Radiation scattering for a general law of frequency redistribution

Some relatively simple radiative-transfer problems are considered in the general case of non-coherent scattering. The approach proposed in the paper is based on representation of the redistribution function in the form of a bilinear expansion with respect to an appropriately orthonormalized set of functions. The new simple, but at the same time rather accurate, method is suggested for solving problems of spectral-line formation to obtain the frequency redistribution. Numerical results are given for profiles of spectral lines formed by diffuse reflection from a semi-infinite medium, as well as for those formed in an isothermal atmosphere. These results illustrate the influence of the various approximations for the redistribution law on the solution of the problem. In particular, the effect of the complete redistribution approximation on the observed characteristics of the radiation field is investigated.