Comparisons between the small-angle approximation and the numerical solution for radiative transfer theory

The small-angle approximation for the radiative transfer theory is based on the assumption that the scattered wave is confined within a small angle in the forward direction. This assumption is generally valid for the turbulence case in which the turbulence size is much greater than the wavelength and the index of refraction is close to 1. However, the validity of this assumption for a discrete random medium with an index of refraction much greater than the surrounding medium is not well known. In spite of this, the small-angle approximation has sometimes been used for discrete random media because of its mathematical simplicity.