Abstract

A new experimental approach is demonstrated to probe the scattering properties of complex media. Using phase-only modulation of the light illuminating a random scattering sample, we induce and record fluctuations in the reflected speckle patterns. Using predictions from diffusion theory, we obtain the scattering and absorption coefficients of the sample from the average change in the speckle amplitude. Our approach, which is based on interference, is in principle able to give better signal to noise ratio as compared to an intensity modulation approach. We compare our results with those obtained from a knife-edge illumination method and enhanced back-scattering cone. Our work can find application in the non-invasive study of biological specimens as well as the study of light propagation in random scattering devices like solar cells or LEDs.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Corrections

6 February 2018: A typographical correction was made to the author listing.


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References

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    [Crossref]

2016 (2)

D. Akbulut, T. Strudley, J. Bertolotti, E. P. A. M. Bakkers, A. Lagendijk, O. L. Muskens, W. L. Vos, and A. P. Mosk, “Optical transmission matrix as a probe of the photonic strength,” Phys. Rev. A 94, 043817 (2016).
[Crossref]

O. S. Ojambati, H. Yılmaz, A. Lagendijk, A. P. Mosk, and W. L. Vos, “Coupling of energy into the fundamental diffusion mode of a complex nanophotonic medium,” New J. Phys. 18, 043032 (2016).
[Crossref]

2014 (1)

2013 (2)

D. S. Wiersma, “Disordered photonics,” Nat. Photon. 7, 188–196 (2013).
[Crossref]

M. Segev, Y. Silberberg, and D. N. Christodoulides, “Anderson localization of light,” Nat. Photon. 7, 197–204 (2013).
[Crossref]

2012 (2)

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, 232–234 (2012).
[Crossref] [PubMed]

F. Scheffold and I. D. Block, “Rapid high resolution imaging of diffusive properties in turbid media,” Opt. Express 20, 192–200 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (1)

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] [PubMed]

2009 (2)

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt. 14, 024012 (2009).
[Crossref] [PubMed]

A. Lagendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Physics Today 62, 24–29 (2009)
[Crossref]

2008 (3)

2004 (1)

2003 (2)

J. Gómez Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, “Experimental determination of the effective refractive index in strongly scattering media,” Opt. Commun. 220, 17–21 (2003).
[Crossref]

P. M. Johnson, A. Imhof, B. P. J. Bret, J. G. Rivas, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E 68, 016604 (2003).
[Crossref]

2000 (1)

1999 (2)

J. G. Rivas, R. Sprik, C. M. Soukoulis, K. Busch, and A. Lagendijk, “Optical transmission through strong scattering and highly polydisperse media,” EPL 48, 22 (1999).
[Crossref]

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]

1997 (1)

1996 (1)

1995 (1)

1994 (1)

1992 (1)

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in-vivo,” Med. Phys. 19, 879–888 (1992).
[Crossref] [PubMed]

1989 (1)

A. Lagendijk, R. Vreeker, and P. De Vries, “Influence of internal reflection on diffusive transport in strongly scattering media,” Phys. Lett. A 136, 81–88 (1989).
[Crossref]

1987 (1)

A. Z. Genack, “Optical Transmission in Disordered Media,” Phys. Rev. Lett. 58, 2043 (1987)
[Crossref] [PubMed]

1985 (2)

P. E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[Crossref] [PubMed]

M. P. van Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[Crossref] [PubMed]

Akbulut, D.

D. Akbulut, T. Strudley, J. Bertolotti, E. P. A. M. Bakkers, A. Lagendijk, O. L. Muskens, W. L. Vos, and A. P. Mosk, “Optical transmission matrix as a probe of the photonic strength,” Phys. Rev. A 94, 043817 (2016).
[Crossref]

Aronson, R.

Ayers, F. R.

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt. 14, 024012 (2009).
[Crossref] [PubMed]

Bakkers, E. P. A. M.

D. Akbulut, T. Strudley, J. Bertolotti, E. P. A. M. Bakkers, A. Lagendijk, O. L. Muskens, W. L. Vos, and A. P. Mosk, “Optical transmission matrix as a probe of the photonic strength,” Phys. Rev. A 94, 043817 (2016).
[Crossref]

Barthelemy, P.

Bertolotti, J.

D. Akbulut, T. Strudley, J. Bertolotti, E. P. A. M. Bakkers, A. Lagendijk, O. L. Muskens, W. L. Vos, and A. P. Mosk, “Optical transmission matrix as a probe of the photonic strength,” Phys. Rev. A 94, 043817 (2016).
[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, 232–234 (2012).
[Crossref] [PubMed]

Bevilacqua, F.

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt. 14, 024012 (2009).
[Crossref] [PubMed]

Block, I. D.

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, 232–234 (2012).
[Crossref] [PubMed]

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] [PubMed]

Bondareff, P.

Bret, B. P. J.

J. Gómez Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, “Experimental determination of the effective refractive index in strongly scattering media,” Opt. Commun. 220, 17–21 (2003).
[Crossref]

P. M. Johnson, A. Imhof, B. P. J. Bret, J. G. Rivas, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E 68, 016604 (2003).
[Crossref]

Burnett, M. G.

Busch, K.

J. G. Rivas, R. Sprik, C. M. Soukoulis, K. Busch, and A. Lagendijk, “Optical transmission through strong scattering and highly polydisperse media,” EPL 48, 22 (1999).
[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] [PubMed]

Christodoulides, D. N.

M. Segev, Y. Silberberg, and D. N. Christodoulides, “Anderson localization of light,” Nat. Photon. 7, 197–204 (2013).
[Crossref]

Chýlek, P.

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, “Effective medium approximations for heterogeneous particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic Press, 2000).
[Crossref]

Combrie, S.

Cuccia, D. J.

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt. 14, 024012 (2009).
[Crossref] [PubMed]

Curry, N.

Dainty, J. C.

J. C. Dainty, “The statistics of speckle patterns,” in Progress in Optics, vol. 14 (Elsevier, 1977)
[Crossref]

Dau, D. H.

J. Gómez Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, “Experimental determination of the effective refractive index in strongly scattering media,” Opt. Commun. 220, 17–21 (2003).
[Crossref]

De Rossi, A.

De Vries, P.

A. Lagendijk, R. Vreeker, and P. De Vries, “Influence of internal reflection on diffusive transport in strongly scattering media,” Phys. Lett. A 136, 81–88 (1989).
[Crossref]

Detre, J. A.

Dobbie, J. S.

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, “Effective medium approximations for heterogeneous particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic Press, 2000).
[Crossref]

Dogariu, A.

Durduran, T.

Durkin, A. J.

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt. 14, 024012 (2009).
[Crossref] [PubMed]

Farrell, T. J.

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in-vivo,” Med. Phys. 19, 879–888 (1992).
[Crossref] [PubMed]

Feng, T. C.

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] [PubMed]

Geldart, D. J. W.

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, “Effective medium approximations for heterogeneous particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic Press, 2000).
[Crossref]

Genack, A. Z.

A. Z. Genack, “Optical Transmission in Disordered Media,” Phys. Rev. Lett. 58, 2043 (1987)
[Crossref] [PubMed]

Gigan, S.

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 (2011).
[Crossref] [PubMed]

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] [PubMed]

Gómez Rivas, J.

J. Gómez Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, “Experimental determination of the effective refractive index in strongly scattering media,” Opt. Commun. 220, 17–21 (2003).
[Crossref]

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company Publishers, 2007).

Greenberg, J. H.

Grésillon, S.

Haskell, R. C.

Hibst, R.

Hijmans, T. W.

J. Gómez Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, “Experimental determination of the effective refractive index in strongly scattering media,” Opt. Commun. 220, 17–21 (2003).
[Crossref]

Imhof, A.

J. Gómez Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, “Experimental determination of the effective refractive index in strongly scattering media,” Opt. Commun. 220, 17–21 (2003).
[Crossref]

P. M. Johnson, A. Imhof, B. P. J. Bret, J. G. Rivas, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E 68, 016604 (2003).
[Crossref]

Intonti, F.

Johnson, P. M.

P. M. Johnson, T. van der Beek, and A. Lagendijk, “Diffuse imaging and radius dependent frequency correlations in strongly scattering media,” Opt. Express 22, 13330 (2014).
[Crossref] [PubMed]

P. M. Johnson, A. Imhof, B. P. J. Bret, J. G. Rivas, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E 68, 016604 (2003).
[Crossref]

J. Gómez Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, “Experimental determination of the effective refractive index in strongly scattering media,” Opt. Commun. 220, 17–21 (2003).
[Crossref]

Kienle, A.

Kohlgraf-Owens, T.

Lagendijk, A.

D. Akbulut, T. Strudley, J. Bertolotti, E. P. A. M. Bakkers, A. Lagendijk, O. L. Muskens, W. L. Vos, and A. P. Mosk, “Optical transmission matrix as a probe of the photonic strength,” Phys. Rev. A 94, 043817 (2016).
[Crossref]

O. S. Ojambati, H. Yılmaz, A. Lagendijk, A. P. Mosk, and W. L. Vos, “Coupling of energy into the fundamental diffusion mode of a complex nanophotonic medium,” New J. Phys. 18, 043032 (2016).
[Crossref]

P. M. Johnson, T. van der Beek, and A. Lagendijk, “Diffuse imaging and radius dependent frequency correlations in strongly scattering media,” Opt. Express 22, 13330 (2014).
[Crossref] [PubMed]

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, 232–234 (2012).
[Crossref] [PubMed]

A. Lagendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Physics Today 62, 24–29 (2009)
[Crossref]

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Demixing light paths inside disordered metamaterials,” Opt. Express 16, 67 (2008).
[Crossref] [PubMed]

O. L. Muskens and A. Lagendijk, “Broadband enhanced backscattering spectroscopy of strongly scattering media,” Opt. Express 16, 1222 (2008).
[Crossref] [PubMed]

P. M. Johnson, A. Imhof, B. P. J. Bret, J. G. Rivas, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E 68, 016604 (2003).
[Crossref]

J. Gómez Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, “Experimental determination of the effective refractive index in strongly scattering media,” Opt. Commun. 220, 17–21 (2003).
[Crossref]

J. G. Rivas, R. Sprik, C. M. Soukoulis, K. Busch, and A. Lagendijk, “Optical transmission through strong scattering and highly polydisperse media,” EPL 48, 22 (1999).
[Crossref]

A. Lagendijk, R. Vreeker, and P. De Vries, “Influence of internal reflection on diffusive transport in strongly scattering media,” Phys. Lett. A 136, 81–88 (1989).
[Crossref]

M. P. van Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[Crossref] [PubMed]

Leclercq, M.

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] [PubMed]

Lilge, L.

Maret, G.

P. E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[Crossref] [PubMed]

McAdams, M. S.

McKinney, J. D.

Mosk, A. P.

O. S. Ojambati, H. Yılmaz, A. Lagendijk, A. P. Mosk, and W. L. Vos, “Coupling of energy into the fundamental diffusion mode of a complex nanophotonic medium,” New J. Phys. 18, 043032 (2016).
[Crossref]

D. Akbulut, T. Strudley, J. Bertolotti, E. P. A. M. Bakkers, A. Lagendijk, O. L. Muskens, W. L. Vos, and A. P. Mosk, “Optical transmission matrix as a probe of the photonic strength,” Phys. Rev. A 94, 043817 (2016).
[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, 232–234 (2012).
[Crossref] [PubMed]

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Demixing light paths inside disordered metamaterials,” Opt. Express 16, 67 (2008).
[Crossref] [PubMed]

Muskens, O. L.

D. Akbulut, T. Strudley, J. Bertolotti, E. P. A. M. Bakkers, A. Lagendijk, O. L. Muskens, W. L. Vos, and A. P. Mosk, “Optical transmission matrix as a probe of the photonic strength,” Phys. Rev. A 94, 043817 (2016).
[Crossref]

O. L. Muskens and A. Lagendijk, “Broadband enhanced backscattering spectroscopy of strongly scattering media,” Opt. Express 16, 1222 (2008).
[Crossref] [PubMed]

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]

Ojambati, O. S.

O. S. Ojambati, H. Yılmaz, A. Lagendijk, A. P. Mosk, and W. L. Vos, “Coupling of energy into the fundamental diffusion mode of a complex nanophotonic medium,” New J. Phys. 18, 043032 (2016).
[Crossref]

Patterson, M. S.

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, and B. C. Wilson, “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. 35, 2304 (1996).
[Crossref] [PubMed]

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in-vivo,” Med. Phys. 19, 879–888 (1992).
[Crossref] [PubMed]

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] [PubMed]

Riboli, F.

Rivas, J. G.

P. M. Johnson, A. Imhof, B. P. J. Bret, J. G. Rivas, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E 68, 016604 (2003).
[Crossref]

J. G. Rivas, R. Sprik, C. M. Soukoulis, K. Busch, and A. Lagendijk, “Optical transmission through strong scattering and highly polydisperse media,” EPL 48, 22 (1999).
[Crossref]

Sapienza, R.

Scheffold, F.

Segev, M.

M. Segev, Y. Silberberg, and D. N. Christodoulides, “Anderson localization of light,” Nat. Photon. 7, 197–204 (2013).
[Crossref]

Silberberg, Y.

M. Segev, Y. Silberberg, and D. N. Christodoulides, “Anderson localization of light,” Nat. Photon. 7, 197–204 (2013).
[Crossref]

Soukoulis, C. M.

J. G. Rivas, R. Sprik, C. M. Soukoulis, K. Busch, and A. Lagendijk, “Optical transmission through strong scattering and highly polydisperse media,” EPL 48, 22 (1999).
[Crossref]

Sprik, R.

J. Gómez Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, “Experimental determination of the effective refractive index in strongly scattering media,” Opt. Commun. 220, 17–21 (2003).
[Crossref]

J. G. Rivas, R. Sprik, C. M. Soukoulis, K. Busch, and A. Lagendijk, “Optical transmission through strong scattering and highly polydisperse media,” EPL 48, 22 (1999).
[Crossref]

Steiner, R.

Strudley, T.

D. Akbulut, T. Strudley, J. Bertolotti, E. P. A. M. Bakkers, A. Lagendijk, O. L. Muskens, W. L. Vos, and A. P. Mosk, “Optical transmission matrix as a probe of the photonic strength,” Phys. Rev. A 94, 043817 (2016).
[Crossref]

Svaasand, L. O.

Thompson, C. A.

Tromberg, B. J.

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt. 14, 024012 (2009).
[Crossref] [PubMed]

R. C. Haskell, L. O. Svaasand, T. T. Tsay, T. C. Feng, B. J. Tromberg, and M. S. McAdams, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727 (1994).
[Crossref]

Tsay, T. T.

Tso, H. C. W.

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, “Effective medium approximations for heterogeneous particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic Press, 2000).
[Crossref]

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, 2692–2695 (1985).
[Crossref] [PubMed]

van der Beek, T.

van Hulst, N. F.

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, 232–234 (2012).
[Crossref] [PubMed]

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, and A. P. Mosk, “Demixing light paths inside disordered metamaterials,” Opt. Express 16, 67 (2008).
[Crossref] [PubMed]

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]

van Tiggelen, B.

A. Lagendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Physics Today 62, 24–29 (2009)
[Crossref]

Vellekoop, I. M.

Videen, G.

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, “Effective medium approximations for heterogeneous particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic Press, 2000).
[Crossref]

Vignolini, S.

Vos, W. L.

O. S. Ojambati, H. Yılmaz, A. Lagendijk, A. P. Mosk, and W. L. Vos, “Coupling of energy into the fundamental diffusion mode of a complex nanophotonic medium,” New J. Phys. 18, 043032 (2016).
[Crossref]

D. Akbulut, T. Strudley, J. Bertolotti, E. P. A. M. Bakkers, A. Lagendijk, O. L. Muskens, W. L. Vos, and A. P. Mosk, “Optical transmission matrix as a probe of the photonic strength,” Phys. Rev. A 94, 043817 (2016).
[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, 232–234 (2012).
[Crossref] [PubMed]

Vreeker, R.

A. Lagendijk, R. Vreeker, and P. De Vries, “Influence of internal reflection on diffusive transport in strongly scattering media,” Phys. Lett. A 136, 81–88 (1989).
[Crossref]

Wang, J.

Webb, K. J.

Webster, M. A.

Weiner, A. M.

Wiersma, D. S.

D. S. Wiersma, “Disordered photonics,” Nat. Photon. 7, 188–196 (2013).
[Crossref]

F. Riboli, P. Barthelemy, S. Vignolini, F. Intonti, A. De Rossi, S. Combrie, and D. S. Wiersma, “Anderson localization of near-visible light in two dimensions,” Opt. Lett. 36, 127–129 (2011)
[Crossref] [PubMed]

A. Lagendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Physics Today 62, 24–29 (2009)
[Crossref]

Wilson, B.

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in-vivo,” Med. Phys. 19, 879–888 (1992).
[Crossref] [PubMed]

Wilson, B. C.

Wolf, P. E.

P. E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[Crossref] [PubMed]

Yilmaz, H.

O. S. Ojambati, H. Yılmaz, A. Lagendijk, A. P. Mosk, and W. L. Vos, “Coupling of energy into the fundamental diffusion mode of a complex nanophotonic medium,” New J. Phys. 18, 043032 (2016).
[Crossref]

Yodh, A. G.

Yu, G.

Zhou, C.

Appl. Opt. (2)

EPL (1)

J. G. Rivas, R. Sprik, C. M. Soukoulis, K. Busch, and A. Lagendijk, “Optical transmission through strong scattering and highly polydisperse media,” EPL 48, 22 (1999).
[Crossref]

J. Biomed. Opt. (1)

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt. 14, 024012 (2009).
[Crossref] [PubMed]

J. Opt. Soc. Am. A (2)

Med. Phys. (1)

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in-vivo,” Med. Phys. 19, 879–888 (1992).
[Crossref] [PubMed]

Nat. Photon. (2)

M. Segev, Y. Silberberg, and D. N. Christodoulides, “Anderson localization of light,” Nat. Photon. 7, 197–204 (2013).
[Crossref]

D. S. Wiersma, “Disordered photonics,” Nat. Photon. 7, 188–196 (2013).
[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, 232–234 (2012).
[Crossref] [PubMed]

New J. Phys. (1)

O. S. Ojambati, H. Yılmaz, A. Lagendijk, A. P. Mosk, and W. L. Vos, “Coupling of energy into the fundamental diffusion mode of a complex nanophotonic medium,” New J. Phys. 18, 043032 (2016).
[Crossref]

Opt. Commun. (1)

J. Gómez Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, “Experimental determination of the effective refractive index in strongly scattering media,” Opt. Commun. 220, 17–21 (2003).
[Crossref]

Opt. Express (5)

Opt. Lett. (4)

Phys. Lett. A (1)

A. Lagendijk, R. Vreeker, and P. De Vries, “Influence of internal reflection on diffusive transport in strongly scattering media,” Phys. Lett. A 136, 81–88 (1989).
[Crossref]

Phys. Rev. A (1)

D. Akbulut, T. Strudley, J. Bertolotti, E. P. A. M. Bakkers, A. Lagendijk, O. L. Muskens, W. L. Vos, and A. P. Mosk, “Optical transmission matrix as a probe of the photonic strength,” Phys. Rev. A 94, 043817 (2016).
[Crossref]

Phys. Rev. E (1)

P. M. Johnson, A. Imhof, B. P. J. Bret, J. G. Rivas, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E 68, 016604 (2003).
[Crossref]

Phys. Rev. Lett. (4)

A. Z. Genack, “Optical Transmission in Disordered Media,” Phys. Rev. Lett. 58, 2043 (1987)
[Crossref] [PubMed]

P. E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[Crossref] [PubMed]

M. P. van Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[Crossref] [PubMed]

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] [PubMed]

Physics Today (1)

A. Lagendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Physics Today 62, 24–29 (2009)
[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]

Other (3)

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company Publishers, 2007).

J. C. Dainty, “The statistics of speckle patterns,” in Progress in Optics, vol. 14 (Elsevier, 1977)
[Crossref]

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, “Effective medium approximations for heterogeneous particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic Press, 2000).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 The experimental setup: a collimated laser (wavelength 633 nm) illuminates the spatial light modulator (SLM) after passing through the polarizer P0. The wavefront-shaped light is polarized again with the polarizer P1 and imaged on the sample with a telescope consisting of a tube lens L1 (f = 20 cm) and a 50× microscope objective. The reflected light is collected with the same objective and its polarization is selected with the analyser P2. A second tube lens L2 (f = 20 cm) images the sample on a CCD camera. Bottom left: a scheme of the phase-step hologram projected on the SLM. Right: the interference between the light coming from the two halves of the SLM (red and blue lines) and exiting the sample at the same point.
Fig. 2
Fig. 2 (a) Knife-edge method: the spatial speckles measured in reflection upon illumination with half a Gaussian beam (bottom part) are compared with the average speckle intensity pattern calculated with diffusion theory (top part). The two cross sections Iin(x, 0) (red dashed line) and 〈IR(x, 0)〉± (green dashed line) from Eq. (5) are also shown. (b) Phase-step method: (Top) an example of measured speckle intensity variations IA(x, y) under phase-modulated illumination, with indicated the rectangular region used for ensemble averaging; (Bottom) the intensity as a function of the phase delay Δϕ for the pixel highlighted by a cross in the upper panel.
Fig. 3
Fig. 3 Phase-step results for the white paint. (a) Average speckle intensity modulation IA(x), normalized to its value at x = 0, for illumination with the phase-step positioned at x = 0. The red solid line shows the best fit curve with ltr = 3.0 μm and la = 14 μm. In the plot we also indicate the model with a transport coefficient altered by ±25% (dotted lines) and the model without absorption (dashed line). (b) The normalized error function in the parameter space (ltr, la), calculated as defined in the text, with indication of the error minimum identifying the best fit parameters for the fit curve in panel (a), with the error bar for ltr.
Fig. 4
Fig. 4 Knife-edge results for the white paint. (a) The average reflected intensity with half of the illumination spot blocked by the knife-edge. The intensity is averaged over the y direction over a 18 μm strip around the center of the illumination spot. Experimental data are fitted with the diffusion model in Eq. (5) to obtain the best fit parameters ltr and la (in red). In the plot we also indicate the same model with a transport coefficient altered by ±25% (dotted lines), and the model without absorption (dashed line). The intensity profile for point-like illumination is plotted for comparison. (b) The normalized error function in the parameter space (ltr, la), calculated as defined in the text, with indication of the error minimum identifying the best fit parameters for the fit curve in panel (a), with the error bar for ltr.

Tables (1)

Tables Icon

Table 1 Transport and absorption mean-free paths ltr and la for λ = 632.8 nm as determined from fits for three different measurement techniques: phase-step method, knife-edge method and enhanced back-scattering (EBS), with indicated n eff assumed in the three methods for each sample.

Equations (6)

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E R ( x , y ) = G ( x , y , x , y ) E in ( x , y ) G ( x , y , x , y ) E in ( x , y ) d x d y
E ± ( x , y ) = G ( x , y , x , y ) [ H ( ± x ) E in ( x , y ) ] ,
I R ( x , y ; Δ ϕ ) I C ( x , y ) + I A ( x , y ) cos ( Δ ϕ + ψ ) ,
R ( ρ ) 1 4 π ( z 0 ( μ eff + 1 r 1 ) exp ( μ eff r 1 ) r 1 2 + ( z 0 + 2 z b ) ( μ eff + 1 r 2 ) exp ( μ eff r 2 ) r 2 2 ) ,
I R ± ( x , y ) = R ( ρ ) I in ( x , y ) R ( ρ ) H ( ± x ) exp ( ρ 2 / w in 2 ) d x d y .
I A ( x , y ) E + ( x , y ) | E ( x , y ) | I R + ( x , y ) I R + ( x , y )

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