Abstract

The diffusion approximation of the radiative transfer equation is a model used widely to describe photon migration in highly diffusing media and is an important matter in biological tissue optics. An analysis of the time-dependent diffusion equation together with its solutions for the slab geometry and for a semi-infinite diffusing medium are reported. These solutions, presented for both the time-dependent and the continuous wave source, account for the refractive index mismatch between the turbid medium and the surrounding medium. The results have been compared with those obtained when different boundary conditions were assumed. The comparison has shown that the effect of the refractive index mismatch cannot be disregarded. This effect is particularly important for the transmittance. The discussion of results also provides an analysis of the role of the absorption coefficient in the expression of the diffusion coefficient.

© 1997 Optical Society of America

Photon migration through a turbid slab described by a model based on diffusion approximation. II. Comparison with Monte Carlo results

Fabrizio Martelli, Daniele Contini, Adriana Taddeucci, and Giovanni Zaccanti
Appl. Opt. 36(19) 4600-4612 (1997)

Effect of the scattering delay on time-dependent photon migration in turbid media

I. V. Yaroslavsky, A. N. Yaroslavsky, V. V. Tuchin, and H.-J. Schwarzmaier
Appl. Opt. 36(25) 6529-6538 (1997)

Independence of the diffusion coefficient from absorption: experimental and numerical evidence

Michele Bassani, Fabrizio Martelli, Giovanni Zaccanti, and Daniele Contini
Opt. Lett. 22(12) 853-855 (1997)

Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium

Alwin Kienle and Michael S. Patterson
J. Opt. Soc. Am. A 14(1) 246-254 (1997)

Analytical approximate solutions of the time-domain diffusion equation in layered slabs

Fabrizio Martelli, Angelo Sassaroli, Yukio Yamada, and Giovanni Zaccanti
J. Opt. Soc. Am. A 19(1) 71-80 (2002)