Abstract

The survival of time-reversal symmetry in the presence of strong multiple scattering lies at the heart of some of the most robust interference effects of light in complex media. Here, the use of time-reversed light paths for imaging in highly scattering environments is investigated. A common-path Sagnac interferometer is constructed that is able to detect objects behind a layer of strongly scattering material at up to 14 mean free paths of total attenuation length. A spatial offset between the two light paths is used to suppress non-specific scattering contributions, limiting the signal to the volume of overlap. Scaling of the specific signal intensity indicates a transition from ballistic to quasi-ballistic contributions as the scattering thickness is increased. The characteristic frequency dependence for the coherent modulation signal provides a path length dependent signature, while the spatial overlap requirement allows for short-range 3D imaging. The technique of common-path, bistatic interferometry offers a conceptually novel approach that could open new applications in diverse areas such as medical imaging, machine vision, sensors, and lidar.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Full Article  |  PDF Article
OSA Recommended Articles
Quasi-ballistic imaging through a dynamic scattering medium with optical-field averaging using Spectral-Ballistic-Imaging

Er’el Granot, Shmuel Sternklar, Yossi Ben-Aderet, and Dan Schermann
Opt. Express 14(19) 8598-8603 (2006)

Single-shot, two-dimensional ballistic imaging through scattering media

Megan Paciaroni and Mark Linne
Appl. Opt. 43(26) 5100-5109 (2004)

Ballistic imaging through an intense scattering medium using a supercontinuum with a roundabout spatial gate

Yipeng Zheng, Wenjiang Tan, Xiaojing Liu, and Junyi Tong
Opt. Express 25(17) 20431-20436 (2017)

References

  • View by:
  • |
  • |
  • |

  1. G. Berkovic and E. Shafir, “Optical methods for distance and displacement measurements,” Adv. Opt. Photonics 4(4), 441–471 (2012).
    [Crossref]
  2. C. Dunsby and P. M. W. French, “Techniques for depth-resolved imaging through turbid media including coherence-gated imaging,” J. Phys. D: Appl. Phys. 36(14), R207–R227 (2003).
    [Crossref]
  3. R. Tobin, A. Halimi, A. McCarthy, M. Laurenzis, F. Christnacher, and G. S. Buller, “Three-dimensional single-photon imaging through obscurants,” Opt. Express 27(4), 4590–4611 (2019).
    [Crossref]
  4. P. Feneyrou, L. Leviandier, J. Minet, G. Pillet, A. Martin, D. Dolfi, J.-P. Schlotterbeck, P. Rondeau, X. Lacondemine, A. Rieu, and T. Midavaine, “Frequency-modulated multifunction LiDAR for anemometry, range finding, and velocimetry-1. Theory and signal processing,” Appl. Opt. 56(35), 9663–9675 (2017).
    [Crossref]
  5. A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003).
    [Crossref]
  6. V. Duc Nguyen, D. J. Faber, E. Van Der Pol, T. G. Van Leeuwen, and J. Kalkman, “Dependent and multiple scattering in transmission and backscattering optical coherence tomography,” Opt. Express 21(24), 29145–29156 (2013).
    [Crossref]
  7. K. Yoo and R. R. Alfano, “Time-resolved coherent and incoherent components of forward light scattering in random media,” Opt. Lett. 15(6), 320–322 (1990).
    [Crossref]
  8. L. Wang, P. Ho, C. Liu, G. Zhang, and R. Alfano, “Ballistic 2-d imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253(5021), 769–771 (1991).
    [Crossref]
  9. Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2(2), 110–115 (2008).
    [Crossref]
  10. S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
    [Crossref]
  11. J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
    [Crossref]
  12. O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6(8), 549–553 (2012).
    [Crossref]
  13. A. V. Kanaev, A. T. Watnik, D. F. Gardner, C. Metzler, K. P. Judd, P. Lebow, K. M. Novak, and J. R. Lindle, “Imaging through extreme scattering in extended dynamic media,” Opt. Lett. 43(13), 3088–3091 (2018).
    [Crossref]
  14. A. Badon, D. Li, G. Lerosey, A. C. Boccara, M. Fink, and A. Aubry, “Smart optical coherence tomography for ultra-deep imaging through highly scattering media,” Sci. Adv. 2(11), e1600370 (2016).
    [Crossref]
  15. O. Tzang, E. Niv, S. Singh, S. Labouesse, G. Myatt, and R. Piestun, “Wavefront shaping in complex media with a 350 kHz modulator via a 1D-to-2D transform,” Nat. Photonics 13(11), 788–793 (2019).
    [Crossref]
  16. P. Matousek, I. P. Clark, E. R. C. Draper, M. D. Morris, A. E. Goodship N. Everall, M. Towrie, W. F. Finney, and A. W. Parker, “Subsurface probing in diffusely scattering media using spatially offset Raman spectroscopy,” Appl. Spectrosc. 59(4), 393–400 (2005).
    [Crossref]
  17. M. Chen, J. Mas, L. H. Forbes, M. R. Andrews, and K. Dholakia, “Depth-resolved multimodal imaging: Wavelength modulated spatially offset Raman spectroscopy with optical coherence tomography,” J. Biophotonics 11(1), e201700129 (2018).
    [Crossref]
  18. T. E. Matthews, M. Medina, J. R. Maher, H. Levinson, W. J. Brown, and A. Wax, “Deep tissue imaging using spectroscopic analysis of multiply scattered light,” Optica 1(2), 105–111 (2014).
    [Crossref]
  19. Y. Zhao, W. J. Eldridge, J. R. Maher, S. Kim, M. Crose, M. Ibrahim, H. Levinson, and A. Wax, “Dual-axis optical coherence tomography for deep tissue imaging,” Opt. Lett. 42(12), 2302–2305 (2017).
    [Crossref]
  20. J. E. Barnes, N. C. P. Sharma, and T. B. Kaplan, “Atmospheric aerosol profiling with a bistatic imaging lidar system,” Appl. Opt. 46(15), 2922–2929 (2007).
    [Crossref]
  21. M. P. Van Albada and A. Lagendijk, “Observation of Weak Localization of Light in a Random Medium,” Phys. Rev. Lett. 55(24), 2692–2695 (1985).
    [Crossref]
  22. P.-E. Wolf and G. Maret, “Weak Localization and Coherent Backscattering of Photons in Disordered Media,” Phys. Rev. Lett. 55(24), 2696–2699 (1985).
    [Crossref]
  23. N. N. Boustany, S. A. Boppart, and V. Backman, “Microscopic Imaging and Spectroscopy with Scattered Light,” Annu. Rev. Biomed. Eng. 12(1), 285–314 (2010).
    [Crossref]
  24. Y. L. Kim, Y. Liu, V. M. Turzhitsky, H. K. Roy, R. K. Wali, H. Subramanian, P. Pradhan, and V. Backman, “Low-coherence enhanced backscattering: review of principles and applications for colon cancer screening,” J. Biomed. Opt. 11(4), 041125 (2006).
    [Crossref]
  25. G. Sagnac, “L’éther lumineux démontré par l’effet du vent relatif d’éther dans un interféromètre en rotation uniforme,” C. R. Hebd. Seances Acad. Sci. 157, 708–710 (1913).
  26. V. Vali and R. W. Shorthill, “Fiber Ring Interferometer,” Appl. Opt. 15(5), 1099–1100 (1976).
    [Crossref]
  27. W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
    [Crossref]
  28. D. H. Hurley and O. B. Wright, “Detection of ultrafast phenomena by use of a modified Sagnac interferometer,” Opt. Lett. 24(18), 1305–1307 (1999).
    [Crossref]
  29. Y. Sugawara, O. B. Wright, O. Matsuda, M. Takigahira, Y. Tanaka, S. Tamura, and V. E. Gusev, “Watching ripples on crystals,” Phys. Rev. Lett. 88(18), 185504 (2002).
    [Crossref]
  30. K.-X. Sun, M. M. Fejer, E. Gustafson, and R. L. Byer, “Sagnac Interferometer for Gravitational-Wave Detection,” Phys. Rev. Lett. 76(17), 3053–3056 (1996).
    [Crossref]
  31. T. L. Beach and R. V. E. Lovelace, “Diffraction by a sinusoidal phase screen,” Radio Sci. 32(3), 913–921 (1997).
    [Crossref]
  32. R. A. Bergh, H. C. Lefevre, and H. J. Shaw, “All-single-mode fiber-optic gyroscope with long-term stability,” Opt. Lett. 6(10), 502–504 (1981).
    [Crossref]
  33. G. B. Malykin and E. G. Malykin, “On Possibility of Using the Lowest Odd Harmonics of the Phase Modulation Frequency in the Output Signal of the Fiber-Optic Ring Interferometer for Detection of the Sagnac Effect,” Opt. Spectrosc. 105(1), 117–123 (2008).
    [Crossref]
  34. D. S. Wiersma, A. Muzzi, M. Colocci, and R. Righini, “Time-resolved experiments on light diffusion in anisotropic random media,” Phys. Rev. E 62(5), 6681–6687 (2000).
    [Crossref]

2019 (2)

R. Tobin, A. Halimi, A. McCarthy, M. Laurenzis, F. Christnacher, and G. S. Buller, “Three-dimensional single-photon imaging through obscurants,” Opt. Express 27(4), 4590–4611 (2019).
[Crossref]

O. Tzang, E. Niv, S. Singh, S. Labouesse, G. Myatt, and R. Piestun, “Wavefront shaping in complex media with a 350 kHz modulator via a 1D-to-2D transform,” Nat. Photonics 13(11), 788–793 (2019).
[Crossref]

2018 (2)

M. Chen, J. Mas, L. H. Forbes, M. R. Andrews, and K. Dholakia, “Depth-resolved multimodal imaging: Wavelength modulated spatially offset Raman spectroscopy with optical coherence tomography,” J. Biophotonics 11(1), e201700129 (2018).
[Crossref]

A. V. Kanaev, A. T. Watnik, D. F. Gardner, C. Metzler, K. P. Judd, P. Lebow, K. M. Novak, and J. R. Lindle, “Imaging through extreme scattering in extended dynamic media,” Opt. Lett. 43(13), 3088–3091 (2018).
[Crossref]

2017 (2)

2016 (1)

A. Badon, D. Li, G. Lerosey, A. C. Boccara, M. Fink, and A. Aubry, “Smart optical coherence tomography for ultra-deep imaging through highly scattering media,” Sci. Adv. 2(11), e1600370 (2016).
[Crossref]

2014 (1)

2013 (1)

2012 (3)

G. Berkovic and E. Shafir, “Optical methods for distance and displacement measurements,” Adv. Opt. Photonics 4(4), 441–471 (2012).
[Crossref]

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6(8), 549–553 (2012).
[Crossref]

2010 (2)

N. N. Boustany, S. A. Boppart, and V. Backman, “Microscopic Imaging and Spectroscopy with Scattered Light,” Annu. Rev. Biomed. Eng. 12(1), 285–314 (2010).
[Crossref]

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

2008 (2)

G. B. Malykin and E. G. Malykin, “On Possibility of Using the Lowest Odd Harmonics of the Phase Modulation Frequency in the Output Signal of the Fiber-Optic Ring Interferometer for Detection of the Sagnac Effect,” Opt. Spectrosc. 105(1), 117–123 (2008).
[Crossref]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2(2), 110–115 (2008).
[Crossref]

2007 (1)

2006 (1)

Y. L. Kim, Y. Liu, V. M. Turzhitsky, H. K. Roy, R. K. Wali, H. Subramanian, P. Pradhan, and V. Backman, “Low-coherence enhanced backscattering: review of principles and applications for colon cancer screening,” J. Biomed. Opt. 11(4), 041125 (2006).
[Crossref]

2005 (1)

2003 (2)

C. Dunsby and P. M. W. French, “Techniques for depth-resolved imaging through turbid media including coherence-gated imaging,” J. Phys. D: Appl. Phys. 36(14), R207–R227 (2003).
[Crossref]

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003).
[Crossref]

2002 (1)

Y. Sugawara, O. B. Wright, O. Matsuda, M. Takigahira, Y. Tanaka, S. Tamura, and V. E. Gusev, “Watching ripples on crystals,” Phys. Rev. Lett. 88(18), 185504 (2002).
[Crossref]

2000 (1)

D. S. Wiersma, A. Muzzi, M. Colocci, and R. Righini, “Time-resolved experiments on light diffusion in anisotropic random media,” Phys. Rev. E 62(5), 6681–6687 (2000).
[Crossref]

1999 (1)

1997 (1)

T. L. Beach and R. V. E. Lovelace, “Diffraction by a sinusoidal phase screen,” Radio Sci. 32(3), 913–921 (1997).
[Crossref]

1996 (1)

K.-X. Sun, M. M. Fejer, E. Gustafson, and R. L. Byer, “Sagnac Interferometer for Gravitational-Wave Detection,” Phys. Rev. Lett. 76(17), 3053–3056 (1996).
[Crossref]

1991 (1)

L. Wang, P. Ho, C. Liu, G. Zhang, and R. Alfano, “Ballistic 2-d imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253(5021), 769–771 (1991).
[Crossref]

1990 (1)

1985 (3)

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

M. P. Van Albada and A. Lagendijk, “Observation of Weak Localization of Light in a Random Medium,” Phys. Rev. Lett. 55(24), 2692–2695 (1985).
[Crossref]

P.-E. Wolf and G. Maret, “Weak Localization and Coherent Backscattering of Photons in Disordered Media,” Phys. Rev. Lett. 55(24), 2696–2699 (1985).
[Crossref]

1981 (1)

1976 (1)

1913 (1)

G. Sagnac, “L’éther lumineux démontré par l’effet du vent relatif d’éther dans un interféromètre en rotation uniforme,” C. R. Hebd. Seances Acad. Sci. 157, 708–710 (1913).

Alfano, R.

L. Wang, P. Ho, C. Liu, G. Zhang, and R. Alfano, “Ballistic 2-d imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253(5021), 769–771 (1991).
[Crossref]

Alfano, R. R.

Andrews, M. R.

M. Chen, J. Mas, L. H. Forbes, M. R. Andrews, and K. Dholakia, “Depth-resolved multimodal imaging: Wavelength modulated spatially offset Raman spectroscopy with optical coherence tomography,” J. Biophotonics 11(1), e201700129 (2018).
[Crossref]

Aubry, A.

A. Badon, D. Li, G. Lerosey, A. C. Boccara, M. Fink, and A. Aubry, “Smart optical coherence tomography for ultra-deep imaging through highly scattering media,” Sci. Adv. 2(11), e1600370 (2016).
[Crossref]

Backman, V.

N. N. Boustany, S. A. Boppart, and V. Backman, “Microscopic Imaging and Spectroscopy with Scattered Light,” Annu. Rev. Biomed. Eng. 12(1), 285–314 (2010).
[Crossref]

Y. L. Kim, Y. Liu, V. M. Turzhitsky, H. K. Roy, R. K. Wali, H. Subramanian, P. Pradhan, and V. Backman, “Low-coherence enhanced backscattering: review of principles and applications for colon cancer screening,” J. Biomed. Opt. 11(4), 041125 (2006).
[Crossref]

Badon, A.

A. Badon, D. Li, G. Lerosey, A. C. Boccara, M. Fink, and A. Aubry, “Smart optical coherence tomography for ultra-deep imaging through highly scattering media,” Sci. Adv. 2(11), e1600370 (2016).
[Crossref]

Barnes, J. E.

Beach, T. L.

T. L. Beach and R. V. E. Lovelace, “Diffraction by a sinusoidal phase screen,” Radio Sci. 32(3), 913–921 (1997).
[Crossref]

Bergh, R. A.

Berkovic, G.

G. Berkovic and E. Shafir, “Optical methods for distance and displacement measurements,” Adv. Opt. Photonics 4(4), 441–471 (2012).
[Crossref]

Bertolotti, J.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Blum, C.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Boccara, A.

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Boccara, A. C.

A. Badon, D. Li, G. Lerosey, A. C. Boccara, M. Fink, and A. Aubry, “Smart optical coherence tomography for ultra-deep imaging through highly scattering media,” Sci. Adv. 2(11), e1600370 (2016).
[Crossref]

Boppart, S. A.

N. N. Boustany, S. A. Boppart, and V. Backman, “Microscopic Imaging and Spectroscopy with Scattered Light,” Annu. Rev. Biomed. Eng. 12(1), 285–314 (2010).
[Crossref]

Boustany, N. N.

N. N. Boustany, S. A. Boppart, and V. Backman, “Microscopic Imaging and Spectroscopy with Scattered Light,” Annu. Rev. Biomed. Eng. 12(1), 285–314 (2010).
[Crossref]

Brown, W. J.

Buller, G. S.

Byer, R. L.

K.-X. Sun, M. M. Fejer, E. Gustafson, and R. L. Byer, “Sagnac Interferometer for Gravitational-Wave Detection,” Phys. Rev. Lett. 76(17), 3053–3056 (1996).
[Crossref]

Carminati, R.

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Chen, M.

M. Chen, J. Mas, L. H. Forbes, M. R. Andrews, and K. Dholakia, “Depth-resolved multimodal imaging: Wavelength modulated spatially offset Raman spectroscopy with optical coherence tomography,” J. Biophotonics 11(1), e201700129 (2018).
[Crossref]

Chow, W. W.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Christnacher, F.

Clark, I. P.

Colocci, M.

D. S. Wiersma, A. Muzzi, M. Colocci, and R. Righini, “Time-resolved experiments on light diffusion in anisotropic random media,” Phys. Rev. E 62(5), 6681–6687 (2000).
[Crossref]

Crose, M.

Dholakia, K.

M. Chen, J. Mas, L. H. Forbes, M. R. Andrews, and K. Dholakia, “Depth-resolved multimodal imaging: Wavelength modulated spatially offset Raman spectroscopy with optical coherence tomography,” J. Biophotonics 11(1), e201700129 (2018).
[Crossref]

Dolfi, D.

Draper, E. R. C.

Drexler, W.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003).
[Crossref]

Duc Nguyen, V.

Dunsby, C.

C. Dunsby and P. M. W. French, “Techniques for depth-resolved imaging through turbid media including coherence-gated imaging,” J. Phys. D: Appl. Phys. 36(14), R207–R227 (2003).
[Crossref]

Eldridge, W. J.

Faber, D. J.

Fejer, M. M.

K.-X. Sun, M. M. Fejer, E. Gustafson, and R. L. Byer, “Sagnac Interferometer for Gravitational-Wave Detection,” Phys. Rev. Lett. 76(17), 3053–3056 (1996).
[Crossref]

Feld, M. S.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2(2), 110–115 (2008).
[Crossref]

Feneyrou, P.

Fercher, A. F.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003).
[Crossref]

Fink, M.

A. Badon, D. Li, G. Lerosey, A. C. Boccara, M. Fink, and A. Aubry, “Smart optical coherence tomography for ultra-deep imaging through highly scattering media,” Sci. Adv. 2(11), e1600370 (2016).
[Crossref]

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Finney, W. F.

Forbes, L. H.

M. Chen, J. Mas, L. H. Forbes, M. R. Andrews, and K. Dholakia, “Depth-resolved multimodal imaging: Wavelength modulated spatially offset Raman spectroscopy with optical coherence tomography,” J. Biophotonics 11(1), e201700129 (2018).
[Crossref]

French, P. M. W.

C. Dunsby and P. M. W. French, “Techniques for depth-resolved imaging through turbid media including coherence-gated imaging,” J. Phys. D: Appl. Phys. 36(14), R207–R227 (2003).
[Crossref]

Gardner, D. F.

Gea-Banacloche, J.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Gigan, S.

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Goodship N. Everall, A. E.

Gusev, V. E.

Y. Sugawara, O. B. Wright, O. Matsuda, M. Takigahira, Y. Tanaka, S. Tamura, and V. E. Gusev, “Watching ripples on crystals,” Phys. Rev. Lett. 88(18), 185504 (2002).
[Crossref]

Gustafson, E.

K.-X. Sun, M. M. Fejer, E. Gustafson, and R. L. Byer, “Sagnac Interferometer for Gravitational-Wave Detection,” Phys. Rev. Lett. 76(17), 3053–3056 (1996).
[Crossref]

Halimi, A.

Hitzenberger, C. K.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003).
[Crossref]

Ho, P.

L. Wang, P. Ho, C. Liu, G. Zhang, and R. Alfano, “Ballistic 2-d imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253(5021), 769–771 (1991).
[Crossref]

Hurley, D. H.

Ibrahim, M.

Judd, K. P.

Kalkman, J.

Kanaev, A. V.

Kaplan, T. B.

Katz, O.

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6(8), 549–553 (2012).
[Crossref]

Kim, S.

Kim, Y. L.

Y. L. Kim, Y. Liu, V. M. Turzhitsky, H. K. Roy, R. K. Wali, H. Subramanian, P. Pradhan, and V. Backman, “Low-coherence enhanced backscattering: review of principles and applications for colon cancer screening,” J. Biomed. Opt. 11(4), 041125 (2006).
[Crossref]

Labouesse, S.

O. Tzang, E. Niv, S. Singh, S. Labouesse, G. Myatt, and R. Piestun, “Wavefront shaping in complex media with a 350 kHz modulator via a 1D-to-2D transform,” Nat. Photonics 13(11), 788–793 (2019).
[Crossref]

Lacondemine, X.

Lagendijk, A.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

M. P. Van Albada and A. Lagendijk, “Observation of Weak Localization of Light in a Random Medium,” Phys. Rev. Lett. 55(24), 2692–2695 (1985).
[Crossref]

Lasser, T.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003).
[Crossref]

Laurenzis, M.

Lebow, P.

Lefevre, H. C.

Lerosey, G.

A. Badon, D. Li, G. Lerosey, A. C. Boccara, M. Fink, and A. Aubry, “Smart optical coherence tomography for ultra-deep imaging through highly scattering media,” Sci. Adv. 2(11), e1600370 (2016).
[Crossref]

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Leviandier, L.

Levinson, H.

Li, D.

A. Badon, D. Li, G. Lerosey, A. C. Boccara, M. Fink, and A. Aubry, “Smart optical coherence tomography for ultra-deep imaging through highly scattering media,” Sci. Adv. 2(11), e1600370 (2016).
[Crossref]

Lindle, J. R.

Liu, C.

L. Wang, P. Ho, C. Liu, G. Zhang, and R. Alfano, “Ballistic 2-d imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253(5021), 769–771 (1991).
[Crossref]

Liu, Y.

Y. L. Kim, Y. Liu, V. M. Turzhitsky, H. K. Roy, R. K. Wali, H. Subramanian, P. Pradhan, and V. Backman, “Low-coherence enhanced backscattering: review of principles and applications for colon cancer screening,” J. Biomed. Opt. 11(4), 041125 (2006).
[Crossref]

Lovelace, R. V. E.

T. L. Beach and R. V. E. Lovelace, “Diffraction by a sinusoidal phase screen,” Radio Sci. 32(3), 913–921 (1997).
[Crossref]

Maher, J. R.

Malykin, E. G.

G. B. Malykin and E. G. Malykin, “On Possibility of Using the Lowest Odd Harmonics of the Phase Modulation Frequency in the Output Signal of the Fiber-Optic Ring Interferometer for Detection of the Sagnac Effect,” Opt. Spectrosc. 105(1), 117–123 (2008).
[Crossref]

Malykin, G. B.

G. B. Malykin and E. G. Malykin, “On Possibility of Using the Lowest Odd Harmonics of the Phase Modulation Frequency in the Output Signal of the Fiber-Optic Ring Interferometer for Detection of the Sagnac Effect,” Opt. Spectrosc. 105(1), 117–123 (2008).
[Crossref]

Maret, G.

P.-E. Wolf and G. Maret, “Weak Localization and Coherent Backscattering of Photons in Disordered Media,” Phys. Rev. Lett. 55(24), 2696–2699 (1985).
[Crossref]

Martin, A.

Mas, J.

M. Chen, J. Mas, L. H. Forbes, M. R. Andrews, and K. Dholakia, “Depth-resolved multimodal imaging: Wavelength modulated spatially offset Raman spectroscopy with optical coherence tomography,” J. Biophotonics 11(1), e201700129 (2018).
[Crossref]

Matousek, P.

Matsuda, O.

Y. Sugawara, O. B. Wright, O. Matsuda, M. Takigahira, Y. Tanaka, S. Tamura, and V. E. Gusev, “Watching ripples on crystals,” Phys. Rev. Lett. 88(18), 185504 (2002).
[Crossref]

Matthews, T. E.

McCarthy, A.

Medina, M.

Metzler, C.

Midavaine, T.

Minet, J.

Morris, M. D.

Mosk, A. P.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Muzzi, A.

D. S. Wiersma, A. Muzzi, M. Colocci, and R. Righini, “Time-resolved experiments on light diffusion in anisotropic random media,” Phys. Rev. E 62(5), 6681–6687 (2000).
[Crossref]

Myatt, G.

O. Tzang, E. Niv, S. Singh, S. Labouesse, G. Myatt, and R. Piestun, “Wavefront shaping in complex media with a 350 kHz modulator via a 1D-to-2D transform,” Nat. Photonics 13(11), 788–793 (2019).
[Crossref]

Niv, E.

O. Tzang, E. Niv, S. Singh, S. Labouesse, G. Myatt, and R. Piestun, “Wavefront shaping in complex media with a 350 kHz modulator via a 1D-to-2D transform,” Nat. Photonics 13(11), 788–793 (2019).
[Crossref]

Novak, K. M.

Parker, A. W.

Pedrotti, L. M.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Piestun, R.

O. Tzang, E. Niv, S. Singh, S. Labouesse, G. Myatt, and R. Piestun, “Wavefront shaping in complex media with a 350 kHz modulator via a 1D-to-2D transform,” Nat. Photonics 13(11), 788–793 (2019).
[Crossref]

Pillet, G.

Popoff, S.

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Pradhan, P.

Y. L. Kim, Y. Liu, V. M. Turzhitsky, H. K. Roy, R. K. Wali, H. Subramanian, P. Pradhan, and V. Backman, “Low-coherence enhanced backscattering: review of principles and applications for colon cancer screening,” J. Biomed. Opt. 11(4), 041125 (2006).
[Crossref]

Psaltis, D.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2(2), 110–115 (2008).
[Crossref]

Rieu, A.

Righini, R.

D. S. Wiersma, A. Muzzi, M. Colocci, and R. Righini, “Time-resolved experiments on light diffusion in anisotropic random media,” Phys. Rev. E 62(5), 6681–6687 (2000).
[Crossref]

Rondeau, P.

Roy, H. K.

Y. L. Kim, Y. Liu, V. M. Turzhitsky, H. K. Roy, R. K. Wali, H. Subramanian, P. Pradhan, and V. Backman, “Low-coherence enhanced backscattering: review of principles and applications for colon cancer screening,” J. Biomed. Opt. 11(4), 041125 (2006).
[Crossref]

Sagnac, G.

G. Sagnac, “L’éther lumineux démontré par l’effet du vent relatif d’éther dans un interféromètre en rotation uniforme,” C. R. Hebd. Seances Acad. Sci. 157, 708–710 (1913).

Sanders, V. E.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Schleich, W.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Schlotterbeck, J.-P.

Scully, M. O.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Shafir, E.

G. Berkovic and E. Shafir, “Optical methods for distance and displacement measurements,” Adv. Opt. Photonics 4(4), 441–471 (2012).
[Crossref]

Sharma, N. C. P.

Shaw, H. J.

Shorthill, R. W.

Silberberg, Y.

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6(8), 549–553 (2012).
[Crossref]

Singh, S.

O. Tzang, E. Niv, S. Singh, S. Labouesse, G. Myatt, and R. Piestun, “Wavefront shaping in complex media with a 350 kHz modulator via a 1D-to-2D transform,” Nat. Photonics 13(11), 788–793 (2019).
[Crossref]

Small, E.

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6(8), 549–553 (2012).
[Crossref]

Subramanian, H.

Y. L. Kim, Y. Liu, V. M. Turzhitsky, H. K. Roy, R. K. Wali, H. Subramanian, P. Pradhan, and V. Backman, “Low-coherence enhanced backscattering: review of principles and applications for colon cancer screening,” J. Biomed. Opt. 11(4), 041125 (2006).
[Crossref]

Sugawara, Y.

Y. Sugawara, O. B. Wright, O. Matsuda, M. Takigahira, Y. Tanaka, S. Tamura, and V. E. Gusev, “Watching ripples on crystals,” Phys. Rev. Lett. 88(18), 185504 (2002).
[Crossref]

Sun, K.-X.

K.-X. Sun, M. M. Fejer, E. Gustafson, and R. L. Byer, “Sagnac Interferometer for Gravitational-Wave Detection,” Phys. Rev. Lett. 76(17), 3053–3056 (1996).
[Crossref]

Takigahira, M.

Y. Sugawara, O. B. Wright, O. Matsuda, M. Takigahira, Y. Tanaka, S. Tamura, and V. E. Gusev, “Watching ripples on crystals,” Phys. Rev. Lett. 88(18), 185504 (2002).
[Crossref]

Tamura, S.

Y. Sugawara, O. B. Wright, O. Matsuda, M. Takigahira, Y. Tanaka, S. Tamura, and V. E. Gusev, “Watching ripples on crystals,” Phys. Rev. Lett. 88(18), 185504 (2002).
[Crossref]

Tanaka, Y.

Y. Sugawara, O. B. Wright, O. Matsuda, M. Takigahira, Y. Tanaka, S. Tamura, and V. E. Gusev, “Watching ripples on crystals,” Phys. Rev. Lett. 88(18), 185504 (2002).
[Crossref]

Tobin, R.

Towrie, M.

Turzhitsky, V. M.

Y. L. Kim, Y. Liu, V. M. Turzhitsky, H. K. Roy, R. K. Wali, H. Subramanian, P. Pradhan, and V. Backman, “Low-coherence enhanced backscattering: review of principles and applications for colon cancer screening,” J. Biomed. Opt. 11(4), 041125 (2006).
[Crossref]

Tzang, O.

O. Tzang, E. Niv, S. Singh, S. Labouesse, G. Myatt, and R. Piestun, “Wavefront shaping in complex media with a 350 kHz modulator via a 1D-to-2D transform,” Nat. Photonics 13(11), 788–793 (2019).
[Crossref]

Vali, V.

Van Albada, M. P.

M. P. Van Albada and A. Lagendijk, “Observation of Weak Localization of Light in a Random Medium,” Phys. Rev. Lett. 55(24), 2692–2695 (1985).
[Crossref]

Van Der Pol, E.

Van Leeuwen, T. G.

van Putten, E. G.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Vos, W. L.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Wali, R. K.

Y. L. Kim, Y. Liu, V. M. Turzhitsky, H. K. Roy, R. K. Wali, H. Subramanian, P. Pradhan, and V. Backman, “Low-coherence enhanced backscattering: review of principles and applications for colon cancer screening,” J. Biomed. Opt. 11(4), 041125 (2006).
[Crossref]

Wang, L.

L. Wang, P. Ho, C. Liu, G. Zhang, and R. Alfano, “Ballistic 2-d imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253(5021), 769–771 (1991).
[Crossref]

Watnik, A. T.

Wax, A.

Wiersma, D. S.

D. S. Wiersma, A. Muzzi, M. Colocci, and R. Righini, “Time-resolved experiments on light diffusion in anisotropic random media,” Phys. Rev. E 62(5), 6681–6687 (2000).
[Crossref]

Wolf, P.-E.

P.-E. Wolf and G. Maret, “Weak Localization and Coherent Backscattering of Photons in Disordered Media,” Phys. Rev. Lett. 55(24), 2696–2699 (1985).
[Crossref]

Wright, O. B.

Y. Sugawara, O. B. Wright, O. Matsuda, M. Takigahira, Y. Tanaka, S. Tamura, and V. E. Gusev, “Watching ripples on crystals,” Phys. Rev. Lett. 88(18), 185504 (2002).
[Crossref]

D. H. Hurley and O. B. Wright, “Detection of ultrafast phenomena by use of a modified Sagnac interferometer,” Opt. Lett. 24(18), 1305–1307 (1999).
[Crossref]

Yang, C.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2(2), 110–115 (2008).
[Crossref]

Yaqoob, Z.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2(2), 110–115 (2008).
[Crossref]

Yoo, K.

Zhang, G.

L. Wang, P. Ho, C. Liu, G. Zhang, and R. Alfano, “Ballistic 2-d imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253(5021), 769–771 (1991).
[Crossref]

Zhao, Y.

Adv. Opt. Photonics (1)

G. Berkovic and E. Shafir, “Optical methods for distance and displacement measurements,” Adv. Opt. Photonics 4(4), 441–471 (2012).
[Crossref]

Annu. Rev. Biomed. Eng. (1)

N. N. Boustany, S. A. Boppart, and V. Backman, “Microscopic Imaging and Spectroscopy with Scattered Light,” Annu. Rev. Biomed. Eng. 12(1), 285–314 (2010).
[Crossref]

Appl. Opt. (3)

Appl. Spectrosc. (1)

C. R. Hebd. Seances Acad. Sci. (1)

G. Sagnac, “L’éther lumineux démontré par l’effet du vent relatif d’éther dans un interféromètre en rotation uniforme,” C. R. Hebd. Seances Acad. Sci. 157, 708–710 (1913).

J. Biomed. Opt. (1)

Y. L. Kim, Y. Liu, V. M. Turzhitsky, H. K. Roy, R. K. Wali, H. Subramanian, P. Pradhan, and V. Backman, “Low-coherence enhanced backscattering: review of principles and applications for colon cancer screening,” J. Biomed. Opt. 11(4), 041125 (2006).
[Crossref]

J. Biophotonics (1)

M. Chen, J. Mas, L. H. Forbes, M. R. Andrews, and K. Dholakia, “Depth-resolved multimodal imaging: Wavelength modulated spatially offset Raman spectroscopy with optical coherence tomography,” J. Biophotonics 11(1), e201700129 (2018).
[Crossref]

J. Phys. D: Appl. Phys. (1)

C. Dunsby and P. M. W. French, “Techniques for depth-resolved imaging through turbid media including coherence-gated imaging,” J. Phys. D: Appl. Phys. 36(14), R207–R227 (2003).
[Crossref]

Nat. Photonics (3)

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2(2), 110–115 (2008).
[Crossref]

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6(8), 549–553 (2012).
[Crossref]

O. Tzang, E. Niv, S. Singh, S. Labouesse, G. Myatt, and R. Piestun, “Wavefront shaping in complex media with a 350 kHz modulator via a 1D-to-2D transform,” Nat. Photonics 13(11), 788–793 (2019).
[Crossref]

Nature (1)

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref]

Opt. Express (2)

Opt. Lett. (5)

Opt. Spectrosc. (1)

G. B. Malykin and E. G. Malykin, “On Possibility of Using the Lowest Odd Harmonics of the Phase Modulation Frequency in the Output Signal of the Fiber-Optic Ring Interferometer for Detection of the Sagnac Effect,” Opt. Spectrosc. 105(1), 117–123 (2008).
[Crossref]

Optica (1)

Phys. Rev. E (1)

D. S. Wiersma, A. Muzzi, M. Colocci, and R. Righini, “Time-resolved experiments on light diffusion in anisotropic random media,” Phys. Rev. E 62(5), 6681–6687 (2000).
[Crossref]

Phys. Rev. Lett. (5)

M. P. Van Albada and A. Lagendijk, “Observation of Weak Localization of Light in a Random Medium,” Phys. Rev. Lett. 55(24), 2692–2695 (1985).
[Crossref]

P.-E. Wolf and G. Maret, “Weak Localization and Coherent Backscattering of Photons in Disordered Media,” Phys. Rev. Lett. 55(24), 2696–2699 (1985).
[Crossref]

Y. Sugawara, O. B. Wright, O. Matsuda, M. Takigahira, Y. Tanaka, S. Tamura, and V. E. Gusev, “Watching ripples on crystals,” Phys. Rev. Lett. 88(18), 185504 (2002).
[Crossref]

K.-X. Sun, M. M. Fejer, E. Gustafson, and R. L. Byer, “Sagnac Interferometer for Gravitational-Wave Detection,” Phys. Rev. Lett. 76(17), 3053–3056 (1996).
[Crossref]

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Radio Sci. (1)

T. L. Beach and R. V. E. Lovelace, “Diffraction by a sinusoidal phase screen,” Radio Sci. 32(3), 913–921 (1997).
[Crossref]

Rep. Prog. Phys. (1)

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003).
[Crossref]

Rev. Mod. Phys. (1)

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Sci. Adv. (1)

A. Badon, D. Li, G. Lerosey, A. C. Boccara, M. Fink, and A. Aubry, “Smart optical coherence tomography for ultra-deep imaging through highly scattering media,” Sci. Adv. 2(11), e1600370 (2016).
[Crossref]

Science (1)

L. Wang, P. Ho, C. Liu, G. Zhang, and R. Alfano, “Ballistic 2-d imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253(5021), 769–771 (1991).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1. Optical setup, including fiber optical system with laser at 1550 nm wavelength, erbium-doped fiber amplifier (EDFA), optical isolator, 75:25 splitter, electro-optic modulator (EOM), and graded-index (GRIN) collimators, and free-space optics with waveplates ($\lambda /2$, $\lambda /4$), optical chopper, galvo scanners and InGaAs avalanche photodetector (APD). Blue and red lines indicate the two counterpropagating light paths to the target and through the scattering medium (grey area).
Fig. 2.
Fig. 2. Measured (a) and calculated (b) modulus of the mixing signal $|S_2|$ at 2$f$ against driving frequency $f$, for a fixed roundtrip time $\tau =5$ ns, corresponding to 1.5 m path length. Different values of the EOM driving voltage correspond to different peak-to-peak phase amplitudes $\phi _0$, shown by calculated curves in (b).
Fig. 3.
Fig. 3. Dependence of reflection signal intensity $|S_2|$ on total attenuation length $2L/l_s$, for the specular reflection from a protected silver mirror (dots, blue) and diffuse reflector (diamonds, red, DG10-220, Thorlabs). Blue and red lines indicate exponential decay using Beer-Lambert law $|S_2| \propto \exp {(-2 L/l_s)}$. Lines on right indicated background (noise) levels for EOM only at $2f$ ($\alpha _\textrm {EOM}$) and chopper only at $f_\textrm {chop}$ ($\alpha _\textrm {chop}$ modulation, as well as sum frequency detection at $2f+f_\textrm {chop}$ ($\alpha _\textrm {sum}$), with NEP indicating the detector noise floor. (b) Angular $\theta _x, \theta _y$ scans (log-scale) of the target showing angular spread of detection signal for attenuation lengths of 0, 2.8, and 5.6 mean free paths. Grey crosses in (a) indicate ballistic intensity corrected for angular spreading calculated using angular scans from (b).
Fig. 4.
Fig. 4. (a) Images taken at different positions $z$, showing position of scattering medium and target diffuse reflector. Top part of image was covered by scattering medium with $2L/l_s=2.8$, bottom part without scattering medium. (b) Dependence of mixing signal intensity $|S_2|$ (log-scale) versus position $z$ for different attenuation lengths from 0 to 8.4 mean free paths. (c) Image of target at $z=75$ mm for attenuation lengths corresponding to (b).
Fig. 5.
Fig. 5. (a) Photograph of chess piece used in experiment. (b) Composite image of 3D chess piece using color channels blue, red, yellow for three distances. (c) corresponding images taken at relative positions $z=-5$ mm, 0 mm and 10 mm.
Fig. 6.
Fig. 6. (a) Frequency sweeps of signal from a mirror reflector, for different attenuation lengths, showing loss of characteristic modulation signature in presence of strong multiple scattering. (b) Probability histogram of 10,000 measurements taken for the $2L/l_s=8.4$ attenuation lengths and normalized to the ensemble average $\left \langle |S_2| \right \rangle$, with black line showing Rayleigh statistics for a speckle contrast of 75%.
Fig. 7.
Fig. 7. Ballistic transmission (red dots) and total transmission (blue open circles) through stacks of teflon slabs of increasing total thickness. Lines are fits using Beer-Lambert equation $I/I_0=\exp {(-L/l_s)}$ (black) and total transmission $T_\textrm {tot}=(1+\tau _e)/(L/l_t+2 \tau _e) \exp {(-L/L_\textrm {abs})}$ (blue). Red line is total transmission scaled by factor $2 \times 10^{-4}$.

Equations (3)

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

S ( ω ) = | E | 2 2 π q , p = J q ( ϕ 0 / 2 ) J p ( ϕ 0 / 2 ) exp ( i 2 π q f τ ) δ [ ω 2 π ( q p ) f ] .
S n = | E | 2 2 π q = J q ( ϕ 0 / 2 ) J q n ( ϕ 0 / 2 ) exp ( i 2 π q f τ ) .
P n = | E | 4 4 π 2 q , r = J q ( ϕ 0 / 2 ) J q n ( ϕ 0 / 2 ) × J r ( ϕ 0 / 2 ) J r n ( ϕ 0 / 2 ) cos [ 2 π f τ ( q r ) ] .