Average path-length parameter of diffuse light in scattering media

We use Monte Carlo simulations to study in detail the propagation of light in a plane-parallel medium containing scattering particles. In particular, we compute the forward and backward average path-length parameters (FAPP and BAPP, respectively) of four-flux radiative transfer models as functions of the optical depth. Strong dependence on the single scattering albedo and phase function asymmetry is found for both quantities. In general the values of the FAPP decrease with increasing absorption, whereas the opposite occurs for the BAPP. A similar effect is produced when changing from isotropic phase functions to phase functions with a large asymmetry in the forward direction. We present analytical results for the asymptotic values of the FAPP and BAPP as functions of albedo for the particular case of isotropic scattering. Our results differ markedly from the predictions obtained recently with two multiple-scattering models by Vargas and Niklasson [J. Opt. Soc. Am. A 14, 2243 (1997); Appl. Opt. 36, 3735 (1997)]. The differences found point out the intrinsic limitations of these models.