Invariance property in inhomogeneous scattering media with refractive-index mismatch

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.