Photon migration through a turbid slab described by a model based on diffusion approximation I Theory

TLDR

The diffusion approximation of the radiative transfer equation is widely used to model photon migration in highly diffusing media and is crucial for biological tissue optics. The study analyzes the time‑dependent diffusion equation and its solutions for slab and semi‑infinite geometries, and examines how the absorption coefficient influences the diffusion coefficient. The authors compared the derived solutions under various boundary conditions. The solutions incorporate refractive index mismatch, which the comparison shows significantly affects transmittance and cannot be ignored.

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.