Abstract

The diffusion approximation is widely invoked to model the propagation of light in turbid media. When absorption is not weak in comparison with scattering, there is currently a controversy as to if, and how, the diffusion coefficient depends on absorption. Here it is shown that better agreement with random walk simulation is obtained if the photon-diffusion coefficient is taken as D=c/3μs+μa. One can reconcile this result with recent work advocating D=c/3μs by noting that the diffusion equation must be correspondingly changed to a telegrapher’s equation.

© 1998 Optical Society of America

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References

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1997 (5)

1994 (2)

1989 (1)

Alfano, R. R.

Aronson, R.

R. Aronson and N. Corngold, “Photon diffusion coefficient in an absorbing medium,” submitted to J. Opt. Soc. Am. A.

Bassani, M.

Boas, D. A.

Case, K. M.

K. M. Case and P. F. Zweifel, Linear Transport Theory (Addison-Wesley, New York, 1979).

Chance, B.

Contini, D.

Corngold, N.

R. Aronson and N. Corngold, “Photon diffusion coefficient in an absorbing medium,” submitted to J. Opt. Soc. Am. A.

Duderstadt, J. J.

J. J. Duderstadt and W. R. Martin, Transport Theory (Wiley, New York, 1967).

Durduran, T.

Durian, D. J.

Feng, T.-C.

Furutsu, K.

K. Furutsu and Y. Yamada, Phys. Rev. E 50, 3634 (1994).
[CrossRef]

Gutman, S.

Haskell, R. C.

Ishimaru, I.

Lax, M.

Martelli, F.

Martin, W. R.

J. J. Duderstadt and W. R. Martin, Transport Theory (Wiley, New York, 1967).

Masoliver, J.

J. M. Porra, J. Masoliver, and G. H. Weiss, Phys. Rev. E 55, 7771 (1997).
[CrossRef]

McAdams, M. S.

Polishchuk, A. Y.

Porra, J. M.

J. M. Porra, J. Masoliver, and G. H. Weiss, Phys. Rev. E 55, 7771 (1997).
[CrossRef]

Rudnick, J.

Svaasand, L. O.

Tromberg, B. J.

Tsay, T.-T.

Weiss, G. H.

J. M. Porra, J. Masoliver, and G. H. Weiss, Phys. Rev. E 55, 7771 (1997).
[CrossRef]

Yamada, Y.

K. Furutsu and Y. Yamada, Phys. Rev. E 50, 3634 (1994).
[CrossRef]

Yodh, A. G.

Zaccanti, G.

Zweifel, P. F.

K. M. Case and P. F. Zweifel, Linear Transport Theory (Addison-Wesley, New York, 1979).

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Figures (2)

Fig. 1
Fig. 1

Concentration versus radial distance for a spreading pulse in an infinite medium at various times t, normalized by the Gaussian prediction Eq. (4) of the simple diffusion equation. The solid and the dashed histograms represent simulation data for g=0 isotropic scattering and g=0.9 anisotropic scattering, respectively; the solid curves represent the telegrapher’s equation prediction, Eq. (3), for various values of a. Note that the data all approach a Gaussian, φ/φ0=1 for all r, at very long times and that the best overall agreement at shorter times is obtained for a=1/3.

Fig. 2
Fig. 2

Concentration versus radial distance for a steady source in an infinite medium with varying levels of absorption, normalized by the simple diffusion equation prediction. The solid histograms represent simulation data for g=0 isotropic scattering; the dashed curves represent the telegrapher’s equation prediction Eq. (5) with various values of a. Note that the data all approach the Gaussian prediction, φ/φ0=1 for all r, for very weak absorption, μa0. The best overall agreement at stronger absorption is obtained for a=1/3.

Equations (5)

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

2φ=3μs+μaφct+3μaμs+μaφ,
2φ=3a2φt2+31+2aμaφt+3μa1+aμaφ,
φr,t=-exp-γ+μat4πrνγ+tr×I0γt2-r/ν2Θνt-r,
φ0r,t=14πD0t3/2 exp-r24D0t-μat,
φr=14πDrexp-rμa/D,

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