Abstract

Diffusing-wave spectroscopy (DWS) experiments require the choice of suitable sample geometry. We study sample geometries for transmission experiments by performing DWS measurements on a variable thickness cell. The data reveal that DWS works well, giving consistent answers to within 5% when the cell is more than 10 random walk step lengths thick, and that the input geometry is less significant when sample cells are immersed in water than when they are surrounded by air. Further, we see that the applicability of the diffusion approximation depends on the anisotropy of individual scattering events.

© 1993 Optical Society of America

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  1. G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B 65, 409–413 (1987).
    [CrossRef]
  2. M. J. Stephen, “Temporal fluctuations in wave propagation in random media,” Phys. Rev. B 37, 1–5 (1988).
    [CrossRef]
  3. D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
    [CrossRef] [PubMed]
  4. K. M. Yoo, Feng Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990);errata 65, 2120–2121 (1992).
    [CrossRef] [PubMed]
  5. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  6. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  7. C. F. Bohren, Clouds in a Glass of Beer, Simple Experiments in Atmospheric Physics (Wiley, New York, 1987).
  8. D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer, “Diffusing-wave spectroscopy, dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris) 51, 2101–2127 (1990).
  9. B. J. Ackerson, R. L. Dougherty, N. M. Reguigui, U. Nobbman, “Correlation transfer: application of radiative transfer solution methods to photon correlation problems,” J. Thermophys. Heat Transfer 6, 577–588 (1992).
    [CrossRef]
  10. E. Jakeman, C. J. Oliver, E. R. Pike, “The effects of spatial coherence on intensity fluctuation distributions of Gaussian light,” J. Phys. A 3, L45–L48 (1970).
    [CrossRef]
  11. M. J. Devon, A. Rudin, “A simple technique for measuring the refractive index of polymer latexes at various wavelengths,” J. Appl. Polymer Sci. 34, 469–476 (1987).
    [CrossRef]
  12. D. J. Durian, D. A. Weitz, D. J. Pine, “Multiple light-scattering probes of foam structure and dynamics,” Science 252, 686–688 (1991).
    [CrossRef] [PubMed]
  13. A. G. Yodh, P. D. Kaplan, D. J. Pine, “Pulsed diffusing-wave spectroscopy: High resolution through nonlinear optical gating,” Phys. Rev. B 42, 4744–4747 (1990).
    [CrossRef]
  14. J. X. Zhu, D. J. Pine, D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
    [CrossRef] [PubMed]
  15. A. Lagendijk, R. Vreeker, P. DeVries, “Influence of internal reflection on diffusive transport in strongly scattering media,” Phys. Lett. A 136, 81–88 (1989).
    [CrossRef]
  16. Th. M. Nieuwenhuizen, Van der Waals-Zeeman Laboratorium, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands, and J. M. Luck, Sérvice de Physique Théorique, Centre d'Etudes de Saclay, 91191 Gif-sur-Yvette Cedex, France (personal communication, 1993).
  17. A. Z. Genack, N. Garcia, W. Polkosnik, “Long-range intensity correlation and the approach to localization,” Waves Random Media 3, s57–s64 (1991).
    [CrossRef]
  18. L. Svaasand, R. Haskell, B. J. Tromberg, T. Tsay, McAdams, “Properties of photon density waves at boundaries,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888 (to be published).
  19. B. J. Tromberg, T. Tsay, R. Haskell, L. Svaasand, A. Braniff, “Influence of boundaries on photon density waves in tissues,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888 (to be published).
  20. R. Aronson, Polytechnic University, Brooklyn, New York 11201 (personal communication, 1993).
  21. C. P. Gonatas, M. Ishii, M. Miwa, J. Schotland, B. C. Chance, J. Leigh, “Determination of optical mean free path from pulse propagation and backscattering,” Phys. Rev. E (to be published).
  22. H. S. Carslaw, J. Jaeger, Conduction of Heat in Solids (Oxford U. Press, New York, 1986).
  23. D. A. Weitz, D. J. Pine, “Diffusing-wave spectroscopy,” in Dynamic Light Scattering, W. Brown, ed. (Oxford U. Press, New York, 1993), Chap. 16.
  24. S. Glasstone, M. C. Edlund, The Elements of Nuclear Reactor Theory (Van Nostrand, Princeton, N.J., 1952), Chap. 1.
  25. M. H. Kao, A. G. Yodh, D. J. Pine, “Observation of Brownian motion on the time scale of hydrodynamic interactions,” Phys. Rev. Lett. 70, 242–245 (1992).
    [CrossRef]
  26. D. A. Weitz, D. J. Pine, P. N. Pusey, R. J. A. Tough, “Nondiffusive Brownian motion studied by diffusing-wave spectroscopy,” Phys. Rev. Lett. 63, 1747–1750 (1989).
    [CrossRef] [PubMed]
  27. E. J. Hinch, “Application of the Langevin equation to fluid suspensions,” J. Fluid Mech. 72, 499–511 (1975).
    [CrossRef]
  28. J. Zhu, “Diffusing-wave spectroscopy,” Ph.D. dissertation (City University of New York, New York, N.Y., 1992).
  29. C. W. J. Beenakker, P. Mazur, “Diffusion of spheres in a concentrated suspension II,” Physica 126A, 349–370 (1984).

1992 (2)

B. J. Ackerson, R. L. Dougherty, N. M. Reguigui, U. Nobbman, “Correlation transfer: application of radiative transfer solution methods to photon correlation problems,” J. Thermophys. Heat Transfer 6, 577–588 (1992).
[CrossRef]

M. H. Kao, A. G. Yodh, D. J. Pine, “Observation of Brownian motion on the time scale of hydrodynamic interactions,” Phys. Rev. Lett. 70, 242–245 (1992).
[CrossRef]

1991 (3)

A. Z. Genack, N. Garcia, W. Polkosnik, “Long-range intensity correlation and the approach to localization,” Waves Random Media 3, s57–s64 (1991).
[CrossRef]

D. J. Durian, D. A. Weitz, D. J. Pine, “Multiple light-scattering probes of foam structure and dynamics,” Science 252, 686–688 (1991).
[CrossRef] [PubMed]

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

1990 (3)

A. G. Yodh, P. D. Kaplan, D. J. Pine, “Pulsed diffusing-wave spectroscopy: High resolution through nonlinear optical gating,” Phys. Rev. B 42, 4744–4747 (1990).
[CrossRef]

K. M. Yoo, Feng Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990);errata 65, 2120–2121 (1992).
[CrossRef] [PubMed]

D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer, “Diffusing-wave spectroscopy, dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris) 51, 2101–2127 (1990).

1989 (2)

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

D. A. Weitz, D. J. Pine, P. N. Pusey, R. J. A. Tough, “Nondiffusive Brownian motion studied by diffusing-wave spectroscopy,” Phys. Rev. Lett. 63, 1747–1750 (1989).
[CrossRef] [PubMed]

1988 (2)

M. J. Stephen, “Temporal fluctuations in wave propagation in random media,” Phys. Rev. B 37, 1–5 (1988).
[CrossRef]

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [PubMed]

1987 (2)

G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B 65, 409–413 (1987).
[CrossRef]

M. J. Devon, A. Rudin, “A simple technique for measuring the refractive index of polymer latexes at various wavelengths,” J. Appl. Polymer Sci. 34, 469–476 (1987).
[CrossRef]

1984 (1)

C. W. J. Beenakker, P. Mazur, “Diffusion of spheres in a concentrated suspension II,” Physica 126A, 349–370 (1984).

1975 (1)

E. J. Hinch, “Application of the Langevin equation to fluid suspensions,” J. Fluid Mech. 72, 499–511 (1975).
[CrossRef]

1970 (1)

E. Jakeman, C. J. Oliver, E. R. Pike, “The effects of spatial coherence on intensity fluctuation distributions of Gaussian light,” J. Phys. A 3, L45–L48 (1970).
[CrossRef]

Ackerson, B. J.

B. J. Ackerson, R. L. Dougherty, N. M. Reguigui, U. Nobbman, “Correlation transfer: application of radiative transfer solution methods to photon correlation problems,” J. Thermophys. Heat Transfer 6, 577–588 (1992).
[CrossRef]

Alfano, R. R.

K. M. Yoo, Feng Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990);errata 65, 2120–2121 (1992).
[CrossRef] [PubMed]

Aronson, R.

R. Aronson, Polytechnic University, Brooklyn, New York 11201 (personal communication, 1993).

Beenakker, C. W. J.

C. W. J. Beenakker, P. Mazur, “Diffusion of spheres in a concentrated suspension II,” Physica 126A, 349–370 (1984).

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

C. F. Bohren, Clouds in a Glass of Beer, Simple Experiments in Atmospheric Physics (Wiley, New York, 1987).

Braniff, A.

B. J. Tromberg, T. Tsay, R. Haskell, L. Svaasand, A. Braniff, “Influence of boundaries on photon density waves in tissues,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888 (to be published).

Carslaw, H. S.

H. S. Carslaw, J. Jaeger, Conduction of Heat in Solids (Oxford U. Press, New York, 1986).

Chaikin, P. M.

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [PubMed]

Chance, B. C.

C. P. Gonatas, M. Ishii, M. Miwa, J. Schotland, B. C. Chance, J. Leigh, “Determination of optical mean free path from pulse propagation and backscattering,” Phys. Rev. E (to be published).

Devon, M. J.

M. J. Devon, A. Rudin, “A simple technique for measuring the refractive index of polymer latexes at various wavelengths,” J. Appl. Polymer Sci. 34, 469–476 (1987).
[CrossRef]

DeVries, P.

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

Dougherty, R. L.

B. J. Ackerson, R. L. Dougherty, N. M. Reguigui, U. Nobbman, “Correlation transfer: application of radiative transfer solution methods to photon correlation problems,” J. Thermophys. Heat Transfer 6, 577–588 (1992).
[CrossRef]

Durian, D. J.

D. J. Durian, D. A. Weitz, D. J. Pine, “Multiple light-scattering probes of foam structure and dynamics,” Science 252, 686–688 (1991).
[CrossRef] [PubMed]

Edlund, M. C.

S. Glasstone, M. C. Edlund, The Elements of Nuclear Reactor Theory (Van Nostrand, Princeton, N.J., 1952), Chap. 1.

Garcia, N.

A. Z. Genack, N. Garcia, W. Polkosnik, “Long-range intensity correlation and the approach to localization,” Waves Random Media 3, s57–s64 (1991).
[CrossRef]

Genack, A. Z.

A. Z. Genack, N. Garcia, W. Polkosnik, “Long-range intensity correlation and the approach to localization,” Waves Random Media 3, s57–s64 (1991).
[CrossRef]

Glasstone, S.

S. Glasstone, M. C. Edlund, The Elements of Nuclear Reactor Theory (Van Nostrand, Princeton, N.J., 1952), Chap. 1.

Gonatas, C. P.

C. P. Gonatas, M. Ishii, M. Miwa, J. Schotland, B. C. Chance, J. Leigh, “Determination of optical mean free path from pulse propagation and backscattering,” Phys. Rev. E (to be published).

Haskell, R.

B. J. Tromberg, T. Tsay, R. Haskell, L. Svaasand, A. Braniff, “Influence of boundaries on photon density waves in tissues,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888 (to be published).

L. Svaasand, R. Haskell, B. J. Tromberg, T. Tsay, McAdams, “Properties of photon density waves at boundaries,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888 (to be published).

Herbolzheimer, E.

D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer, “Diffusing-wave spectroscopy, dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris) 51, 2101–2127 (1990).

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [PubMed]

Hinch, E. J.

E. J. Hinch, “Application of the Langevin equation to fluid suspensions,” J. Fluid Mech. 72, 499–511 (1975).
[CrossRef]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Ishii, M.

C. P. Gonatas, M. Ishii, M. Miwa, J. Schotland, B. C. Chance, J. Leigh, “Determination of optical mean free path from pulse propagation and backscattering,” Phys. Rev. E (to be published).

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).

Jaeger, J.

H. S. Carslaw, J. Jaeger, Conduction of Heat in Solids (Oxford U. Press, New York, 1986).

Jakeman, E.

E. Jakeman, C. J. Oliver, E. R. Pike, “The effects of spatial coherence on intensity fluctuation distributions of Gaussian light,” J. Phys. A 3, L45–L48 (1970).
[CrossRef]

Kao, M. H.

M. H. Kao, A. G. Yodh, D. J. Pine, “Observation of Brownian motion on the time scale of hydrodynamic interactions,” Phys. Rev. Lett. 70, 242–245 (1992).
[CrossRef]

Kaplan, P. D.

A. G. Yodh, P. D. Kaplan, D. J. Pine, “Pulsed diffusing-wave spectroscopy: High resolution through nonlinear optical gating,” Phys. Rev. B 42, 4744–4747 (1990).
[CrossRef]

Lagendijk, A.

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

Leigh, J.

C. P. Gonatas, M. Ishii, M. Miwa, J. Schotland, B. C. Chance, J. Leigh, “Determination of optical mean free path from pulse propagation and backscattering,” Phys. Rev. E (to be published).

Liu, Feng

K. M. Yoo, Feng Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990);errata 65, 2120–2121 (1992).
[CrossRef] [PubMed]

Maret, G.

G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B 65, 409–413 (1987).
[CrossRef]

Mazur, P.

C. W. J. Beenakker, P. Mazur, “Diffusion of spheres in a concentrated suspension II,” Physica 126A, 349–370 (1984).

McAdams,

L. Svaasand, R. Haskell, B. J. Tromberg, T. Tsay, McAdams, “Properties of photon density waves at boundaries,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888 (to be published).

Miwa, M.

C. P. Gonatas, M. Ishii, M. Miwa, J. Schotland, B. C. Chance, J. Leigh, “Determination of optical mean free path from pulse propagation and backscattering,” Phys. Rev. E (to be published).

Nieuwenhuizen, Th. M.

Th. M. Nieuwenhuizen, Van der Waals-Zeeman Laboratorium, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands, and J. M. Luck, Sérvice de Physique Théorique, Centre d'Etudes de Saclay, 91191 Gif-sur-Yvette Cedex, France (personal communication, 1993).

Nobbman, U.

B. J. Ackerson, R. L. Dougherty, N. M. Reguigui, U. Nobbman, “Correlation transfer: application of radiative transfer solution methods to photon correlation problems,” J. Thermophys. Heat Transfer 6, 577–588 (1992).
[CrossRef]

Oliver, C. J.

E. Jakeman, C. J. Oliver, E. R. Pike, “The effects of spatial coherence on intensity fluctuation distributions of Gaussian light,” J. Phys. A 3, L45–L48 (1970).
[CrossRef]

Pike, E. R.

E. Jakeman, C. J. Oliver, E. R. Pike, “The effects of spatial coherence on intensity fluctuation distributions of Gaussian light,” J. Phys. A 3, L45–L48 (1970).
[CrossRef]

Pine, D. J.

M. H. Kao, A. G. Yodh, D. J. Pine, “Observation of Brownian motion on the time scale of hydrodynamic interactions,” Phys. Rev. Lett. 70, 242–245 (1992).
[CrossRef]

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

D. J. Durian, D. A. Weitz, D. J. Pine, “Multiple light-scattering probes of foam structure and dynamics,” Science 252, 686–688 (1991).
[CrossRef] [PubMed]

A. G. Yodh, P. D. Kaplan, D. J. Pine, “Pulsed diffusing-wave spectroscopy: High resolution through nonlinear optical gating,” Phys. Rev. B 42, 4744–4747 (1990).
[CrossRef]

D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer, “Diffusing-wave spectroscopy, dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris) 51, 2101–2127 (1990).

D. A. Weitz, D. J. Pine, P. N. Pusey, R. J. A. Tough, “Nondiffusive Brownian motion studied by diffusing-wave spectroscopy,” Phys. Rev. Lett. 63, 1747–1750 (1989).
[CrossRef] [PubMed]

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [PubMed]

D. A. Weitz, D. J. Pine, “Diffusing-wave spectroscopy,” in Dynamic Light Scattering, W. Brown, ed. (Oxford U. Press, New York, 1993), Chap. 16.

Polkosnik, W.

A. Z. Genack, N. Garcia, W. Polkosnik, “Long-range intensity correlation and the approach to localization,” Waves Random Media 3, s57–s64 (1991).
[CrossRef]

Pusey, P. N.

D. A. Weitz, D. J. Pine, P. N. Pusey, R. J. A. Tough, “Nondiffusive Brownian motion studied by diffusing-wave spectroscopy,” Phys. Rev. Lett. 63, 1747–1750 (1989).
[CrossRef] [PubMed]

Reguigui, N. M.

B. J. Ackerson, R. L. Dougherty, N. M. Reguigui, U. Nobbman, “Correlation transfer: application of radiative transfer solution methods to photon correlation problems,” J. Thermophys. Heat Transfer 6, 577–588 (1992).
[CrossRef]

Rudin, A.

M. J. Devon, A. Rudin, “A simple technique for measuring the refractive index of polymer latexes at various wavelengths,” J. Appl. Polymer Sci. 34, 469–476 (1987).
[CrossRef]

Schotland, J.

C. P. Gonatas, M. Ishii, M. Miwa, J. Schotland, B. C. Chance, J. Leigh, “Determination of optical mean free path from pulse propagation and backscattering,” Phys. Rev. E (to be published).

Stephen, M. J.

M. J. Stephen, “Temporal fluctuations in wave propagation in random media,” Phys. Rev. B 37, 1–5 (1988).
[CrossRef]

Svaasand, L.

B. J. Tromberg, T. Tsay, R. Haskell, L. Svaasand, A. Braniff, “Influence of boundaries on photon density waves in tissues,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888 (to be published).

L. Svaasand, R. Haskell, B. J. Tromberg, T. Tsay, McAdams, “Properties of photon density waves at boundaries,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888 (to be published).

Tough, R. J. A.

D. A. Weitz, D. J. Pine, P. N. Pusey, R. J. A. Tough, “Nondiffusive Brownian motion studied by diffusing-wave spectroscopy,” Phys. Rev. Lett. 63, 1747–1750 (1989).
[CrossRef] [PubMed]

Tromberg, B. J.

L. Svaasand, R. Haskell, B. J. Tromberg, T. Tsay, McAdams, “Properties of photon density waves at boundaries,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888 (to be published).

B. J. Tromberg, T. Tsay, R. Haskell, L. Svaasand, A. Braniff, “Influence of boundaries on photon density waves in tissues,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888 (to be published).

Tsay, T.

B. J. Tromberg, T. Tsay, R. Haskell, L. Svaasand, A. Braniff, “Influence of boundaries on photon density waves in tissues,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888 (to be published).

L. Svaasand, R. Haskell, B. J. Tromberg, T. Tsay, McAdams, “Properties of photon density waves at boundaries,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888 (to be published).

Vreeker, R.

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

Weitz, D. A.

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

D. J. Durian, D. A. Weitz, D. J. Pine, “Multiple light-scattering probes of foam structure and dynamics,” Science 252, 686–688 (1991).
[CrossRef] [PubMed]

D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer, “Diffusing-wave spectroscopy, dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris) 51, 2101–2127 (1990).

D. A. Weitz, D. J. Pine, P. N. Pusey, R. J. A. Tough, “Nondiffusive Brownian motion studied by diffusing-wave spectroscopy,” Phys. Rev. Lett. 63, 1747–1750 (1989).
[CrossRef] [PubMed]

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [PubMed]

D. A. Weitz, D. J. Pine, “Diffusing-wave spectroscopy,” in Dynamic Light Scattering, W. Brown, ed. (Oxford U. Press, New York, 1993), Chap. 16.

Wolf, P. E.

G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B 65, 409–413 (1987).
[CrossRef]

Yodh, A. G.

M. H. Kao, A. G. Yodh, D. J. Pine, “Observation of Brownian motion on the time scale of hydrodynamic interactions,” Phys. Rev. Lett. 70, 242–245 (1992).
[CrossRef]

A. G. Yodh, P. D. Kaplan, D. J. Pine, “Pulsed diffusing-wave spectroscopy: High resolution through nonlinear optical gating,” Phys. Rev. B 42, 4744–4747 (1990).
[CrossRef]

Yoo, K. M.

K. M. Yoo, Feng Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990);errata 65, 2120–2121 (1992).
[CrossRef] [PubMed]

Zhu, J.

J. Zhu, “Diffusing-wave spectroscopy,” Ph.D. dissertation (City University of New York, New York, N.Y., 1992).

Zhu, J. X.

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

D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer, “Diffusing-wave spectroscopy, dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris) 51, 2101–2127 (1990).

J. Appl. Polymer Sci. (1)

M. J. Devon, A. Rudin, “A simple technique for measuring the refractive index of polymer latexes at various wavelengths,” J. Appl. Polymer Sci. 34, 469–476 (1987).
[CrossRef]

J. Fluid Mech. (1)

E. J. Hinch, “Application of the Langevin equation to fluid suspensions,” J. Fluid Mech. 72, 499–511 (1975).
[CrossRef]

J. Phys. (Paris) (1)

D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer, “Diffusing-wave spectroscopy, dynamic light scattering in the multiple scattering limit,” J. Phys. (Paris) 51, 2101–2127 (1990).

J. Phys. A (1)

E. Jakeman, C. J. Oliver, E. R. Pike, “The effects of spatial coherence on intensity fluctuation distributions of Gaussian light,” J. Phys. A 3, L45–L48 (1970).
[CrossRef]

J. Thermophys. Heat Transfer (1)

B. J. Ackerson, R. L. Dougherty, N. M. Reguigui, U. Nobbman, “Correlation transfer: application of radiative transfer solution methods to photon correlation problems,” J. Thermophys. Heat Transfer 6, 577–588 (1992).
[CrossRef]

Phys. Lett. A (1)

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

Phys. Rev. A (1)

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

Phys. Rev. B (2)

A. G. Yodh, P. D. Kaplan, D. J. Pine, “Pulsed diffusing-wave spectroscopy: High resolution through nonlinear optical gating,” Phys. Rev. B 42, 4744–4747 (1990).
[CrossRef]

M. J. Stephen, “Temporal fluctuations in wave propagation in random media,” Phys. Rev. B 37, 1–5 (1988).
[CrossRef]

Phys. Rev. Lett. (4)

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [PubMed]

K. M. Yoo, Feng Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990);errata 65, 2120–2121 (1992).
[CrossRef] [PubMed]

M. H. Kao, A. G. Yodh, D. J. Pine, “Observation of Brownian motion on the time scale of hydrodynamic interactions,” Phys. Rev. Lett. 70, 242–245 (1992).
[CrossRef]

D. A. Weitz, D. J. Pine, P. N. Pusey, R. J. A. Tough, “Nondiffusive Brownian motion studied by diffusing-wave spectroscopy,” Phys. Rev. Lett. 63, 1747–1750 (1989).
[CrossRef] [PubMed]

Physica (1)

C. W. J. Beenakker, P. Mazur, “Diffusion of spheres in a concentrated suspension II,” Physica 126A, 349–370 (1984).

Science (1)

D. J. Durian, D. A. Weitz, D. J. Pine, “Multiple light-scattering probes of foam structure and dynamics,” Science 252, 686–688 (1991).
[CrossRef] [PubMed]

Waves Random Media (1)

A. Z. Genack, N. Garcia, W. Polkosnik, “Long-range intensity correlation and the approach to localization,” Waves Random Media 3, s57–s64 (1991).
[CrossRef]

Z. Phys. B (1)

G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B 65, 409–413 (1987).
[CrossRef]

Other (12)

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

C. F. Bohren, Clouds in a Glass of Beer, Simple Experiments in Atmospheric Physics (Wiley, New York, 1987).

L. Svaasand, R. Haskell, B. J. Tromberg, T. Tsay, McAdams, “Properties of photon density waves at boundaries,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888 (to be published).

B. J. Tromberg, T. Tsay, R. Haskell, L. Svaasand, A. Braniff, “Influence of boundaries on photon density waves in tissues,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1888 (to be published).

R. Aronson, Polytechnic University, Brooklyn, New York 11201 (personal communication, 1993).

C. P. Gonatas, M. Ishii, M. Miwa, J. Schotland, B. C. Chance, J. Leigh, “Determination of optical mean free path from pulse propagation and backscattering,” Phys. Rev. E (to be published).

H. S. Carslaw, J. Jaeger, Conduction of Heat in Solids (Oxford U. Press, New York, 1986).

D. A. Weitz, D. J. Pine, “Diffusing-wave spectroscopy,” in Dynamic Light Scattering, W. Brown, ed. (Oxford U. Press, New York, 1993), Chap. 16.

S. Glasstone, M. C. Edlund, The Elements of Nuclear Reactor Theory (Van Nostrand, Princeton, N.J., 1952), Chap. 1.

Th. M. Nieuwenhuizen, Van der Waals-Zeeman Laboratorium, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands, and J. M. Luck, Sérvice de Physique Théorique, Centre d'Etudes de Saclay, 91191 Gif-sur-Yvette Cedex, France (personal communication, 1993).

J. Zhu, “Diffusing-wave spectroscopy,” Ph.D. dissertation (City University of New York, New York, N.Y., 1992).

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Figures (9)

Fig. 1
Fig. 1

Experimental apparatus. The beam from a cw Ar+ ion laser is expanded by spatial filter SF and collimated with lens L. The flat, central 2 cm of this beam passes through iris I1 and then illuminates a slab of scattering particles that may or may not be immersed in water. A single speckle of transmitted light is selected by two pinholes (I2 and I3) and split (by beam splitter BS) between two photomultiplier tubes. The intensity cross-correlation function of the two tubes is monitored by a commercial correlator. To measure transmission coefficients, the laser power is sampled by a beam splitter placed in front of the sample so that the ratio of transmitted intensity to laser intensity can be monitored.

Fig. 2
Fig. 2

Normalized correlation function g1(τ) obtained from a ϕ = 0.0443 sample of 460-nm-diameter spheres, with L = 750 μm, l* = 51 μm, and T = 25 °C. The solid curve is the best fit, from the procedures described in the appendixes, with a reflection coefficient of 0.02.

Fig. 3
Fig. 3

l* measured by static transmission for (a) the 460-nm system in water, (b) the 205-nm system in water. The units are normalized to the average measured l* for L/l* > 10.

Fig. 4
Fig. 4

l* measured by fitting to g2(τ). The cells containing (a) 460-nm particles and (b) 205-nm particles are submerged in a water bath.

Fig. 5
Fig. 5

l* measured by fitting to g2(τ) for the cell of 460-nm particles after the water was drained from the index-matching bath. This fit was done twice. The first time, the correct reflection coefficient was included (circles), and the data appear flat down to L/l* of ∼3. The second fits (triangles) were done without reflection, and a systematic slope is present for samples thinner than ∼ 12l*.

Fig. 6
Fig. 6

Static transmission measured for the 460-nm particles after the water was drained from the index-matching bath.

Fig. 7
Fig. 7

l* determined for various sizes of the input spot size. It appears that the plane-wave approximation works well for beam diameters larger than 5 times the cell thickness.

Fig. 8
Fig. 8

Energy density U is displayed for the one-dimensional steady-state problem. From this solution to the diffusion equation, we derive the transmission coefficient of a slab of optical thickness L/l* in appendix A.

Fig. 9
Fig. 9

Light leaving the cell of diameter D at an angle of θ1 travels in the cell wall of thickness d at an angle θ2, which is calculated by Snell's law. For θ2 greater than the angle for total internal reflection, all light will be either reflected or carried along the cell wall to its edge. The total reflection coefficient can be greatly reduced by submerging the cell in water, which increases the angle of total internal reflection.

Tables (1)

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Table 1 Samples Studieda

Equations (22)

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l * l = 2 k 0 2 q 2 ,
I ( 0 ) I ( τ ) I ( 0 ) 2 = 1 + β G | g 1 ( τ ) | 2 ,
T = ( 5 / 3 ) ( l * / L ) [ 1 + ( 4 / 3 ) ( l * / L ) ] 1 .
g 1 ( s ) ( τ ) = E ( s ) * ( 0 ) E ( s ) ( τ ) | E ( s ) ( 0 ) | 2 = exp [ 2 k 0 2 Δ r 2 ( τ ) ( s / l * ) / 6 ] ,
g 1 ( τ ) = 0 P ( s ) exp [ 2 k 0 2 ( s / l * ) D τ ] d s ,
g 1 ( τ ) = ( L / l * + 2 β α + β ) × sinh ( α x ) + β x cosh ( α x ) ( 1 + β 2 x 2 ) sinh ( x L / l * ) + 2 β x cosh ( x L / l * ) ,
T = 5 l * 3 L ( 1 + 4 l * 3 L ) 1 .
t U = D γ 2 U ,
z 2 U = 0 ,
U = { A l + B l z for z < α l * A r + B r z for z > α l * .
J · = J + J = D · U .
J ± = U c 4 D γ 2 z U .
J + ( 0 ) = R J ( 0 ) ,
J ( L ) = R J + ( L ) ,
U = U 0 { ( 1 + z / h l * ) for z < α l * 1 + α / h L + ( h α ) l * ( L + h l * z ) for z > α l * ,
T = J + ( L ) J + ( L ) + J ( 0 ) ,
T = ( l * L ) 2 3 ( 1 + R 1 R ) + α 1 + 4 3 ( 1 + R 1 R ) l * L .
R ( θ ) = R 12 ( θ 1 ) + T 12 ( θ 1 ) R 23 ( θ 2 ) T 21 ( θ 2 ) × j = 0 j = N m ( θ 2 ) [ R 21 ( θ 2 ) R 23 ( θ 2 ) ] j
= R 12 ( θ 1 ) + T 12 ( θ 1 ) R 23 ( θ 2 ) T 21 ( θ 2 ) × 1 [ R 21 ( θ 2 ) R 23 ( θ 2 ) ] N m ( θ 2 ) 1 R 21 ( θ 2 ) R 23 ( θ 2 ) ,
Δ r 2 ( τ ) = 6 D { τ 2 ( τ ν τ π ) 1 / 2 + 2 9 τ ν ( 4 ρ ρ ) + 3 [ τ ν ( 5 8 ρ ρ ) ] 1 / 2 [ 1 a + 3 exp ( a + 2 τ ) × erfc ( a + τ ) 1 a 3 exp ( a 2 τ ) erfc ( a τ ) ] } ,
a ± = 3 2 3 ± ( 5 8 ρ ρ ) 1 / 2 τ ν ( 1 + 2 ρ ρ ) ,
Δ r 2 ( τ ) + [ A ( q , τ ) ] [ S ( q ) ] ,

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