Abstract

We demonstrate a method for fully characterizing diffuse transport of light in a statistically anisotropic opaque material. Our technique provides a simple means of determining all parameters governing anisotropic diffusion. Anisotropy in the diffusion constant, the mean free path, and the extrapolation length are, for the first time, determined independently. These results show that the anisotropic diffusion model is effective for modeling transport in anisotropic samples, providing that the light is allowed to travel several times the transport mean free path from the source.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. H. Kao, K. A. Jester, A. G. Yodh, and P. J. Collings, "Observation of light diffusion and correlation transport in nematic liquid crystals," Phys. Rev. Lett. 77, 2233-2236 (1996).
    [CrossRef] [PubMed]
  2. D. S. Wiersma, A. Muzzi, M. Colocci, and R. Righini, "Time-resolved anisotropic multiple light scattering in nematic liquid crystals," Phys. Rev. Lett. 83, 4321-4324 (1999).
    [CrossRef]
  3. A. Sviridov, V. Chernomordik, M. Hassan, A. Russo, A. Eidsath, P. Smith, and A. H. Gandjbakhche, "Intensity profiles of linearly polarized light backscattered from skin and tissue-like phantoms," J. Biomed. Opt. 10, 014012 (9 pages) (2005).
    [CrossRef]
  4. T. Binzoni, C. Courvoisier, R. Giust, G. Tribillon, T. Gharbi, J. C. Hebden, T. S. Leung, J. Roux, and D. T. Delpy "Anisotropic photon migration in human skeletal muscle," Phys. Med. Biol. 51, N79-N90 (2006).
    [CrossRef] [PubMed]
  5. A. Kienle and R. Hibst, "Light guiding in biological tissue due to scattering," Phys. Rev. Lett. 97, 018104 (4 pages) (2006).
    [CrossRef] [PubMed]
  6. S. Nickell, M. Hermann, M. Essenpreis, T. J. Farrell, U. Krämer, and M. S. Patterson, "Anisotropy of light propagation in human skin," Phys. Med. Biol. 45, 2873-2886 (2000).
    [CrossRef] [PubMed]
  7. A. Kienle, F. K. Forster, and R. Hibst, "Anisotropy of light propagation in biological tissue," Opt. Lett. 29, 2617-2619 (2004).
    [CrossRef] [PubMed]
  8. C. Baravian, F. Caton, J. Dillet, G. Toussaint, and P. Flaud, "Incoherent light transport in an anisotropic random medium: A probe of human erythrocyte aggregation and deformation," Phys. Rev. E 76, 011409 (7 pages) (2007).
    [CrossRef]
  9. P. M. Johnson, B. P. J. Bret, J. G. Rivas, J. J. Kelly, and A. Lagendijk, "Anisotropic Diffusion of Light in a Strongly Scattering Material," Phys. Rev. Lett. 89, 243901 (4 pages) (2002).
    [CrossRef] [PubMed]
  10. B. P. J. Bret and A. Lagendijk, "Anisotropic enhanced backscattering induced by anisotropic diffusion," Phys. Rev. E 70,036601 (5 pages) (2004).
    [CrossRef]
  11. B. van Tiggelen and H. Stark, "Nematic liquid crystals as a new challenge for radiative transfer," Rev. Mod. Phys. 72, 1017-1039 (2000).
    [CrossRef]
  12. B. Kaas, B. van Tiggelen, and A. Lagendijk, "Anisotropy and interference in wave transport: An analytic theory," Phys. Rev. Lett. 100, 243901 (4 pages) (2008). (This reference describes angle dependent mean free path and velocity vectors which are the product of the unit vector in the direction of the wave vector and the mean free path and velocity tensors respectively.)
    [CrossRef]
  13. B. A. van Tiggelen, R. Maynard, and A. Heiderich, "Anisotropic light diffusion in oriented nematic liquid crystals," Phys. Rev. Lett. 77, 639-642 (1996).
    [CrossRef] [PubMed]
  14. H. Stark and T. C. Lubensky, "Multiple light scattering in nematic liquid crystals," Phys. Rev. Lett. 77, 2229-2232 (1996).
    [CrossRef] [PubMed]
  15. L. Margerin, "Attenuation, transport and diffusion of scalar waves in textured random media," Tectonophysics 416, 229-244 (2006).
    [CrossRef]
  16. A. Z. Genack, "Optical transmission in disordered media," Phys. Rev. Lett. 58, 2043-2046 (1987).
    [CrossRef] [PubMed]
  17. 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]
  18. J. X. Zhu, D. J. Pine, and D. A. Weitz, "Internal reflection of diffusive light in random media," Phys. Rev. A 44, 3948-3959 (1991).
    [CrossRef] [PubMed]
  19. L. Dagdug, G. H. Weiss, and A. H. Gandjbakhche, "Effects ofanisotropic optical properties on photon migration in structured tissues," Phys. Med. Biol. 48, 1361-1370 (2003).
    [CrossRef] [PubMed]
  20. J. Heino, S. Arridge, J. Sikora, and E. Somersalo, "Anisotropic effects in highly scattering media," Phys. Rev. E 68, 031908 (8 pages) (2003).
    [CrossRef]
  21. A. Kienle, "Anisotropic light diffusion: An oxymoron?" Phys. Rev. Lett. 98, 218104 (4 pages) (2007).
    [CrossRef] [PubMed]
  22. J. Taniguchi, H. Murata, and Y. Okamura, "Light diffusion model for determination of optical properties of rectangular parallelepiped highly scattering media," Appl. Opt. 46, 2649-2655 (2007).
    [CrossRef] [PubMed]
  23. The effect of absorption has been treated for the isotropic case in reference [24]. For the samples studied here, the expressions given sufficiently described the data without the inclusion of absorption.
  24. A. Kienle, "Light diffusion through a turbid parallelepiped," J. Opt. Soc. Am. A 22, 1883-1888 (2005).
    [CrossRef]
  25. E. Akkermans, P. E. Wolf, and R. Maynard, "Coherent Backscattering of light by disordered media: Analysis of the peak line shape," Phys. Rev. Lett. 56, 1471-1474 (1986).
    [CrossRef] [PubMed]
  26. M. U. Vera and D. J. Durian, "Angular distribution of diffusely transmitted light," Phys. Rev. E 53, 3215-3224 (1996).
    [CrossRef]
  27. J. C. Hebden, J. J. G. Guerrero, V. Chernomordik, and A. H. Gandjbakhche, "Experimental evaluation of an anisotropic scattering model of a slab geometry," Opt. Lett. 29, 2518-2520 (2004).
    [CrossRef] [PubMed]
  28. F. J. P. Schuurmans, D. Vanmaekelbergh, J. v. d. Lagemaat, and A. Lagendijk, "Strongly photonic macroporous gallium phosphide networks," Science 284, 141-143 (1999).
    [CrossRef] [PubMed]

2008 (1)

B. Kaas, B. van Tiggelen, and A. Lagendijk, "Anisotropy and interference in wave transport: An analytic theory," Phys. Rev. Lett. 100, 243901 (4 pages) (2008). (This reference describes angle dependent mean free path and velocity vectors which are the product of the unit vector in the direction of the wave vector and the mean free path and velocity tensors respectively.)
[CrossRef]

2007 (2)

2006 (2)

T. Binzoni, C. Courvoisier, R. Giust, G. Tribillon, T. Gharbi, J. C. Hebden, T. S. Leung, J. Roux, and D. T. Delpy "Anisotropic photon migration in human skeletal muscle," Phys. Med. Biol. 51, N79-N90 (2006).
[CrossRef] [PubMed]

L. Margerin, "Attenuation, transport and diffusion of scalar waves in textured random media," Tectonophysics 416, 229-244 (2006).
[CrossRef]

2005 (1)

2004 (3)

2003 (2)

L. Dagdug, G. H. Weiss, and A. H. Gandjbakhche, "Effects ofanisotropic optical properties on photon migration in structured tissues," Phys. Med. Biol. 48, 1361-1370 (2003).
[CrossRef] [PubMed]

J. Heino, S. Arridge, J. Sikora, and E. Somersalo, "Anisotropic effects in highly scattering media," Phys. Rev. E 68, 031908 (8 pages) (2003).
[CrossRef]

2002 (1)

P. M. Johnson, B. P. J. Bret, J. G. Rivas, J. J. Kelly, and A. Lagendijk, "Anisotropic Diffusion of Light in a Strongly Scattering Material," Phys. Rev. Lett. 89, 243901 (4 pages) (2002).
[CrossRef] [PubMed]

2000 (2)

B. van Tiggelen and H. Stark, "Nematic liquid crystals as a new challenge for radiative transfer," Rev. Mod. Phys. 72, 1017-1039 (2000).
[CrossRef]

S. Nickell, M. Hermann, M. Essenpreis, T. J. Farrell, U. Krämer, and M. S. Patterson, "Anisotropy of light propagation in human skin," Phys. Med. Biol. 45, 2873-2886 (2000).
[CrossRef] [PubMed]

1999 (2)

D. S. Wiersma, A. Muzzi, M. Colocci, and R. Righini, "Time-resolved anisotropic multiple light scattering in nematic liquid crystals," Phys. Rev. Lett. 83, 4321-4324 (1999).
[CrossRef]

F. J. P. Schuurmans, D. Vanmaekelbergh, J. v. d. Lagemaat, and A. Lagendijk, "Strongly photonic macroporous gallium phosphide networks," Science 284, 141-143 (1999).
[CrossRef] [PubMed]

1996 (4)

M. U. Vera and D. J. Durian, "Angular distribution of diffusely transmitted light," Phys. Rev. E 53, 3215-3224 (1996).
[CrossRef]

M. H. Kao, K. A. Jester, A. G. Yodh, and P. J. Collings, "Observation of light diffusion and correlation transport in nematic liquid crystals," Phys. Rev. Lett. 77, 2233-2236 (1996).
[CrossRef] [PubMed]

B. A. van Tiggelen, R. Maynard, and A. Heiderich, "Anisotropic light diffusion in oriented nematic liquid crystals," Phys. Rev. Lett. 77, 639-642 (1996).
[CrossRef] [PubMed]

H. Stark and T. C. Lubensky, "Multiple light scattering in nematic liquid crystals," Phys. Rev. Lett. 77, 2229-2232 (1996).
[CrossRef] [PubMed]

1991 (1)

J. X. Zhu, D. J. Pine, and D. A. Weitz, "Internal reflection of diffusive light in random media," Phys. Rev. A 44, 3948-3959 (1991).
[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, 2043-2046 (1987).
[CrossRef] [PubMed]

1986 (1)

E. Akkermans, P. E. Wolf, and R. Maynard, "Coherent Backscattering of light by disordered media: Analysis of the peak line shape," Phys. Rev. Lett. 56, 1471-1474 (1986).
[CrossRef] [PubMed]

Akkermans, E.

E. Akkermans, P. E. Wolf, and R. Maynard, "Coherent Backscattering of light by disordered media: Analysis of the peak line shape," Phys. Rev. Lett. 56, 1471-1474 (1986).
[CrossRef] [PubMed]

Arridge, S.

J. Heino, S. Arridge, J. Sikora, and E. Somersalo, "Anisotropic effects in highly scattering media," Phys. Rev. E 68, 031908 (8 pages) (2003).
[CrossRef]

Binzoni, T.

T. Binzoni, C. Courvoisier, R. Giust, G. Tribillon, T. Gharbi, J. C. Hebden, T. S. Leung, J. Roux, and D. T. Delpy "Anisotropic photon migration in human skeletal muscle," Phys. Med. Biol. 51, N79-N90 (2006).
[CrossRef] [PubMed]

Bret, B. P. J.

B. P. J. Bret and A. Lagendijk, "Anisotropic enhanced backscattering induced by anisotropic diffusion," Phys. Rev. E 70,036601 (5 pages) (2004).
[CrossRef]

P. M. Johnson, B. P. J. Bret, J. G. Rivas, J. J. Kelly, and A. Lagendijk, "Anisotropic Diffusion of Light in a Strongly Scattering Material," Phys. Rev. Lett. 89, 243901 (4 pages) (2002).
[CrossRef] [PubMed]

Chernomordik, V.

Collings, P. J.

M. H. Kao, K. A. Jester, A. G. Yodh, and P. J. Collings, "Observation of light diffusion and correlation transport in nematic liquid crystals," Phys. Rev. Lett. 77, 2233-2236 (1996).
[CrossRef] [PubMed]

Colocci, M.

D. S. Wiersma, A. Muzzi, M. Colocci, and R. Righini, "Time-resolved anisotropic multiple light scattering in nematic liquid crystals," Phys. Rev. Lett. 83, 4321-4324 (1999).
[CrossRef]

Courvoisier, C.

T. Binzoni, C. Courvoisier, R. Giust, G. Tribillon, T. Gharbi, J. C. Hebden, T. S. Leung, J. Roux, and D. T. Delpy "Anisotropic photon migration in human skeletal muscle," Phys. Med. Biol. 51, N79-N90 (2006).
[CrossRef] [PubMed]

Dagdug, L.

L. Dagdug, G. H. Weiss, and A. H. Gandjbakhche, "Effects ofanisotropic optical properties on photon migration in structured tissues," Phys. Med. Biol. 48, 1361-1370 (2003).
[CrossRef] [PubMed]

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]

Delpy, D. T.

T. Binzoni, C. Courvoisier, R. Giust, G. Tribillon, T. Gharbi, J. C. Hebden, T. S. Leung, J. Roux, and D. T. Delpy "Anisotropic photon migration in human skeletal muscle," Phys. Med. Biol. 51, N79-N90 (2006).
[CrossRef] [PubMed]

Durian, D. J.

M. U. Vera and D. J. Durian, "Angular distribution of diffusely transmitted light," Phys. Rev. E 53, 3215-3224 (1996).
[CrossRef]

Essenpreis, M.

S. Nickell, M. Hermann, M. Essenpreis, T. J. Farrell, U. Krämer, and M. S. Patterson, "Anisotropy of light propagation in human skin," Phys. Med. Biol. 45, 2873-2886 (2000).
[CrossRef] [PubMed]

Farrell, T. J.

S. Nickell, M. Hermann, M. Essenpreis, T. J. Farrell, U. Krämer, and M. S. Patterson, "Anisotropy of light propagation in human skin," Phys. Med. Biol. 45, 2873-2886 (2000).
[CrossRef] [PubMed]

Forster, F. K.

Gandjbakhche, A. H.

J. C. Hebden, J. J. G. Guerrero, V. Chernomordik, and A. H. Gandjbakhche, "Experimental evaluation of an anisotropic scattering model of a slab geometry," Opt. Lett. 29, 2518-2520 (2004).
[CrossRef] [PubMed]

L. Dagdug, G. H. Weiss, and A. H. Gandjbakhche, "Effects ofanisotropic optical properties on photon migration in structured tissues," Phys. Med. Biol. 48, 1361-1370 (2003).
[CrossRef] [PubMed]

Genack, A. Z.

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

Gharbi, T.

T. Binzoni, C. Courvoisier, R. Giust, G. Tribillon, T. Gharbi, J. C. Hebden, T. S. Leung, J. Roux, and D. T. Delpy "Anisotropic photon migration in human skeletal muscle," Phys. Med. Biol. 51, N79-N90 (2006).
[CrossRef] [PubMed]

Giust, R.

T. Binzoni, C. Courvoisier, R. Giust, G. Tribillon, T. Gharbi, J. C. Hebden, T. S. Leung, J. Roux, and D. T. Delpy "Anisotropic photon migration in human skeletal muscle," Phys. Med. Biol. 51, N79-N90 (2006).
[CrossRef] [PubMed]

Guerrero, J. J. G.

Hebden, J. C.

T. Binzoni, C. Courvoisier, R. Giust, G. Tribillon, T. Gharbi, J. C. Hebden, T. S. Leung, J. Roux, and D. T. Delpy "Anisotropic photon migration in human skeletal muscle," Phys. Med. Biol. 51, N79-N90 (2006).
[CrossRef] [PubMed]

J. C. Hebden, J. J. G. Guerrero, V. Chernomordik, and A. H. Gandjbakhche, "Experimental evaluation of an anisotropic scattering model of a slab geometry," Opt. Lett. 29, 2518-2520 (2004).
[CrossRef] [PubMed]

Heiderich, A.

B. A. van Tiggelen, R. Maynard, and A. Heiderich, "Anisotropic light diffusion in oriented nematic liquid crystals," Phys. Rev. Lett. 77, 639-642 (1996).
[CrossRef] [PubMed]

Heino, J.

J. Heino, S. Arridge, J. Sikora, and E. Somersalo, "Anisotropic effects in highly scattering media," Phys. Rev. E 68, 031908 (8 pages) (2003).
[CrossRef]

Hermann, M.

S. Nickell, M. Hermann, M. Essenpreis, T. J. Farrell, U. Krämer, and M. S. Patterson, "Anisotropy of light propagation in human skin," Phys. Med. Biol. 45, 2873-2886 (2000).
[CrossRef] [PubMed]

Hibst, R.

Jester, K. A.

M. H. Kao, K. A. Jester, A. G. Yodh, and P. J. Collings, "Observation of light diffusion and correlation transport in nematic liquid crystals," Phys. Rev. Lett. 77, 2233-2236 (1996).
[CrossRef] [PubMed]

Johnson, P. M.

P. M. Johnson, B. P. J. Bret, J. G. Rivas, J. J. Kelly, and A. Lagendijk, "Anisotropic Diffusion of Light in a Strongly Scattering Material," Phys. Rev. Lett. 89, 243901 (4 pages) (2002).
[CrossRef] [PubMed]

Kaas, B.

B. Kaas, B. van Tiggelen, and A. Lagendijk, "Anisotropy and interference in wave transport: An analytic theory," Phys. Rev. Lett. 100, 243901 (4 pages) (2008). (This reference describes angle dependent mean free path and velocity vectors which are the product of the unit vector in the direction of the wave vector and the mean free path and velocity tensors respectively.)
[CrossRef]

Kao, M. H.

M. H. Kao, K. A. Jester, A. G. Yodh, and P. J. Collings, "Observation of light diffusion and correlation transport in nematic liquid crystals," Phys. Rev. Lett. 77, 2233-2236 (1996).
[CrossRef] [PubMed]

Kelly, J. J.

P. M. Johnson, B. P. J. Bret, J. G. Rivas, J. J. Kelly, and A. Lagendijk, "Anisotropic Diffusion of Light in a Strongly Scattering Material," Phys. Rev. Lett. 89, 243901 (4 pages) (2002).
[CrossRef] [PubMed]

Kienle, A.

Krämer, U.

S. Nickell, M. Hermann, M. Essenpreis, T. J. Farrell, U. Krämer, and M. S. Patterson, "Anisotropy of light propagation in human skin," Phys. Med. Biol. 45, 2873-2886 (2000).
[CrossRef] [PubMed]

Lagendijk, A.

B. Kaas, B. van Tiggelen, and A. Lagendijk, "Anisotropy and interference in wave transport: An analytic theory," Phys. Rev. Lett. 100, 243901 (4 pages) (2008). (This reference describes angle dependent mean free path and velocity vectors which are the product of the unit vector in the direction of the wave vector and the mean free path and velocity tensors respectively.)
[CrossRef]

B. P. J. Bret and A. Lagendijk, "Anisotropic enhanced backscattering induced by anisotropic diffusion," Phys. Rev. E 70,036601 (5 pages) (2004).
[CrossRef]

P. M. Johnson, B. P. J. Bret, J. G. Rivas, J. J. Kelly, and A. Lagendijk, "Anisotropic Diffusion of Light in a Strongly Scattering Material," Phys. Rev. Lett. 89, 243901 (4 pages) (2002).
[CrossRef] [PubMed]

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]

Leung, T. S.

T. Binzoni, C. Courvoisier, R. Giust, G. Tribillon, T. Gharbi, J. C. Hebden, T. S. Leung, J. Roux, and D. T. Delpy "Anisotropic photon migration in human skeletal muscle," Phys. Med. Biol. 51, N79-N90 (2006).
[CrossRef] [PubMed]

Lubensky, T. C.

H. Stark and T. C. Lubensky, "Multiple light scattering in nematic liquid crystals," Phys. Rev. Lett. 77, 2229-2232 (1996).
[CrossRef] [PubMed]

Margerin, L.

L. Margerin, "Attenuation, transport and diffusion of scalar waves in textured random media," Tectonophysics 416, 229-244 (2006).
[CrossRef]

Maynard, R.

B. A. van Tiggelen, R. Maynard, and A. Heiderich, "Anisotropic light diffusion in oriented nematic liquid crystals," Phys. Rev. Lett. 77, 639-642 (1996).
[CrossRef] [PubMed]

E. Akkermans, P. E. Wolf, and R. Maynard, "Coherent Backscattering of light by disordered media: Analysis of the peak line shape," Phys. Rev. Lett. 56, 1471-1474 (1986).
[CrossRef] [PubMed]

Murata, H.

Muzzi, A.

D. S. Wiersma, A. Muzzi, M. Colocci, and R. Righini, "Time-resolved anisotropic multiple light scattering in nematic liquid crystals," Phys. Rev. Lett. 83, 4321-4324 (1999).
[CrossRef]

Nickell, S.

S. Nickell, M. Hermann, M. Essenpreis, T. J. Farrell, U. Krämer, and M. S. Patterson, "Anisotropy of light propagation in human skin," Phys. Med. Biol. 45, 2873-2886 (2000).
[CrossRef] [PubMed]

Okamura, Y.

Patterson, M. S.

S. Nickell, M. Hermann, M. Essenpreis, T. J. Farrell, U. Krämer, and M. S. Patterson, "Anisotropy of light propagation in human skin," Phys. Med. Biol. 45, 2873-2886 (2000).
[CrossRef] [PubMed]

Pine, D. J.

J. X. Zhu, D. J. Pine, and D. A. Weitz, "Internal reflection of diffusive light in random media," Phys. Rev. A 44, 3948-3959 (1991).
[CrossRef] [PubMed]

Righini, R.

D. S. Wiersma, A. Muzzi, M. Colocci, and R. Righini, "Time-resolved anisotropic multiple light scattering in nematic liquid crystals," Phys. Rev. Lett. 83, 4321-4324 (1999).
[CrossRef]

Rivas, J. G.

P. M. Johnson, B. P. J. Bret, J. G. Rivas, J. J. Kelly, and A. Lagendijk, "Anisotropic Diffusion of Light in a Strongly Scattering Material," Phys. Rev. Lett. 89, 243901 (4 pages) (2002).
[CrossRef] [PubMed]

Roux, J.

T. Binzoni, C. Courvoisier, R. Giust, G. Tribillon, T. Gharbi, J. C. Hebden, T. S. Leung, J. Roux, and D. T. Delpy "Anisotropic photon migration in human skeletal muscle," Phys. Med. Biol. 51, N79-N90 (2006).
[CrossRef] [PubMed]

Schuurmans, F. J. P.

F. J. P. Schuurmans, D. Vanmaekelbergh, J. v. d. Lagemaat, and A. Lagendijk, "Strongly photonic macroporous gallium phosphide networks," Science 284, 141-143 (1999).
[CrossRef] [PubMed]

Sikora, J.

J. Heino, S. Arridge, J. Sikora, and E. Somersalo, "Anisotropic effects in highly scattering media," Phys. Rev. E 68, 031908 (8 pages) (2003).
[CrossRef]

Somersalo, E.

J. Heino, S. Arridge, J. Sikora, and E. Somersalo, "Anisotropic effects in highly scattering media," Phys. Rev. E 68, 031908 (8 pages) (2003).
[CrossRef]

Stark, H.

B. van Tiggelen and H. Stark, "Nematic liquid crystals as a new challenge for radiative transfer," Rev. Mod. Phys. 72, 1017-1039 (2000).
[CrossRef]

H. Stark and T. C. Lubensky, "Multiple light scattering in nematic liquid crystals," Phys. Rev. Lett. 77, 2229-2232 (1996).
[CrossRef] [PubMed]

Taniguchi, J.

Tribillon, G.

T. Binzoni, C. Courvoisier, R. Giust, G. Tribillon, T. Gharbi, J. C. Hebden, T. S. Leung, J. Roux, and D. T. Delpy "Anisotropic photon migration in human skeletal muscle," Phys. Med. Biol. 51, N79-N90 (2006).
[CrossRef] [PubMed]

van Tiggelen, B.

B. Kaas, B. van Tiggelen, and A. Lagendijk, "Anisotropy and interference in wave transport: An analytic theory," Phys. Rev. Lett. 100, 243901 (4 pages) (2008). (This reference describes angle dependent mean free path and velocity vectors which are the product of the unit vector in the direction of the wave vector and the mean free path and velocity tensors respectively.)
[CrossRef]

B. van Tiggelen and H. Stark, "Nematic liquid crystals as a new challenge for radiative transfer," Rev. Mod. Phys. 72, 1017-1039 (2000).
[CrossRef]

van Tiggelen, B. A.

B. A. van Tiggelen, R. Maynard, and A. Heiderich, "Anisotropic light diffusion in oriented nematic liquid crystals," Phys. Rev. Lett. 77, 639-642 (1996).
[CrossRef] [PubMed]

Vanmaekelbergh, D.

F. J. P. Schuurmans, D. Vanmaekelbergh, J. v. d. Lagemaat, and A. Lagendijk, "Strongly photonic macroporous gallium phosphide networks," Science 284, 141-143 (1999).
[CrossRef] [PubMed]

Vera, M. U.

M. U. Vera and D. J. Durian, "Angular distribution of diffusely transmitted light," Phys. Rev. E 53, 3215-3224 (1996).
[CrossRef]

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]

Weiss, G. H.

L. Dagdug, G. H. Weiss, and A. H. Gandjbakhche, "Effects ofanisotropic optical properties on photon migration in structured tissues," Phys. Med. Biol. 48, 1361-1370 (2003).
[CrossRef] [PubMed]

Weitz, D. A.

J. X. Zhu, D. J. Pine, and D. A. Weitz, "Internal reflection of diffusive light in random media," Phys. Rev. A 44, 3948-3959 (1991).
[CrossRef] [PubMed]

Wiersma, D. S.

D. S. Wiersma, A. Muzzi, M. Colocci, and R. Righini, "Time-resolved anisotropic multiple light scattering in nematic liquid crystals," Phys. Rev. Lett. 83, 4321-4324 (1999).
[CrossRef]

Wolf, P. E.

E. Akkermans, P. E. Wolf, and R. Maynard, "Coherent Backscattering of light by disordered media: Analysis of the peak line shape," Phys. Rev. Lett. 56, 1471-1474 (1986).
[CrossRef] [PubMed]

Yodh, A. G.

M. H. Kao, K. A. Jester, A. G. Yodh, and P. J. Collings, "Observation of light diffusion and correlation transport in nematic liquid crystals," Phys. Rev. Lett. 77, 2233-2236 (1996).
[CrossRef] [PubMed]

Zhu, J. X.

J. X. Zhu, D. J. Pine, and D. A. Weitz, "Internal reflection of diffusive light in random media," Phys. Rev. A 44, 3948-3959 (1991).
[CrossRef] [PubMed]

Appl. Opt. (1)

J. Opt. Soc. Am. A (1)

Opt. Lett. (2)

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. Med. Biol. (3)

T. Binzoni, C. Courvoisier, R. Giust, G. Tribillon, T. Gharbi, J. C. Hebden, T. S. Leung, J. Roux, and D. T. Delpy "Anisotropic photon migration in human skeletal muscle," Phys. Med. Biol. 51, N79-N90 (2006).
[CrossRef] [PubMed]

L. Dagdug, G. H. Weiss, and A. H. Gandjbakhche, "Effects ofanisotropic optical properties on photon migration in structured tissues," Phys. Med. Biol. 48, 1361-1370 (2003).
[CrossRef] [PubMed]

S. Nickell, M. Hermann, M. Essenpreis, T. J. Farrell, U. Krämer, and M. S. Patterson, "Anisotropy of light propagation in human skin," Phys. Med. Biol. 45, 2873-2886 (2000).
[CrossRef] [PubMed]

Phys. Rev. A (1)

J. X. Zhu, D. J. Pine, and D. A. Weitz, "Internal reflection of diffusive light in random media," Phys. Rev. A 44, 3948-3959 (1991).
[CrossRef] [PubMed]

Phys. Rev. E (3)

J. Heino, S. Arridge, J. Sikora, and E. Somersalo, "Anisotropic effects in highly scattering media," Phys. Rev. E 68, 031908 (8 pages) (2003).
[CrossRef]

B. P. J. Bret and A. Lagendijk, "Anisotropic enhanced backscattering induced by anisotropic diffusion," Phys. Rev. E 70,036601 (5 pages) (2004).
[CrossRef]

M. U. Vera and D. J. Durian, "Angular distribution of diffusely transmitted light," Phys. Rev. E 53, 3215-3224 (1996).
[CrossRef]

Phys. Rev. Lett. (9)

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

E. Akkermans, P. E. Wolf, and R. Maynard, "Coherent Backscattering of light by disordered media: Analysis of the peak line shape," Phys. Rev. Lett. 56, 1471-1474 (1986).
[CrossRef] [PubMed]

P. M. Johnson, B. P. J. Bret, J. G. Rivas, J. J. Kelly, and A. Lagendijk, "Anisotropic Diffusion of Light in a Strongly Scattering Material," Phys. Rev. Lett. 89, 243901 (4 pages) (2002).
[CrossRef] [PubMed]

B. Kaas, B. van Tiggelen, and A. Lagendijk, "Anisotropy and interference in wave transport: An analytic theory," Phys. Rev. Lett. 100, 243901 (4 pages) (2008). (This reference describes angle dependent mean free path and velocity vectors which are the product of the unit vector in the direction of the wave vector and the mean free path and velocity tensors respectively.)
[CrossRef]

B. A. van Tiggelen, R. Maynard, and A. Heiderich, "Anisotropic light diffusion in oriented nematic liquid crystals," Phys. Rev. Lett. 77, 639-642 (1996).
[CrossRef] [PubMed]

H. Stark and T. C. Lubensky, "Multiple light scattering in nematic liquid crystals," Phys. Rev. Lett. 77, 2229-2232 (1996).
[CrossRef] [PubMed]

A. Kienle, "Anisotropic light diffusion: An oxymoron?" Phys. Rev. Lett. 98, 218104 (4 pages) (2007).
[CrossRef] [PubMed]

M. H. Kao, K. A. Jester, A. G. Yodh, and P. J. Collings, "Observation of light diffusion and correlation transport in nematic liquid crystals," Phys. Rev. Lett. 77, 2233-2236 (1996).
[CrossRef] [PubMed]

D. S. Wiersma, A. Muzzi, M. Colocci, and R. Righini, "Time-resolved anisotropic multiple light scattering in nematic liquid crystals," Phys. Rev. Lett. 83, 4321-4324 (1999).
[CrossRef]

Rev. Mod. Phys. (1)

B. van Tiggelen and H. Stark, "Nematic liquid crystals as a new challenge for radiative transfer," Rev. Mod. Phys. 72, 1017-1039 (2000).
[CrossRef]

Science (1)

F. J. P. Schuurmans, D. Vanmaekelbergh, J. v. d. Lagemaat, and A. Lagendijk, "Strongly photonic macroporous gallium phosphide networks," Science 284, 141-143 (1999).
[CrossRef] [PubMed]

Tectonophysics (1)

L. Margerin, "Attenuation, transport and diffusion of scalar waves in textured random media," Tectonophysics 416, 229-244 (2006).
[CrossRef]

Other (4)

C. Baravian, F. Caton, J. Dillet, G. Toussaint, and P. Flaud, "Incoherent light transport in an anisotropic random medium: A probe of human erythrocyte aggregation and deformation," Phys. Rev. E 76, 011409 (7 pages) (2007).
[CrossRef]

A. Sviridov, V. Chernomordik, M. Hassan, A. Russo, A. Eidsath, P. Smith, and A. H. Gandjbakhche, "Intensity profiles of linearly polarized light backscattered from skin and tissue-like phantoms," J. Biomed. Opt. 10, 014012 (9 pages) (2005).
[CrossRef]

A. Kienle and R. Hibst, "Light guiding in biological tissue due to scattering," Phys. Rev. Lett. 97, 018104 (4 pages) (2006).
[CrossRef] [PubMed]

The effect of absorption has been treated for the isotropic case in reference [24]. For the samples studied here, the expressions given sufficiently described the data without the inclusion of absorption.

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 (5)

Fig. 1.
Fig. 1.

Cartoon of the imaging geometry. A beam is weakly focused on one (input) side of the sample. The emitted light is imaged on a side perpendicular to the input side (the image plane). The focus point is a distance L from the image plane. The focus spot size is much smaller than L, justifying a point source approximation. The sample is chosen such that w 1,w 2L, i.e. the slab is effectively semi-infinite in the image plane.

Fig. 2.
Fig. 2.

Porous plastic fiber sample (Porex). The scale bar to the lower left is 1 mm. The inset shows a magnified view of the same sample with a scale bar of 100 µm. From this SEM, it is clear that the fiber orientations are both highly correlated and highly connected.

Fig. 3.
Fig. 3.

Iso-intensity lines for a single measured image (thin lines) and for a fit (thick lines) to Eq. 9 with L=2.0 mm for the parallel (top) and perpendicular (bottom) orientations of the beam with respect to the fibers. The fiber orientation for both plots is indicated by the double-sided arrow. The same scales are used for both axes and both plots to depict the distortion introduced by the anisotropy depending of the sample orientation. The contour lines delineate steps of 0.5, from 0.5 to 3.5 in the top plot, and from 0.2 to 2.7 in the bottom plot in units that are arbitrary in overall scale but consistent from measurement to measurement. The strong sample anisotropy in the diffusion constants is qualitatively clear. Furthermore, the extension of the data and fit over the edge (i.e. the fact that some of the low intensity contours are not closed but come to an abrupt end at the edge of the sample) indicates the effect of the extrapolation length and suggests a method for its measurement. The excellent overlap of the fit on the data indicates that the diffusion model describes the light propagation for this value of L.

Fig. 4.
Fig. 4.

Data and residuals (open symbols) and fits (solid lines), showing the intensity with the incoming beam parallel (circles) and perpendicular (triangles) to the fibers along the x=0 line. I.e. this is the intensity measured along the line parallel to the incoming beam. The inset shows the narrow range of data near the input edge of the sample (y=0), showing the negative values of the I=0 intercept of the fit. This intercept is the extrapolation length. The much larger intercept for the parallel orientation clearly indicates the larger extrapolation length at this input surface.

Fig. 5.
Fig. 5.

Parameters determined by fitting to the images for each value of L for the two sample orientations. The open and closed circles were measured with the incoming beam parallel and perpendicular to the sample respectively. The diffusion model becomes consistent at values of L of larger than 0.75 mm, thus the fits were performed on these data points. The average values values of β ‖,⊥ and e ‖,⊥ were computed with L>0.75 mm as shown by the horizontal line in plots (a) and (b). In the plot (c) the data was fit to Eq. 11, which is nearly linear for the values of L measured.

Equations (13)

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

S ( x , y , z , l ¯ , L ) = · D ¯ · U ( x , y , z ) ,
D ¯ = ( D xx 0 0 0 D yy 0 0 0 D zz )
l ¯ = ( l xx 0 0 0 l yy 0 0 0 l zz ) .
S ( x , y , z , l yy , L ) = S 0 δ ( x ) δ ( y l yy ) δ ( z L ) .
S ( x , y , z , l ¯ , L ) = D Δ U ( x , y , z ) ,
I ( x , y , 0 ) = 3 π S 0 ( L + e z ) ( l yy + e y ) D yy ( D xx D zz ) 1 2 y ×
( ( D xx D yy ) x 2 + ( y + e y ) 2 + ( D zz D yy ) L 2 ) 5 2 .
I tot = + d y 0 I ( x , y , 0 ) d x = ( 2 π S 0 D zz D yy ) l yy + e y L + e z .
I ( x , y , 0 ) = A y ( ( β x ) 2 + ( y + e y ) 2 + L 2 ) 5 2
m D D l + e l + e .
I tot ( finite ) = I tot f ( L d )
D D = e e = l l ,
v v = 1.0 .

Metrics