Diffuse reflection and transmission of light by a medium with an arbitrary scattering indicatrix

The diffuse reflection and transmission of light by a plane-parallel medium is considered, taking into account only the azimuth-independent part of the scattering indicatrix. The scattering indicatrix is expressed in terms of an expansion in an arbitrary number of Legendre polynomials. Two approaches to the problem are analyzed using Sobolev’s theory. Two systems of linear algebraic equations for the coefficients of the auxiliary polynomials q _i(μ) and s _i(μ) are derived and compared. It is shown that one of these approaches is less preferable, since it is not valid for conservative scattering.