817 (2012).
[Crossref]

Zyuzin, A. U.

A. U. Zyuzin and B. Z. Spivak, “Langevin description of mesoscopic fluctuations in disordered media,” JETP Lett. 66, 560–566 (1987).

ACM Trans. Graph. (1)

P. Sen, B. Chen, G. Garg, S. R. Marschner, M. Horowitz, M. Levoy, and H. P. A. Lensch, “Dual photography,” ACM Trans. Graph. 24, 745 (2005).
[Crossref]

Appl. Phys. Lett. (1)

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

IEEE Signal Process. Mag. (1)

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, 83–91 (2008).
[Crossref]

JETP Lett. (1)

A. U. Zyuzin and B. Z. Spivak, “Langevin description of mesoscopic fluctuations in disordered media,” JETP Lett. 66, 560–566 (1987).

Nat. Photonics (2)

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
[Crossref]

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

Nature (1)

J. Bertolotti, E. van Putten, C. Blum, A. Lagendijk, W. Vos, and A. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

New J. Phys. (1)

R. S. Aspden, D. S. Tasca, R. W. Boyd, and M. J. Padgett, “EPR-based ghost imaging using a single-photon-sensitive camera,” New J. Phys. 15, 073032 (2013).
[Crossref]

Opt. Express (1)

Philos. Trans. R. Soc. A (1)

M. J. Padgett and R. W. Boyd, “An introduction to ghost imaging: quantum and classical,” Philos. Trans. R. Soc. A 375, 20160233 (2017).
[Crossref]

Phys. Rev. A (4)

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, R3429–R3432 (1995).
[Crossref]

P. Zerom, Z. Shi, M. N. O’Sullivan, K. W. C. Chan, M. Krogstad, J. H. Shapiro, and R. W. Boyd, “Thermal ghost imaging with averaged speckle patterns,” Phys. Rev. A 86, 063817 (2012).
[Crossref]

N. Fayard, A. Cazé, R. Pierrat, and R. Carminati, “Intensity correlations between reflected and transmitted speckle patterns,” Phys. Rev. A 92, 033827 (2015).
[Crossref]

N. D. Hardy and J. H. Shapiro, “Reflective ghost imaging through turbulence,” Phys. Rev. A 84, 063824 (2011).
[Crossref]

Phys. Rev. B (3)

R. Pnini and B. Shapiro, “Fluctuations in transmission of waves through disordered slabs,” Phys. Rev. B 39, 6986–6994 (1989).
[Crossref]

J. F. de Boer, M. P. van Albada, and A. Lagendijk, “Transmission and intensity correlations in wave propagation through random media,” Phys. Rev. B 45, 658–666 (1992).
[Crossref]

D. B. Rogozkin and M. Y. Cherkasov, “Long-range intensity correlations in wave reflection from a disordered medium,” Phys. Rev. B 51, 12256–12267 (1995).
[Crossref]

Phys. Rev. Lett. (8)

M. van Albada, J. De Boer, and A. Lagendijk, “Observation of long-range intensity correlation in the transport of coherent light through a random medium,” Phys. Rev. Lett. 64, 2787–2790 (1990).
[Crossref]

A. Z. Genack, N. Garcia, and W. Polkosnik, “Long-range intensity correlation in random media,” Phys. Rev. Lett. 65, 2129–2132 (1990).
[Crossref]

N. Fayard, A. Goetschy, R. Pierrat, and R. Carminati, “Mutual information between reflected and transmitted speckle images,” Phys. Rev. Lett. 120, 073901 (2018).
[Crossref]

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110, 083901 (2013).
[Crossref]

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[Crossref]

M. J. Stephen and G. Cwilich, “Intensity correlation functions and fluctuations in light scattered from a random medium,” Phys. Rev. Lett. 59, 285–287 (1987).
[Crossref]

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Two-photon coincidence imaging with a classical source,” Phys. Rev. Lett. 89, 113601 (2002).
[Crossref]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[Crossref]

Phys. Rev. X (1)

I. Starshynov, A. M. Paniagua-Diaz, N. Fayard, A. Goetschy, R. Pierrat, R. Carminati, and J. Bertolotti, “Non-Gaussian correlations between reflected and transmitted intensity patterns emerging from opaque disordered media,” Phys. Rev. X 8, 021041 (2018).
[Crossref]

Physica A (1)

L. Froufe-Perez, A. Garcia-Martin, G. Cwilich, and J. Sáenz, “Fluctuations and correlations in wave transport through complex media,” Physica A 386, 625–632 (2007).
[Crossref]

Rep. Prog. Phys. (1)

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
[Crossref]

Rev. Mod. Phys. (1)

M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
[Crossref]

Sci. Adv. (1)

D. B. Phillips, M.-J. Sun, J. M. Taylor, M. P. Edgar, S. M. Barnett, G. M. Gibson, and M. J. Padgett, “Adaptive foveated single-pixel imaging with dynamic supersampling,” Sci. Adv. 3, e1601782 (2017).
[Crossref]

Other (1)

University of Exeter, Open Research Exeter (ORE), https://doi.org/10.24378/exe.1224 .

Supplementary Material (1)

NameDescription
» Supplement 1       Supplemental theory and experimental methods

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Figures (4)

Fig. 1.
Fig. 1. (a) Experimental apparatus. A cw laser illuminates an opaque scattering material and an object hidden behind (insets). An imaging system records the reflected speckle pattern from the surface of the scattering sample and a bucket detector collects the intensity transmitted by the object. (b) Elements 5 and 6 of Group 4 of the resolution target used as object to image in this experiment, highlighted by the pink square in the inset of panel (a). (c) Typical speckle pattern collected in reflection with the imaging system presented. (d) Retrieved image using BGI with 2.27 × 10 6 disorder realizations.
Fig. 2.
Fig. 2. (a) Experimental apparatus used for noninvasive BGI. A 450 nm laser is incident on the scattering sample at 45 ° . The resolution target is placed on the back surface of the scattering material, and right behind it we have a fluorescent layer (cerium-doped YAG), acting as a fluorescent object. The bucket detector is in this case also in reflection from the sample, filtering the fluorescent light with a 500 nm long pass filter. (b) Elements 5 and 6 of Group 4 of the resolution target used as the object, and the image retrieved using BGI with 4 × 10 6 disorder realizations. (c) Object representing Groups 5, 6, and 7 from the resolution target, and the image retrieved using BGI with 1.5 × 10 6 disorder realizations.
Fig. 3.
Fig. 3. (a) Two-dimensional (2D) map and a 1D cross section along Δ y = 0 of the averaged correlation between the transmitted and reflected speckle patterns. (b) and (c) Expected images obtained by numerically convolving the objects shown in Figs. 2(b) and 2(c) with the correlation function shown in (a).
Fig. 4.
Fig. 4. (a) and (b) Correlation functions between the reflected and transmitted speckle patterns measured 80 μm and 160 μm, respectively, away from the transmission and reflection surfaces. (c) Object separated by a cover slip of 150 μm from the scattering medium and retrieved image using BGI with 5.65 × 10 5 disorder realizations.

Equations (2)

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I ˜ ( r ) = i = 1 N b i R i ( r ) .
I ˜ ( r ) = O ( r ) T ( r ) R ( r ) d r = O ( r ) T ( r ) R ( r ) d r = T R [ O * C R T + O ( r ) d r ] O * C RT + A ,

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