Accuracy of the diffusion equation with extrapolated-boundary condition for transmittance of light through a turbid medium

TL;DR

This paper evaluates the accuracy of the diffusion equation with extrapolated boundary conditions in predicting light transmittance through turbid media by comparing it with numerical Boltzmann equation solutions.

Contribution

It provides a validation of the diffusion approximation's accuracy for light transmittance in turbid media using numerical comparisons.

Findings

Diffusion equation with extrapolated boundary condition closely matches Boltzmann solutions.

Analytical formulas derived from the diffusion model are validated.

The study clarifies the limits of diffusion approximation in optical transport.

Abstract

The linear intensity profile of multiply scattered light in a slab geometry extrapolates to zero at a certain distance beyond the boundary. The diffusion equation with this "extrapolated boundary condition" has been used in the literature to obtain analytical formulas for the transmittance of light through the slab as a function of angle of incidence and refractive index. The accuracy of these formulas is determined by comparison with a numerical solution of the Boltzmann equation for radiative transfer.