Abstract

Propagation of an ultrashort laser pulse through a scattering medium forms a speckle pattern in the spatio-spectral domain. This pattern arises from the contribution of the randomly phased electric fields associated with the different optical paths in the medium. Studying the speckle field provides information both about the diffusion properties of the medium and spatio-temporal control of the transmitted or scattered light. In this paper a spatio-temporal characterization of the near-IR 120 fs pulse transmitted through a thick strongly scattering medium is undertaken using spatially and spectrally resolved Fourier-transform interferometry (SSI). The advantages of SSI over conventional pulse measurement techniques are discussed. The diffusion properties of the scattering samples are measured. We find a good agreement between our measured diffusion properties and those obtained using another method. The implications of this measurement technique are discussed.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  34. D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2011

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photon. 5, 372–377 (2011).
[CrossRef]

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef]

N. Curry, P. Bondareff, M. Leclercq, N. F. van Hulst, R. Sapienza, S. Gigan, and S. Grésillon, “Direct determination of diffusion properties of random media from speckle contrast,” Opt. Lett. 36, 3332–3334 (2011).
[CrossRef]

2010

A. Monmayrant, S. Weber, and B. Chatel, “A newcomer’s guide to ultrashort pulse shaping and characterization,” J. Phys. B 43, 103001 (2010).
[CrossRef]

W. J. Liu, R. X. Gao, and S. L. Qu, “Measurements of femtosecond temporal speckle field of a random medium,” Chin. Phys. B 19, 024204 (2010).
[CrossRef]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. 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, 100601 (2010).
[CrossRef]

2009

S. Faez, P. M. Johnson, and A. Lagendijk, “Varying the effective refractive index to measure optical transport in random media,” Phys. Rev. Lett. 103, 53903 (2009).
[CrossRef]

D. R. Austin, T. Witting, and I. A. Walmsey, “Broadband astigmatism-free Czerny–Turner imaging spectrometer using spherical mirrors,” Appl. Opt. 48, 3846–3853 (2009).
[CrossRef]

2008

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

2007

C. Lopez, P. D. Garcia, R. Sapienza, and A. Blanco, “Photonic glass: a novel random material for light,” Adv. Mater. 19, 2597–2602 (2007).
[CrossRef]

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32, 2309–2311 (2007).
[CrossRef]

S. Farsiu, J. Christofferson, B. Eriksson, P. Milanfar, B. Friedlander, A. Shakouri, and R. Nowak, “Statistical detection and imaging of objects hidden in turbid media using ballistic photons,” Appl. Opt. 46, 5805–5822 (2007).
[CrossRef]

R. Sapienza, P. D. Garcia, J. Bertolotti, M. D. Martin, A. Blanco, L. Vina, C. Lopez, and D. S. Wiersma, “Observation of resonant behavior in the energy velocity of diffused light,” Phys. Rev. Lett. 99, 233902 (2007).
[CrossRef]

2005

I. M. Vellekoop, P. Lodahl, and A. Lagendijk, “Determination of the diffusion constant using phase-sensitive measurements,” Phys. Rev. E 71, 056604 (2005).
[CrossRef]

2004

H. Ramachandran and S. Mujumdar, “Imaging through turbid media using polarization modulation: dependence on scattering anisotropy,” Opt. Commun. 241, 1–9 (2004).
[CrossRef]

2002

2000

J. D. McKinney, M. A. Webster, K. J. Webb, and A. M. Weiner, “Characterization and imaging in optically scattering media by use of laser speckle and a variable-coherence source,” Opt. Lett. 25, 4–6 (2000).
[CrossRef]

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

1998

H. Ramachandran and A. Narayanan, “Two-dimensional imaging through turbid media using a continuous wave light source,” Opt. Commun. 154, 255–260 (1998).
[CrossRef]

C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792–794 (1998).
[CrossRef]

1997

1996

O. Emile, F. Bretenaker, and A. LeFloch, “Rotating polarization imaging in turbid media,” Opt. Lett. 21, 1706–1708 (1996).
[CrossRef]

S. K. Gayen and R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photon. News 7(3), 16 (1996).
[CrossRef]

W. Cai, B. B. Das, F. Liu, M. Zevallos, M. Lax, and R. R. Alfano, “Time-resolved optical diffusion tomographic image reconstruction in highly scattering turbid media,” Proc. Natl. Acad. Sci. USA 93, 13561–13564 (1996).
[CrossRef]

1995

1994

1992

1991

M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, and J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue,” Appl. Opt. 30, 4474–4476 (1991).
[CrossRef]

D. S. Dilworth, E. N. Leith, and J. L. Lopez, “Three-dimensional confocal imaging of objects embedded within thick diffusing media,” Appl. Opt. 30, 1796–1803 (1991).
[CrossRef]

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

M. P. Vanalbada, B. A. Vantiggelen, A. Lagendijk, and A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
[CrossRef]

1990

1988

P. E. Wolf, G. Maret, E. Akkermans, and R. Maynard, “Optical coherent backscattering by random media—an experimental study,” J. Phys. 49, 63–75 (1988).
[CrossRef]

1987

A. Z. Genack, “Optical-transmission in disordered media,” Phys. Rev. Lett. 58, 2043–2046 (1987).
[CrossRef]

1978

M. V. Berry, “Disruption of wavefronts: Statistics of dislocations in incoherent gaussian random waves,” J. Phys. A 11, 27–37 (1978).
[CrossRef]

1977

D. J. Thouless, “Maximum metallic resistance in thin wires,” Phys. Rev. Lett. 39, 1167–1169 (1977).
[CrossRef]

1976

Akkermans, E.

P. E. Wolf, G. Maret, E. Akkermans, and R. Maynard, “Optical coherent backscattering by random media—an experimental study,” J. Phys. 49, 63–75 (1988).
[CrossRef]

Alfano, R. R.

W. Cai, B. B. Das, F. Liu, M. Zevallos, M. Lax, and R. R. Alfano, “Time-resolved optical diffusion tomographic image reconstruction in highly scattering turbid media,” Proc. Natl. Acad. Sci. USA 93, 13561–13564 (1996).
[CrossRef]

S. K. Gayen and R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photon. News 7(3), 16 (1996).
[CrossRef]

L. Feng, K. M. Yoo, and R. R. Alfano, “Transmitted photon intensity through biological tissues within various time windows,” Opt. Lett. 19, 740–742 (1994).
[CrossRef]

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

K. M. Yoo and R. R. Alfano, “Time-resolved coherent and incoherent components of forward light-scattering in random-media,” Opt. Lett. 15, 320–322 (1990).
[CrossRef]

Aulbach, J.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

Austin, D. R.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef]

D. R. Austin, T. Witting, and I. A. Walmsey, “Broadband astigmatism-free Czerny–Turner imaging spectrometer using spherical mirrors,” Appl. Opt. 48, 3846–3853 (2009).
[CrossRef]

Berndt, K. W.

Berry, M. V.

M. V. Berry, “Disruption of wavefronts: Statistics of dislocations in incoherent gaussian random waves,” J. Phys. A 11, 27–37 (1978).
[CrossRef]

Bertolotti, J.

R. Sapienza, P. D. Garcia, J. Bertolotti, M. D. Martin, A. Blanco, L. Vina, C. Lopez, and D. S. Wiersma, “Observation of resonant behavior in the energy velocity of diffused light,” Phys. Rev. Lett. 99, 233902 (2007).
[CrossRef]

Blanco, A.

R. Sapienza, P. D. Garcia, J. Bertolotti, M. D. Martin, A. Blanco, L. Vina, C. Lopez, and D. S. Wiersma, “Observation of resonant behavior in the energy velocity of diffused light,” Phys. Rev. Lett. 99, 233902 (2007).
[CrossRef]

C. Lopez, P. D. Garcia, R. Sapienza, and A. Blanco, “Photonic glass: a novel random material for light,” Adv. Mater. 19, 2597–2602 (2007).
[CrossRef]

Boccara, A. C.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. 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, 100601 (2010).
[CrossRef]

Bondareff, P.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef]

N. Curry, P. Bondareff, M. Leclercq, N. F. van Hulst, R. Sapienza, S. Gigan, and S. Grésillon, “Direct determination of diffusion properties of random media from speckle contrast,” Opt. Lett. 36, 3332–3334 (2011).
[CrossRef]

Bonner, R. F.

Bretenaker, F.

Bromberg, Y.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photon. 5, 372–377 (2011).
[CrossRef]

Cai, W.

W. Cai, B. B. Das, F. Liu, M. Zevallos, M. Lax, and R. R. Alfano, “Time-resolved optical diffusion tomographic image reconstruction in highly scattering turbid media,” Proc. Natl. Acad. Sci. USA 93, 13561–13564 (1996).
[CrossRef]

Carminati, R.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. 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, 100601 (2010).
[CrossRef]

Chance, B.

A. Yodh and B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 34–40 (1995).
[CrossRef]

Chatel, B.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef]

A. Monmayrant, S. Weber, and B. Chatel, “A newcomer’s guide to ultrashort pulse shaping and characterization,” J. Phys. B 43, 103001 (2010).
[CrossRef]

Christofferson, J.

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, 6681–6687 (2000).
[CrossRef]

Curry, N.

Das, B. B.

W. Cai, B. B. Das, F. Liu, M. Zevallos, M. Lax, and R. R. Alfano, “Time-resolved optical diffusion tomographic image reconstruction in highly scattering turbid media,” Proc. Natl. Acad. Sci. USA 93, 13561–13564 (1996).
[CrossRef]

Dilworth, D. S.

Emile, O.

Eriksson, B.

Faez, S.

S. Faez, P. M. Johnson, and A. Lagendijk, “Varying the effective refractive index to measure optical transport in random media,” Phys. Rev. Lett. 103, 53903 (2009).
[CrossRef]

Farsiu, S.

Feld, M. S.

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

Feng, L.

Fink, M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. 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, 100601 (2010).
[CrossRef]

Friedlander, B.

Gandjbakhche, A. H.

Gao, R. X.

W. J. Liu, R. X. Gao, and S. L. Qu, “Measurements of femtosecond temporal speckle field of a random medium,” Chin. Phys. B 19, 024204 (2010).
[CrossRef]

Garcia, P. D.

R. Sapienza, P. D. Garcia, J. Bertolotti, M. D. Martin, A. Blanco, L. Vina, C. Lopez, and D. S. Wiersma, “Observation of resonant behavior in the energy velocity of diffused light,” Phys. Rev. Lett. 99, 233902 (2007).
[CrossRef]

C. Lopez, P. D. Garcia, R. Sapienza, and A. Blanco, “Photonic glass: a novel random material for light,” Adv. Mater. 19, 2597–2602 (2007).
[CrossRef]

Gayen, S. K.

S. K. Gayen and R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photon. News 7(3), 16 (1996).
[CrossRef]

Genack, A. Z.

A. Z. Genack, “Optical-transmission in disordered media,” Phys. Rev. Lett. 58, 2043–2046 (1987).
[CrossRef]

Gigan, S.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef]

N. Curry, P. Bondareff, M. Leclercq, N. F. van Hulst, R. Sapienza, S. Gigan, and S. Grésillon, “Direct determination of diffusion properties of random media from speckle contrast,” Opt. Lett. 36, 3332–3334 (2011).
[CrossRef]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. 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, 100601 (2010).
[CrossRef]

Gjonaj, B.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

Goodman, J. W.

Grésillon, S.

Ho, P. P.

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

Iaconis, C.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, Oxford University, 1997).

Johnson, P. M.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

S. Faez, P. M. Johnson, and A. Lagendijk, “Varying the effective refractive index to measure optical transport in random media,” Phys. Rev. Lett. 103, 53903 (2009).
[CrossRef]

Kannari, F.

Katz, O.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photon. 5, 372–377 (2011).
[CrossRef]

Lagendijk, A.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

S. Faez, P. M. Johnson, and A. Lagendijk, “Varying the effective refractive index to measure optical transport in random media,” Phys. Rev. Lett. 103, 53903 (2009).
[CrossRef]

I. M. Vellekoop, P. Lodahl, and A. Lagendijk, “Determination of the diffusion constant using phase-sensitive measurements,” Phys. Rev. E 71, 056604 (2005).
[CrossRef]

M. P. Vanalbada, B. A. Vantiggelen, A. Lagendijk, and A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
[CrossRef]

Lakowicz, J. R.

Lax, M.

W. Cai, B. B. Das, F. Liu, M. Zevallos, M. Lax, and R. R. Alfano, “Time-resolved optical diffusion tomographic image reconstruction in highly scattering turbid media,” Proc. Natl. Acad. Sci. USA 93, 13561–13564 (1996).
[CrossRef]

Leclercq, M.

LeFloch, A.

Leith, E. N.

Lerosey, G.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. 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, 100601 (2010).
[CrossRef]

Liu, C.

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

Liu, F.

W. Cai, B. B. Das, F. Liu, M. Zevallos, M. Lax, and R. R. Alfano, “Time-resolved optical diffusion tomographic image reconstruction in highly scattering turbid media,” Proc. Natl. Acad. Sci. USA 93, 13561–13564 (1996).
[CrossRef]

Liu, W. J.

W. J. Liu, R. X. Gao, and S. L. Qu, “Measurements of femtosecond temporal speckle field of a random medium,” Chin. Phys. B 19, 024204 (2010).
[CrossRef]

Lodahl, P.

I. M. Vellekoop, P. Lodahl, and A. Lagendijk, “Determination of the diffusion constant using phase-sensitive measurements,” Phys. Rev. E 71, 056604 (2005).
[CrossRef]

Lopez, C.

R. Sapienza, P. D. Garcia, J. Bertolotti, M. D. Martin, A. Blanco, L. Vina, C. Lopez, and D. S. Wiersma, “Observation of resonant behavior in the energy velocity of diffused light,” Phys. Rev. Lett. 99, 233902 (2007).
[CrossRef]

C. Lopez, P. D. Garcia, R. Sapienza, and A. Blanco, “Photonic glass: a novel random material for light,” Adv. Mater. 19, 2597–2602 (2007).
[CrossRef]

Lopez, J. L.

Maret, G.

P. E. Wolf, G. Maret, E. Akkermans, and R. Maynard, “Optical coherent backscattering by random media—an experimental study,” J. Phys. 49, 63–75 (1988).
[CrossRef]

Martin, M. D.

R. Sapienza, P. D. Garcia, J. Bertolotti, M. D. Martin, A. Blanco, L. Vina, C. Lopez, and D. S. Wiersma, “Observation of resonant behavior in the energy velocity of diffused light,” Phys. Rev. Lett. 99, 233902 (2007).
[CrossRef]

Matsumoto, T.

Maynard, R.

P. E. Wolf, G. Maret, E. Akkermans, and R. Maynard, “Optical coherent backscattering by random media—an experimental study,” J. Phys. 49, 63–75 (1988).
[CrossRef]

McCabe, D. J.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef]

McKinney, J. D.

Milanfar, P.

Monmayrant, A.

A. Monmayrant, S. Weber, and B. Chatel, “A newcomer’s guide to ultrashort pulse shaping and characterization,” J. Phys. B 43, 103001 (2010).
[CrossRef]

Mosk, A. P.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32, 2309–2311 (2007).
[CrossRef]

Moulton, J. D.

Mujumdar, S.

H. Ramachandran and S. Mujumdar, “Imaging through turbid media using polarization modulation: dependence on scattering anisotropy,” Opt. Commun. 241, 1–9 (2004).
[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, 6681–6687 (2000).
[CrossRef]

Narayanan, A.

H. Ramachandran and A. Narayanan, “Two-dimensional imaging through turbid media using a continuous wave light source,” Opt. Commun. 154, 255–260 (1998).
[CrossRef]

Nowak, R.

Patterson, M. S.

Popoff, S. M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. 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, 100601 (2010).
[CrossRef]

Psaltis, D.

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

Qu, S. L.

W. J. Liu, R. X. Gao, and S. L. Qu, “Measurements of femtosecond temporal speckle field of a random medium,” Chin. Phys. B 19, 024204 (2010).
[CrossRef]

Ramachandran, H.

H. Ramachandran and S. Mujumdar, “Imaging through turbid media using polarization modulation: dependence on scattering anisotropy,” Opt. Commun. 241, 1–9 (2004).
[CrossRef]

H. Ramachandran and A. Narayanan, “Two-dimensional imaging through turbid media using a continuous wave light source,” Opt. Commun. 154, 255–260 (1998).
[CrossRef]

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, 6681–6687 (2000).
[CrossRef]

Sapienza, R.

N. Curry, P. Bondareff, M. Leclercq, N. F. van Hulst, R. Sapienza, S. Gigan, and S. Grésillon, “Direct determination of diffusion properties of random media from speckle contrast,” Opt. Lett. 36, 3332–3334 (2011).
[CrossRef]

C. Lopez, P. D. Garcia, R. Sapienza, and A. Blanco, “Photonic glass: a novel random material for light,” Adv. Mater. 19, 2597–2602 (2007).
[CrossRef]

R. Sapienza, P. D. Garcia, J. Bertolotti, M. D. Martin, A. Blanco, L. Vina, C. Lopez, and D. S. Wiersma, “Observation of resonant behavior in the energy velocity of diffused light,” Phys. Rev. Lett. 99, 233902 (2007).
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Sebbah, P. E.

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Shakouri, A.

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[CrossRef]

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O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photon. 5, 372–377 (2011).
[CrossRef]

Tajalli, A.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef]

Tanabe, H.

Tanabe, T.

Teramura, Y.

Thompson, C. A.

Thouless, D. J.

D. J. Thouless, “Maximum metallic resistance in thin wires,” Phys. Rev. Lett. 39, 1167–1169 (1977).
[CrossRef]

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[CrossRef]

Tomita, M.

van Hulst, N. F.

Vanalbada, M. P.

M. P. Vanalbada, B. A. Vantiggelen, A. Lagendijk, and A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
[CrossRef]

Vantiggelen, B. A.

M. P. Vanalbada, B. A. Vantiggelen, A. Lagendijk, and A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
[CrossRef]

Vellekoop, I. M.

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32, 2309–2311 (2007).
[CrossRef]

I. M. Vellekoop, P. Lodahl, and A. Lagendijk, “Determination of the diffusion constant using phase-sensitive measurements,” Phys. Rev. E 71, 056604 (2005).
[CrossRef]

Vina, L.

R. Sapienza, P. D. Garcia, J. Bertolotti, M. D. Martin, A. Blanco, L. Vina, C. Lopez, and D. S. Wiersma, “Observation of resonant behavior in the energy velocity of diffused light,” Phys. Rev. Lett. 99, 233902 (2007).
[CrossRef]

Walmsey, I. A.

Walmsley, I. A.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
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[CrossRef]

Wang, L.

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

Webb, K. J.

Weber, S.

A. Monmayrant, S. Weber, and B. Chatel, “A newcomer’s guide to ultrashort pulse shaping and characterization,” J. Phys. B 43, 103001 (2010).
[CrossRef]

Webster, M. A.

Weiner, A. M.

Wiersma, D. S.

R. Sapienza, P. D. Garcia, J. Bertolotti, M. D. Martin, A. Blanco, L. Vina, C. Lopez, and D. S. Wiersma, “Observation of resonant behavior in the energy velocity of diffused light,” Phys. Rev. Lett. 99, 233902 (2007).
[CrossRef]

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

Wilson, B. C.

Witting, T.

Wolf, P. E.

P. E. Wolf, G. Maret, E. Akkermans, and R. Maynard, “Optical coherent backscattering by random media—an experimental study,” J. Phys. 49, 63–75 (1988).
[CrossRef]

Yang, C. H.

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

Yaqoob, Z.

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

Yodh, A.

A. Yodh and B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 34–40 (1995).
[CrossRef]

Yoo, K. M.

Zevallos, M.

W. Cai, B. B. Das, F. Liu, M. Zevallos, M. Lax, and R. R. Alfano, “Time-resolved optical diffusion tomographic image reconstruction in highly scattering turbid media,” Proc. Natl. Acad. Sci. USA 93, 13561–13564 (1996).
[CrossRef]

Zhang, G.

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

Adv. Mater.

C. Lopez, P. D. Garcia, R. Sapienza, and A. Blanco, “Photonic glass: a novel random material for light,” Adv. Mater. 19, 2597–2602 (2007).
[CrossRef]

Appl. Opt.

Chin. Phys. B

W. J. Liu, R. X. Gao, and S. L. Qu, “Measurements of femtosecond temporal speckle field of a random medium,” Chin. Phys. B 19, 024204 (2010).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

J. Phys.

P. E. Wolf, G. Maret, E. Akkermans, and R. Maynard, “Optical coherent backscattering by random media—an experimental study,” J. Phys. 49, 63–75 (1988).
[CrossRef]

J. Phys. A

M. V. Berry, “Disruption of wavefronts: Statistics of dislocations in incoherent gaussian random waves,” J. Phys. A 11, 27–37 (1978).
[CrossRef]

J. Phys. B

A. Monmayrant, S. Weber, and B. Chatel, “A newcomer’s guide to ultrashort pulse shaping and characterization,” J. Phys. B 43, 103001 (2010).
[CrossRef]

Nat. Commun.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef]

Nat. Photon.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photon. 5, 372–377 (2011).
[CrossRef]

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

Opt. Commun.

H. Ramachandran and A. Narayanan, “Two-dimensional imaging through turbid media using a continuous wave light source,” Opt. Commun. 154, 255–260 (1998).
[CrossRef]

H. Ramachandran and S. Mujumdar, “Imaging through turbid media using polarization modulation: dependence on scattering anisotropy,” Opt. Commun. 241, 1–9 (2004).
[CrossRef]

Opt. Lett.

Opt. Photon. News

S. K. Gayen and R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photon. News 7(3), 16 (1996).
[CrossRef]

Phys. Rev. E

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

I. M. Vellekoop, P. Lodahl, and A. Lagendijk, “Determination of the diffusion constant using phase-sensitive measurements,” Phys. Rev. E 71, 056604 (2005).
[CrossRef]

Phys. Rev. Lett.

S. Faez, P. M. Johnson, and A. Lagendijk, “Varying the effective refractive index to measure optical transport in random media,” Phys. Rev. Lett. 103, 53903 (2009).
[CrossRef]

M. P. Vanalbada, B. A. Vantiggelen, A. Lagendijk, and A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
[CrossRef]

R. Sapienza, P. D. Garcia, J. Bertolotti, M. D. Martin, A. Blanco, L. Vina, C. Lopez, and D. S. Wiersma, “Observation of resonant behavior in the energy velocity of diffused light,” Phys. Rev. Lett. 99, 233902 (2007).
[CrossRef]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. 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, 100601 (2010).
[CrossRef]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

A. Z. Genack, “Optical-transmission in disordered media,” Phys. Rev. Lett. 58, 2043–2046 (1987).
[CrossRef]

D. J. Thouless, “Maximum metallic resistance in thin wires,” Phys. Rev. Lett. 39, 1167–1169 (1977).
[CrossRef]

Phys. Today

A. Yodh and B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 34–40 (1995).
[CrossRef]

Proc. Natl. Acad. Sci. USA

W. Cai, B. B. Das, F. Liu, M. Zevallos, M. Lax, and R. R. Alfano, “Time-resolved optical diffusion tomographic image reconstruction in highly scattering turbid media,” Proc. Natl. Acad. Sci. USA 93, 13561–13564 (1996).
[CrossRef]

Science

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

Other

A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, Oxford University, 1997).

P. E. Sebbah, Waves and Imaging through Complex Media (Kluwer Academic, 2001).

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Figures (5)

Fig. 1.
Fig. 1.

Experimental setup. The laser oscillator beam (Osc) is divided in to sample and reference arms by a beam splitter (BS). The sample arm is focused on to the sample (S) by lens L1. The sample is mounted on a translation stage (TS) moving perpendicular to the laser beam. Lens L2 images the transmitted-diffracted light on to the spectrometer slit (2D-SM). The reference arm is combined with the sample arm with an adjustable delay and angle at the entrance slit of the spectrometer.

Fig. 2.
Fig. 2.

Fourier filtering process. (a) The interference pattern of the reference and sample arm is detected by an imaging spectrometer. (b) A two-dimensional Fourier transform (FT) is performed. An a.c. term is filtered out within the Fourier domain. (c) An inverse two-dimensional Fourier transform (IFT) of this term isolates the interferometric term. (d) The spectral phase difference, which is extracted from the filtered complex interference term via the argument function (Arg), recovers the transfer function of the sample plus residual phase of the optics in the sample arm. The color is set to white where the signal amplitude is low and the extracted phase becomes meaningless.

Fig. 3.
Fig. 3.

Experimental reconstruction of the spatio-spectral electric field of the scattered-transmitted light from a thick scattering sample consisting of ZnO grains. (a) Spatio-spectral intensity |E(ω,y)|2 of the speckle. (b) Speckle spatio-spectral phase ϕ(ω,y). (c) Solid black (upper), green (middle), and red (lower) lines, spectral intensities at black (upper), green (middle), and red (lower) indicated positions of the speckle, respectively; blue dashed line, spatially integrated spectral intensity. (d) Spectral phases at different positions of the speckle. (e) Spatio-spectral correlation function |Eout(ω,y)Eout*(ω+Ω,y+Y)| demonstrating that the speckle is well resolved both spatially and spectrally. The spatial correlation length is related to the speckle grain size, while the spectral correlation length is the bandwidth of the medium, inversely proportional to the Thouless time.

Fig. 4.
Fig. 4.

Spatio-temporal electric field of the scattered, transmitted light from 19 μm thick sample. (a) Reconstructed spatio-temporal intensity |E(t,y)|2of the speckle from Fourier transform of the complex spatio-spectral electric field. (b) Solid gray (upper) and red (lower) lines, temporal intensities along gray (upper) and red (lower) spatial slices, respectively; dashed line, spatially integrated temporal intensity.

Fig. 5.
Fig. 5.

Position-averaged spatio-temporal intensity I(t,y). (a) Ensemble average of spatio-temporal intensity from 40 different positions of the sample with thickness of 17 μm. (b) Spatially integrated ensemble-averaged spatio-temporal intensity of (a). An exponential fit of the intensity decay yields a sample decay time of 1046 fs. (c) Position average of the spatio-temporal intensity from 40 different positions of the sample with thickness of 20 μm. (d) Spatially integrated ensemble-averaged spatio-temporal intensity of (c). The decay time of the sample is 1233 fs.

Equations (1)

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I(ω,y)=|Er(ω,y)|2+|Es(ω,y)|2+2|Er(ω,y)||Es(ω,y)|cos[ϕr(ω,y)ϕs(ω,y)ωτkyy].

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