Radiation field in Rayleigh–Cabannes scattering atmosphere: the nonconservative Milne problem

Abstract

The radiation field in a nonconservative homogeneous plane-parallel semi-infinite atmosphere is determined using the method of discrete ordinates while the scattering processes in the atmosphere are described by the Rayleigh–Cabannes phase matrix and the primary radiation sources are situated infinitely deep in the atmosphere. The dependence of the Rubenson degree of polarization on the albedo of single scattering and the depolarization factor is discussed. It appeared that contrary to the situation in a conservative Rayleigh–Cabannes scattering atmosphere, in a nonconservative atmosphere the linear degree of polarization does not approach zero in deep layers but a constant value which does not depend on the direction of photon flight. Also, contrary to expectations it occurs that inside the atmosphere the maximum value of the degree of polarization is not situated at μ=0 but at negative values of the angular variable.