About the precision and application range of the small angle approximation in the theory of radiative transfer

The analytical complexities of the radiative transfer equation (RTE) have allowed formulating only superficial, qualitative estimations of the precision and application range of the small angle approximation (SAA). Another approach based on the comparison of the calculations in SAA with the similar numerical solutions of RTE is possible. However numerical methods of the RTE solution in media with strong anisotropic scattering are ineffective. The numerical solution of RTE for turbid media with the arbitrary anisotropy of scattering irradiated by a plane monodirectional (PM) source suggested in(3) gives the opportunity of solving this problem. SAA was offered in paper(4) and is based on the approximate equality of the trajectory path of photons by the anisotropic scattering to the nonscattered path. The analytical complexities of the RTE solution have established three forms of SAA. Comparisons with the numerical solution 3 have shown, that all three forms use extra assumptions to(8)(4) exceptthe case of the normal irradiation by PM source in(8). The analysis of SAA has allowed offering the development completely relevant to the ideas of(4), from which all three forms follow at various assumptions. The generalization of this approach for cases of arbitrary boundary conditions doesn't present any troubles.