Diffuse radiation intensity propagating through a particulate slab

A multiple-scattering approach is used to solve the radiative transfer equation in order to describe the angular and optical depth dependence of diffuse intensity propagating through an unsupported particulate slab perpendicularly illuminated with unpolarized electromagnetic radiation. Boundary reflections are taken into account for the unscattered radiation, as is each of the successive reflection and scattering orders, which are characterized by corresponding average path-length parameters and forward-scattering ratios. The optical depth dependence of the reflection- and scattering-order coefficients is displayed for given values of the particle size parameter, particle volume fraction, relative refractive index, and optical thickness of the slab. Diffuse intensity patterns at a given optical depth, and the angular dependence of the reflected and transmitted intensities, are also considered.