Invariance property in inhomogeneous scattering media with refractive-index mismatch

TL;DR

This paper extends the mean path length invariance property to inhomogeneous scattering media with refractive index mismatches, showing it remains valid with a correction factor and confirming results through numerical simulations.

Contribution

It introduces a correction to the invariance property for media with refractive index mismatch, broadening its applicability.

Findings

Invariance property holds with a correction factor for inhomogeneous media.

Theoretical results agree with numerical simulations in 2D and 3D.

Refractive index mismatch affects the mean path length, but invariance is preserved.

Abstract

The mean path length invariance property is a very important property of scattering media illuminated by an isotropic and homogeneous radiation. Here we investigate the case of inhomogeneous media with refractive index mismatch between the external environment and also among their subdomains. The invariance property remains valid by the introduction of a correction, dependent on the refractive index, of the mean path length value. It is a consequence of the stationary solution of the radiative transfer equation in a medium subjected to an isotropic and homogeneous radiance. The theoretical results are in agreement with the reported results for numerical simulations for both the three-dimensional and the two-dimensional media.