Analytical Approximation for Homogeneous Slab Brightness Coefficients in the Case of Strongly Elongated Phase Functions

摘要

Based fitting parametrization and transformations of the exact non-linear integral equation for the unified function E of radiation exit from a homogeneous slab of an arbitrary optical thickness, approximate analytical expressions have been obtained for the corresponding slab brightness coefficients in the case of strongly elongated phase functions. The accuracy of the obtained fitting analytical approximations has been evaluated by using appropriate calculations in the visible spectrum region (λ = 400-800 nm) for Heyney-Greenstein phase functions in dependence of the single scattering albedo, vision angles, solar zenith distance and azimuths.