Abstract

The recent controversy over whether the photon diffusion coefficient depends on absorption is addressed by use of the analytical solution of the photon transport equation in an infinite homogeneous scattering medium. The diffusion coefficient is found to be independent of absorption but temporally dependent. After a long period of time, the photon diffusion coefficient approaches D=1/3µs, which supports a claim made by Furutsu and Yamada [Phys. Rev. E 50, 3634 (1994)]. At early times, the diffusion coefficient is smaller than D=1/3µs, but this reduction cannot be expressed as D=1/3µs+μa, since the time-dependent diffusion coefficient is found to be unrelated to absorption.

© 2002 Optical Society of America

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References

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  1. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.
  2. S. Glasstone and M. C. Edlund, The Elements of Nuclear Reactor Theory (Van Nostrand, New York, 1952).
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    [CrossRef]
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    [CrossRef]
  17. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

2000 (2)

W. Cai, M. Lax, and R. R. Alfano, Phys. Rev. E 61, 3871 (2000).
[CrossRef]

W. Cai, M. Lax, and R. R. Alfano, J. Phys. Chem. B 104, 3996 (2000).
[CrossRef]

1999 (1)

1998 (2)

1997 (4)

1995 (1)

1994 (1)

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

1990 (1)

K. M. Yoo, F. Liu, and R. R. Alfano, Phys. Rev. Lett. 64, 2647 (1990).
[CrossRef] [PubMed]

1988 (1)

W. M. Star, J. P. Marijnissen, and M. J. C. van Gemert, Phys. Med. Biol. 33, 437 (1988).
[CrossRef] [PubMed]

Alfano, R. R.

W. Cai, M. Lax, and R. R. Alfano, Phys. Rev. E 61, 3871 (2000).
[CrossRef]

W. Cai, M. Lax, and R. R. Alfano, J. Phys. Chem. B 104, 3996 (2000).
[CrossRef]

K. M. Yoo, F. Liu, and R. R. Alfano, Phys. Rev. Lett. 64, 2647 (1990).
[CrossRef] [PubMed]

Aronson, R.

Bassani, M.

Boas, D. A.

Bohren, C. F.

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

Cai, W.

W. Cai, M. Lax, and R. R. Alfano, J. Phys. Chem. B 104, 3996 (2000).
[CrossRef]

W. Cai, M. Lax, and R. R. Alfano, Phys. Rev. E 61, 3871 (2000).
[CrossRef]

Chance, B.

Contini, D.

Corngold, N.

Duderstadt, J. J.

J. J. Duderstadt and W. R. Martin, Transport Theory (Wiley, New York, 1979).

Durduran, T.

Durian, D. J.

Edlund, M. C.

S. Glasstone and M. C. Edlund, The Elements of Nuclear Reactor Theory (Van Nostrand, New York, 1952).

Furutsu, K.

K. Furutsu, J. Opt. Soc. Am. A 14, 267 (1997).
[CrossRef]

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

Glasstone, S.

S. Glasstone and M. C. Edlund, The Elements of Nuclear Reactor Theory (Van Nostrand, New York, 1952).

Huffman, D. R.

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

Ishimaru, A.

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

Lax, M.

W. Cai, M. Lax, and R. R. Alfano, Phys. Rev. E 61, 3871 (2000).
[CrossRef]

W. Cai, M. Lax, and R. R. Alfano, J. Phys. Chem. B 104, 3996 (2000).
[CrossRef]

Liu, F.

K. M. Yoo, F. Liu, and R. R. Alfano, Phys. Rev. Lett. 64, 2647 (1990).
[CrossRef] [PubMed]

Marijnissen, J. P.

W. M. Star, J. P. Marijnissen, and M. J. C. van Gemert, Phys. Med. Biol. 33, 437 (1988).
[CrossRef] [PubMed]

Martelli, F.

Martin, W. R.

J. J. Duderstadt and W. R. Martin, Transport Theory (Wiley, New York, 1979).

Murrer, L. H. P.

Nakai, T.

T. Nakai, G. Nishimura, K. Yamamoto, and M. Tamura, Phys. Med. Biol. 42, 2541 (1997).
[CrossRef]

Nishimura, G.

T. Nakai, G. Nishimura, K. Yamamoto, and M. Tamura, Phys. Med. Biol. 42, 2541 (1997).
[CrossRef]

Patterson, M. S.

Rinzema, K.

Star, W. M.

K. Rinzema, L. H. P. Murrer, and W. M. Star, J. Opt. Soc. Am. A 15, 2078 (1998).
[CrossRef]

W. M. Star, J. P. Marijnissen, and M. J. C. van Gemert, Phys. Med. Biol. 33, 437 (1988).
[CrossRef] [PubMed]

Tamura, M.

T. Nakai, G. Nishimura, K. Yamamoto, and M. Tamura, Phys. Med. Biol. 42, 2541 (1997).
[CrossRef]

van Gemert, M. J. C.

W. M. Star, J. P. Marijnissen, and M. J. C. van Gemert, Phys. Med. Biol. 33, 437 (1988).
[CrossRef] [PubMed]

Wilson, B. C.

Yamada, Y.

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

Yamamoto, K.

T. Nakai, G. Nishimura, K. Yamamoto, and M. Tamura, Phys. Med. Biol. 42, 2541 (1997).
[CrossRef]

Yodh, A. G.

Yoo, K. M.

K. M. Yoo, F. Liu, and R. R. Alfano, Phys. Rev. Lett. 64, 2647 (1990).
[CrossRef] [PubMed]

Zaccanti, G.

Appl. Opt. (1)

J. Opt. Soc. Am. A (4)

J. Phys. Chem. B (1)

W. Cai, M. Lax, and R. R. Alfano, J. Phys. Chem. B 104, 3996 (2000).
[CrossRef]

Opt. Lett. (2)

Phys. Med. Biol. (2)

T. Nakai, G. Nishimura, K. Yamamoto, and M. Tamura, Phys. Med. Biol. 42, 2541 (1997).
[CrossRef]

W. M. Star, J. P. Marijnissen, and M. J. C. van Gemert, Phys. Med. Biol. 33, 437 (1988).
[CrossRef] [PubMed]

Phys. Rev. E (2)

W. Cai, M. Lax, and R. R. Alfano, Phys. Rev. E 61, 3871 (2000).
[CrossRef]

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

Phys. Rev. Lett. (1)

K. M. Yoo, F. Liu, and R. R. Alfano, Phys. Rev. Lett. 64, 2647 (1990).
[CrossRef] [PubMed]

Other (4)

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

J. J. Duderstadt and W. R. Martin, Transport Theory (Wiley, New York, 1979).

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

S. Glasstone and M. C. Edlund, The Elements of Nuclear Reactor Theory (Van Nostrand, New York, 1952).

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Figures (2)

Fig. 1
Fig. 1

Diffusion coefficients Dzz and Dxx from Eqs. (6) and (7) as a function of time t.

Fig. 2
Fig. 2

Steady-state photon density as a function of distance from the source (along the incident direction) for different absorption coefficients μa with unit 1/lt obtained with the CMDA and the CUMA. The unit of length is lt; the unit of time is lt/c.

Equations (9)

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

D=1/3µs+μa,
D=lt/3=1/3µs,
Nr,t=14πDct3/2exp-r-ltzˆ24Dct-μact,
Nr,t=14πDzzct1/214πDxxctexp-z-Rz24Dzzct×exp-x2+y24Dxxctexp-μact,
Rz=c1-exp-g1t/g1.
Dzz=c3ttg1-3g1-g2g12g1-g21-exp-g1t+2g2g1-g21-exp-g2t-32g121-exp-g1t2,
Dxx=Dyy=c3ttg1+g2g12g1-g21-exp-g1t-1g2g1-g21-exp-g2t.
Pcos θ=1/4πlalPlcos θ.
Nr=14πDcr-ltzˆexp-r-ltzˆμa/D1/2.

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