Abstract

The depth at which diffusing photons are assumed to be deposited in a random scattering medium has traditionally been treated as a phenomenological parameter comparable to the photon transport mean free path. We show how to average properly over an exponential distribution of depositions weighted additionally by the transmission probability, and compare our prediction for the autocorrelation of intensity fluctuations in the transmitted light with experimental data on an ideal system. The improved correlation function, where distinguishable from the prior form, provides slightly better agreement with data as long as the sample is thicker than approximately 10 transport mean free paths. However, in contrast with static transmission, proper averaging over a range of penetration depths does not extend the validity of diffusing-wave spectroscopy to significantly smaller slab thicknesses. The most significant errors in the theory must therefore arise from approximations other than the treatment of the source of diffusing photons.

© 1995 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. J. X. Zhu, D. J. Durian, J. Müller, D. A. Weitz, D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559–2562 (1992).
    [CrossRef] [PubMed]
  5. M. H. Kao, A. G. Yodh, D. J. Pine, “Observation of Brownian motion on the time scale of hydrodynamic interaction,” Phys. Rev. Lett. 70, 242–245 (1992).
    [CrossRef]
  6. P. D. Kaplan, A. G. Yodh, D. J. Pine, “Diffusion and structure in dense binary suspensions,” Phys. Rev. Lett. 68, 393–396 (1992).
    [CrossRef] [PubMed]
  7. A. Meller, J. Stavans, “Glass transition and phase diagrams of strongly interacting binary colloidal mixtures,” Phys. Rev. Lett. 68, 3646–3649 (1992).
    [CrossRef] [PubMed]
  8. J. Z. Xue, E. Herbolzheimer, M. A. Rutgers, W. B. Russel, P. M. Chaikin, “Diffusion, dispersion, and settling of hard spheres,” Phys. Rev. Lett. 69, 1715–1718 (1992).
    [CrossRef] [PubMed]
  9. 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]
  10. 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).
  11. 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]
  12. P. D. Kaplan, M. H. Kao, A. G. Yodh, D. J. Pine, “Geometric constraints for the design of diffusive-wave spectroscopy experiments,” Appl. Opt. 32, 3828–3836 (1993).
    [PubMed]
  13. D. J. Durian, “The influence of boundary reflection and refraction on diffusive photon transport,” Phys. Rev. E 50, 857–866 (1994).
    [CrossRef]
  14. B. J. Ackerson, R. L. Doughtery, N. M. Reguigui, U. Nobbmann, “Correlation transfer: application of radiative transfer solution methods to photon correlation problems,” J. Thermophys. Heat Transfer 6, 577–588 (1992).
    [CrossRef]
  15. J. H. Li, A. A. Lisyansky, T. D. Cheung, D. Livdan, A. Z. Genack, “Transmission and surface intensity profiles in random media,” Europhys. Lett 22, 675–680 (1993).
    [CrossRef]
  16. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978) Vol. I, Chap. 9.
  17. E. J. Hinch, “Application of the Langevin equation to fluid suspensions,” J. Fluid Mech. 72, 499–511 (1975).
    [CrossRef]
  18. I. Thormahlen, J. Straub, U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
    [CrossRef]
  19. D. E. Grey, coordinating ed., American Institute of Phsyics Handbook, 3rd. ed. (McGraw-Hill, New York, 1972), pp. 6–109; interpolated assuming normal dispersion.
  20. See, e.g., H. C. van de Hulst, Light Scattering by Small Spheres (Dover, New York, 1981).
  21. A. A. Middleton, D. S. Fisher, “Discrete scatterers and autocorrelations of multiply scattered light,” Phys. Rev. B 43, 5934–5938 (1991).
    [CrossRef]

1994 (1)

D. J. Durian, “The influence of boundary reflection and refraction on diffusive photon transport,” Phys. Rev. E 50, 857–866 (1994).
[CrossRef]

1993 (2)

J. H. Li, A. A. Lisyansky, T. D. Cheung, D. Livdan, A. Z. Genack, “Transmission and surface intensity profiles in random media,” Europhys. Lett 22, 675–680 (1993).
[CrossRef]

P. D. Kaplan, M. H. Kao, A. G. Yodh, D. J. Pine, “Geometric constraints for the design of diffusive-wave spectroscopy experiments,” Appl. Opt. 32, 3828–3836 (1993).
[PubMed]

1992 (6)

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

J. X. Zhu, D. J. Durian, J. Müller, D. A. Weitz, D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559–2562 (1992).
[CrossRef] [PubMed]

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

P. D. Kaplan, A. G. Yodh, D. J. Pine, “Diffusion and structure in dense binary suspensions,” Phys. Rev. Lett. 68, 393–396 (1992).
[CrossRef] [PubMed]

A. Meller, J. Stavans, “Glass transition and phase diagrams of strongly interacting binary colloidal mixtures,” Phys. Rev. Lett. 68, 3646–3649 (1992).
[CrossRef] [PubMed]

J. Z. Xue, E. Herbolzheimer, M. A. Rutgers, W. B. Russel, P. M. Chaikin, “Diffusion, dispersion, and settling of hard spheres,” Phys. Rev. Lett. 69, 1715–1718 (1992).
[CrossRef] [PubMed]

1991 (3)

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]

A. A. Middleton, D. S. Fisher, “Discrete scatterers and autocorrelations of multiply scattered light,” Phys. Rev. B 43, 5934–5938 (1991).
[CrossRef]

1990 (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).

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 (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]

1985 (1)

I. Thormahlen, J. Straub, U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

1975 (1)

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

Ackerson, B. J.

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

Chaikin, P. M.

J. Z. Xue, E. Herbolzheimer, M. A. Rutgers, W. B. Russel, P. M. Chaikin, “Diffusion, dispersion, and settling of hard spheres,” Phys. Rev. Lett. 69, 1715–1718 (1992).
[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]

Cheung, T. D.

J. H. Li, A. A. Lisyansky, T. D. Cheung, D. Livdan, A. Z. Genack, “Transmission and surface intensity profiles in random media,” Europhys. Lett 22, 675–680 (1993).
[CrossRef]

Doughtery, R. L.

B. J. Ackerson, R. L. Doughtery, N. M. Reguigui, U. Nobbmann, “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, “The influence of boundary reflection and refraction on diffusive photon transport,” Phys. Rev. E 50, 857–866 (1994).
[CrossRef]

J. X. Zhu, D. J. Durian, J. Müller, D. A. Weitz, D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559–2562 (1992).
[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]

Fisher, D. S.

A. A. Middleton, D. S. Fisher, “Discrete scatterers and autocorrelations of multiply scattered light,” Phys. Rev. B 43, 5934–5938 (1991).
[CrossRef]

Genack, A. Z.

J. H. Li, A. A. Lisyansky, T. D. Cheung, D. Livdan, A. Z. Genack, “Transmission and surface intensity profiles in random media,” Europhys. Lett 22, 675–680 (1993).
[CrossRef]

Grigull, U.

I. Thormahlen, J. Straub, U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

Herbolzheimer, E.

J. Z. Xue, E. Herbolzheimer, M. A. Rutgers, W. B. Russel, P. M. Chaikin, “Diffusion, dispersion, and settling of hard spheres,” Phys. Rev. Lett. 69, 1715–1718 (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).

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]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978) Vol. I, Chap. 9.

Kao, M. H.

P. D. Kaplan, M. H. Kao, A. G. Yodh, D. J. Pine, “Geometric constraints for the design of diffusive-wave spectroscopy experiments,” Appl. Opt. 32, 3828–3836 (1993).
[PubMed]

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

Kaplan, P. D.

P. D. Kaplan, M. H. Kao, A. G. Yodh, D. J. Pine, “Geometric constraints for the design of diffusive-wave spectroscopy experiments,” Appl. Opt. 32, 3828–3836 (1993).
[PubMed]

P. D. Kaplan, A. G. Yodh, D. J. Pine, “Diffusion and structure in dense binary suspensions,” Phys. Rev. Lett. 68, 393–396 (1992).
[CrossRef] [PubMed]

Li, J. H.

J. H. Li, A. A. Lisyansky, T. D. Cheung, D. Livdan, A. Z. Genack, “Transmission and surface intensity profiles in random media,” Europhys. Lett 22, 675–680 (1993).
[CrossRef]

Lisyansky, A. A.

J. H. Li, A. A. Lisyansky, T. D. Cheung, D. Livdan, A. Z. Genack, “Transmission and surface intensity profiles in random media,” Europhys. Lett 22, 675–680 (1993).
[CrossRef]

Livdan, D.

J. H. Li, A. A. Lisyansky, T. D. Cheung, D. Livdan, A. Z. Genack, “Transmission and surface intensity profiles in random media,” Europhys. Lett 22, 675–680 (1993).
[CrossRef]

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]

Meller, A.

A. Meller, J. Stavans, “Glass transition and phase diagrams of strongly interacting binary colloidal mixtures,” Phys. Rev. Lett. 68, 3646–3649 (1992).
[CrossRef] [PubMed]

Middleton, A. A.

A. A. Middleton, D. S. Fisher, “Discrete scatterers and autocorrelations of multiply scattered light,” Phys. Rev. B 43, 5934–5938 (1991).
[CrossRef]

Müller, J.

J. X. Zhu, D. J. Durian, J. Müller, D. A. Weitz, D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559–2562 (1992).
[CrossRef] [PubMed]

Nobbmann, U.

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

Pine, D. J.

P. D. Kaplan, M. H. Kao, A. G. Yodh, D. J. Pine, “Geometric constraints for the design of diffusive-wave spectroscopy experiments,” Appl. Opt. 32, 3828–3836 (1993).
[PubMed]

P. D. Kaplan, A. G. Yodh, D. J. Pine, “Diffusion and structure in dense binary suspensions,” Phys. Rev. Lett. 68, 393–396 (1992).
[CrossRef] [PubMed]

J. X. Zhu, D. J. Durian, J. Müller, D. A. Weitz, D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559–2562 (1992).
[CrossRef] [PubMed]

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

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]

Reguigui, N. M.

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

Russel, W. B.

J. Z. Xue, E. Herbolzheimer, M. A. Rutgers, W. B. Russel, P. M. Chaikin, “Diffusion, dispersion, and settling of hard spheres,” Phys. Rev. Lett. 69, 1715–1718 (1992).
[CrossRef] [PubMed]

Rutgers, M. A.

J. Z. Xue, E. Herbolzheimer, M. A. Rutgers, W. B. Russel, P. M. Chaikin, “Diffusion, dispersion, and settling of hard spheres,” Phys. Rev. Lett. 69, 1715–1718 (1992).
[CrossRef] [PubMed]

Stavans, J.

A. Meller, J. Stavans, “Glass transition and phase diagrams of strongly interacting binary colloidal mixtures,” Phys. Rev. Lett. 68, 3646–3649 (1992).
[CrossRef] [PubMed]

Stephen, M. J.

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

Straub, J.

I. Thormahlen, J. Straub, U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

Thormahlen, I.

I. Thormahlen, J. Straub, U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

van de Hulst, H. C.

See, e.g., H. C. van de Hulst, Light Scattering by Small Spheres (Dover, New York, 1981).

Weitz, D. A.

J. X. Zhu, D. J. Durian, J. Müller, D. A. Weitz, D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559–2562 (1992).
[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]

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

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]

Xue, J. Z.

J. Z. Xue, E. Herbolzheimer, M. A. Rutgers, W. B. Russel, P. M. Chaikin, “Diffusion, dispersion, and settling of hard spheres,” Phys. Rev. Lett. 69, 1715–1718 (1992).
[CrossRef] [PubMed]

Yodh, A. G.

P. D. Kaplan, M. H. Kao, A. G. Yodh, D. J. Pine, “Geometric constraints for the design of diffusive-wave spectroscopy experiments,” Appl. Opt. 32, 3828–3836 (1993).
[PubMed]

P. D. Kaplan, A. G. Yodh, D. J. Pine, “Diffusion and structure in dense binary suspensions,” Phys. Rev. Lett. 68, 393–396 (1992).
[CrossRef] [PubMed]

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

Zhu, J. X.

J. X. Zhu, D. J. Durian, J. Müller, D. A. Weitz, D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559–2562 (1992).
[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]

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).

Appl. Opt. (1)

Europhys. Lett (1)

J. H. Li, A. A. Lisyansky, T. D. Cheung, D. Livdan, A. Z. Genack, “Transmission and surface intensity profiles in random media,” Europhys. Lett 22, 675–680 (1993).
[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. Chem. Ref. Data (1)

I. Thormahlen, J. Straub, U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

J. Thermophys. Heat Transfer (1)

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

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

A. A. Middleton, D. S. Fisher, “Discrete scatterers and autocorrelations of multiply scattered light,” Phys. Rev. B 43, 5934–5938 (1991).
[CrossRef]

Phys. Rev. E (1)

D. J. Durian, “The influence of boundary reflection and refraction on diffusive photon transport,” Phys. Rev. E 50, 857–866 (1994).
[CrossRef]

Phys. Rev. Lett. (6)

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

J. X. Zhu, D. J. Durian, J. Müller, D. A. Weitz, D. J. Pine, “Scaling of transient hydrodynamic interactions in concentrated suspensions,” Phys. Rev. Lett. 68, 2559–2562 (1992).
[CrossRef] [PubMed]

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

P. D. Kaplan, A. G. Yodh, D. J. Pine, “Diffusion and structure in dense binary suspensions,” Phys. Rev. Lett. 68, 393–396 (1992).
[CrossRef] [PubMed]

A. Meller, J. Stavans, “Glass transition and phase diagrams of strongly interacting binary colloidal mixtures,” Phys. Rev. Lett. 68, 3646–3649 (1992).
[CrossRef] [PubMed]

J. Z. Xue, E. Herbolzheimer, M. A. Rutgers, W. B. Russel, P. M. Chaikin, “Diffusion, dispersion, and settling of hard spheres,” Phys. Rev. Lett. 69, 1715–1718 (1992).
[CrossRef] [PubMed]

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]

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 (3)

D. E. Grey, coordinating ed., American Institute of Phsyics Handbook, 3rd. ed. (McGraw-Hill, New York, 1972), pp. 6–109; interpolated assuming normal dispersion.

See, e.g., H. C. van de Hulst, Light Scattering by Small Spheres (Dover, New York, 1981).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978) Vol. I, Chap. 9.

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