Forward-scattering ratios and average pathlength parameter in radiative transfer models

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Abstract
Optical properties of films containing spherical particles in a non-absorbing matrix have been modelled by a four-flux radiative transfer theory. In this paper we demonstrate methods to calculate all parameters in this model. Scattering and absorption coefficients can easily be computed from Lorenz - Mie theory if the particle concentration is not too high. Forward-scattering ratios for collimated and diffuse radiation, and , respectively, are in general not equal. We establish a method to evaluate the forward-scattering ratios from Lorenz - Mie theory and an improved version of Hartel theory, both for perfectly diffuse isotropic radiation as well as for anisotropic conditions. We also give an explicit way to calculate the average pathlength parameter in terms of particle refractive index, particle concentration, size parameter and distance from the illuminated film interface. The characterization of forward-scattering ratios and the average pathlength parameter leads to an improved understanding of the applicability of the standard four-flux model.