J. B. Fishkin, S. Fantini, M. J. van de Ven, and E. Gratton, “Gigahertz photon density waves in a turbid medium: theory and experiment,” Phys. Rev. E 53, 2307–2319 (1996).

[CrossRef]

M. U. Vera and D. J. Durian, “The angular distribution of diffusely transmitted light,” Phys. Rev. E 53, 3215–3224 (1996).

[CrossRef]

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

[CrossRef]

J. M. Porra, G. H. Weiss, and J. Masoliver, “A diffusion model incorporating anisotropic properties,” Physica A 218, 229–236 (1995).

[CrossRef]

D. J. Durian, “Penetration depth for diffusing-wave spectroscopy,” Appl. Opt. 34, 7100–7105 (1995).

[CrossRef]
[PubMed]

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorr-Nowkoorani, and U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transf. 52, 713–727 (1994).

[CrossRef]

I. J. D. Craig and A. M. Thompson, “Why Laplace transforms are difficult to invert numerically,” Comput. Phys. 8, 648–654 (1994).

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. S. McAdams, and B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2741 (1994).

[CrossRef]

J. B. Fishkin and E. Gratton, “Propagation of photon-density waves in strongly scattering media containing an absorbing semi-infinite plane bounded by a straight edge,” J. Opt. Soc. Am. A 10, 127–140 (1993).

[CrossRef]
[PubMed]

J. Masoliver, J. M. Porra, and G. H. Weiss, “Solution to the telegrapher's equation in the presence of reflecting and partly reflecting boundaries,” Phys. Rev. E 48, 939–944 (1993).

[CrossRef]

R. Aronson, “ Extrapolation distance for diffusion of light,”in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano and B. Chance, eds., (1993).Proc. SPIE 1888, 297–305(1993).

[CrossRef]

B. J. Tromberg, L. O. Svaasand, T.-T. Tsay, and R. C. Haskell, “Properties of photon density waves in multiple-scattering media,” Appl. Opt. 32, 607–616 (1993).

[CrossRef]
[PubMed]

J. M. Schmitt, A. Knuttel, and R. R. Knutson, “Interference of diffusive light waves,” J. Opt. Soc. Am. A 9, 1832–1843 (1992).

[CrossRef]
[PubMed]

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).

[CrossRef]
[PubMed]

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]

K. M. Yoo, F. Liu, and R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990).

[CrossRef]
[PubMed]

I. Ishimaru, “Diffusion of light in turbid media,” Appl. Opt. 28, 2210–2215 (1989).

[CrossRef]
[PubMed]

M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).

[CrossRef]
[PubMed]

D. D. Joseph and L. Preziosi, “Heat waves,” Rev. Mod. Phys. 61, 41–73 (1989).

[CrossRef]

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

[CrossRef]
[PubMed]

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

[CrossRef]

C. F. Bohren, “Multiple scattering of light and some of its observable consequences,” Am. J. Phys. 55, 524–533 (1987).

[CrossRef]

G. Maret and 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. Kac, “A stochastic model related to the telegrapher's equation,” Rocky Mount. J. Math. 4, 479–509 (1974).

[CrossRef]

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).

[CrossRef]

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorr-Nowkoorani, and U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transf. 52, 713–727 (1994).

[CrossRef]

K. M. Yoo, F. Liu, and R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990).

[CrossRef]
[PubMed]

R. Aronson, “ Extrapolation distance for diffusion of light,”in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano and B. Chance, eds., (1993).Proc. SPIE 1888, 297–305(1993).

[CrossRef]

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).

[CrossRef]
[PubMed]

C. F. Bohren, “Multiple scattering of light and some of its observable consequences,” Am. J. Phys. 55, 524–533 (1987).

[CrossRef]

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

[CrossRef]
[PubMed]

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

[CrossRef]

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).

[CrossRef]
[PubMed]

M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).

[CrossRef]
[PubMed]

I. J. D. Craig and A. M. Thompson, “Why Laplace transforms are difficult to invert numerically,” Comput. Phys. 8, 648–654 (1994).

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorr-Nowkoorani, and U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transf. 52, 713–727 (1994).

[CrossRef]

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorr-Nowkoorani, and U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transf. 52, 713–727 (1994).

[CrossRef]

J. B. Fishkin, S. Fantini, M. J. van de Ven, and E. Gratton, “Gigahertz photon density waves in a turbid medium: theory and experiment,” Phys. Rev. E 53, 2307–2319 (1996).

[CrossRef]

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).

[CrossRef]

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. S. McAdams, and B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2741 (1994).

[CrossRef]

B. J. Tromberg, L. O. Svaasand, T.-T. Tsay, and R. C. Haskell, “Properties of photon density waves in multiple-scattering media,” Appl. Opt. 32, 607–616 (1993).

[CrossRef]
[PubMed]

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).

[CrossRef]

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

[CrossRef]
[PubMed]

D. D. Joseph and L. Preziosi, “Heat waves,” Rev. Mod. Phys. 61, 41–73 (1989).

[CrossRef]

M. Kac, “A stochastic model related to the telegrapher's equation,” Rocky Mount. J. Math. 4, 479–509 (1974).

[CrossRef]

K. M. Yoo, F. Liu, and R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990).

[CrossRef]
[PubMed]

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

[CrossRef]

J. M. Porra, G. H. Weiss, and J. Masoliver, “A diffusion model incorporating anisotropic properties,” Physica A 218, 229–236 (1995).

[CrossRef]

J. Masoliver, J. M. Porra, and G. H. Weiss, “Solution to the telegrapher's equation in the presence of reflecting and partly reflecting boundaries,” Phys. Rev. E 48, 939–944 (1993).

[CrossRef]

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorr-Nowkoorani, and U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transf. 52, 713–727 (1994).

[CrossRef]

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).

[CrossRef]
[PubMed]

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]

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

[CrossRef]
[PubMed]

J. M. Porra, G. H. Weiss, and J. Masoliver, “A diffusion model incorporating anisotropic properties,” Physica A 218, 229–236 (1995).

[CrossRef]

J. Masoliver, J. M. Porra, and G. H. Weiss, “Solution to the telegrapher's equation in the presence of reflecting and partly reflecting boundaries,” Phys. Rev. E 48, 939–944 (1993).

[CrossRef]

D. D. Joseph and L. Preziosi, “Heat waves,” Rev. Mod. Phys. 61, 41–73 (1989).

[CrossRef]

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorr-Nowkoorani, and U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transf. 52, 713–727 (1994).

[CrossRef]

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

[CrossRef]

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. S. McAdams, and B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2741 (1994).

[CrossRef]

B. J. Tromberg, L. O. Svaasand, T.-T. Tsay, and R. C. Haskell, “Properties of photon density waves in multiple-scattering media,” Appl. Opt. 32, 607–616 (1993).

[CrossRef]
[PubMed]

I. J. D. Craig and A. M. Thompson, “Why Laplace transforms are difficult to invert numerically,” Comput. Phys. 8, 648–654 (1994).

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. S. McAdams, and B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2741 (1994).

[CrossRef]

B. J. Tromberg, L. O. Svaasand, T.-T. Tsay, and R. C. Haskell, “Properties of photon density waves in multiple-scattering media,” Appl. Opt. 32, 607–616 (1993).

[CrossRef]
[PubMed]

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. S. McAdams, and B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2741 (1994).

[CrossRef]

B. J. Tromberg, L. O. Svaasand, T.-T. Tsay, and R. C. Haskell, “Properties of photon density waves in multiple-scattering media,” Appl. Opt. 32, 607–616 (1993).

[CrossRef]
[PubMed]

J. B. Fishkin, S. Fantini, M. J. van de Ven, and E. Gratton, “Gigahertz photon density waves in a turbid medium: theory and experiment,” Phys. Rev. E 53, 2307–2319 (1996).

[CrossRef]

M. U. Vera and D. J. Durian, “The angular distribution of diffusely transmitted light,” Phys. Rev. E 53, 3215–3224 (1996).

[CrossRef]

J. M. Porra, G. H. Weiss, and J. Masoliver, “A diffusion model incorporating anisotropic properties,” Physica A 218, 229–236 (1995).

[CrossRef]

J. Masoliver, J. M. Porra, and G. H. Weiss, “Solution to the telegrapher's equation in the presence of reflecting and partly reflecting boundaries,” Phys. Rev. E 48, 939–944 (1993).

[CrossRef]

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]

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

[CrossRef]
[PubMed]

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

[CrossRef]

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

[CrossRef]

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).

[CrossRef]
[PubMed]

K. M. Yoo, F. Liu, and R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990).

[CrossRef]
[PubMed]

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]

C. F. Bohren, “Multiple scattering of light and some of its observable consequences,” Am. J. Phys. 55, 524–533 (1987).

[CrossRef]

I. Ishimaru, “Diffusion of light in turbid media,” Appl. Opt. 28, 2210–2215 (1989).

[CrossRef]
[PubMed]

M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).

[CrossRef]
[PubMed]

B. J. Tromberg, L. O. Svaasand, T.-T. Tsay, and R. C. Haskell, “Properties of photon density waves in multiple-scattering media,” Appl. Opt. 32, 607–616 (1993).

[CrossRef]
[PubMed]

D. J. Durian, “Penetration depth for diffusing-wave spectroscopy,” Appl. Opt. 34, 7100–7105 (1995).

[CrossRef]
[PubMed]

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).

[CrossRef]

I. J. D. Craig and A. M. Thompson, “Why Laplace transforms are difficult to invert numerically,” Comput. Phys. 8, 648–654 (1994).

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. S. McAdams, and B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2741 (1994).

[CrossRef]

J. B. Fishkin and E. Gratton, “Propagation of photon-density waves in strongly scattering media containing an absorbing semi-infinite plane bounded by a straight edge,” J. Opt. Soc. Am. A 10, 127–140 (1993).

[CrossRef]
[PubMed]

J. M. Schmitt, A. Knuttel, and R. R. Knutson, “Interference of diffusive light waves,” J. Opt. Soc. Am. A 9, 1832–1843 (1992).

[CrossRef]
[PubMed]

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorr-Nowkoorani, and U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transf. 52, 713–727 (1994).

[CrossRef]

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]

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

[CrossRef]

M. U. Vera and D. J. Durian, “The angular distribution of diffusely transmitted light,” Phys. Rev. E 53, 3215–3224 (1996).

[CrossRef]

J. B. Fishkin, S. Fantini, M. J. van de Ven, and E. Gratton, “Gigahertz photon density waves in a turbid medium: theory and experiment,” Phys. Rev. E 53, 2307–2319 (1996).

[CrossRef]

J. Masoliver, J. M. Porra, and G. H. Weiss, “Solution to the telegrapher's equation in the presence of reflecting and partly reflecting boundaries,” Phys. Rev. E 48, 939–944 (1993).

[CrossRef]

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

[CrossRef]
[PubMed]

K. M. Yoo, F. Liu, and R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 64, 2647–2650 (1990).

[CrossRef]
[PubMed]

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).

[CrossRef]
[PubMed]

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

[CrossRef]

J. M. Porra, G. H. Weiss, and J. Masoliver, “A diffusion model incorporating anisotropic properties,” Physica A 218, 229–236 (1995).

[CrossRef]

R. Aronson, “ Extrapolation distance for diffusion of light,”in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano and B. Chance, eds., (1993).Proc. SPIE 1888, 297–305(1993).

[CrossRef]

D. D. Joseph and L. Preziosi, “Heat waves,” Rev. Mod. Phys. 61, 41–73 (1989).

[CrossRef]

M. Kac, “A stochastic model related to the telegrapher's equation,” Rocky Mount. J. Math. 4, 479–509 (1974).

[CrossRef]

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

[CrossRef]

H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids (Clarendon, Oxford, 1959).

B. J. Berne and R. Pecora, Dynamic Light Scattering, with Applications to Chemistry, Biology, and Physics (Wiley, New York, 1976), pp. 83–88. This is not surprising, since in both cases the velocity autocorrelation function, from which the mean-squared displacement may be calculated, is an exponential. It is unlikely that the detailed shape of a spreading pulse is the same at very short times, however, since the Langevin case assumes a Maxwell distribution of particle speeds.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

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

[CrossRef]

W. E. Meador and W. R. Weaver, “Two-stream approximations to radiative transfer in planetary atmospheres: a unified description of existing methods and new improvement,” J. Atm. Sci. 37, 630–643 (1980).

[CrossRef]

C. Acquista, F. House, and J. Jafolla, “N-Stream approximations to radiative transfer,” J. Atm. Sci. 38, 1446–1451 (1981).

D. A. Weitz and D. J. Pine, in Dynamic Light Scattering: The Method and Some Applications, W. Brown, ed. (Clarendon, Oxford, 1993), pp. 652–720.

B. Chance and R. R. Alfano, eds., Optical Tomography, Photon Migration and Model Media: Theory, Human Studies, and Instrumentation, Proc. SPIE 2389 (1995).