Forward average path-length parameter in four-flux radiative transfer models.

The optical properties of films containing spherical particles in a nonabsorbing matrix have been modeled by using a four-flux radiative transfer theory. The forward average path-length parameter takes into account the different path lengths for collimated and diffuse components of the radiation field. This parameter, whose value was known only in special cases, has been used previously as a fitting quantity. We establish a method for evaluating the forward average path-length parameter in a rigorous way. Single-scattering parameters are evaluated from the Lorenz-Mie theory, and multiple-scattering effects are taken into account by means of an extended Hartel's theory.