Results of computations of the intensity, degree of polarization, and the direction of polarization of the radiation transmitted after one, two, and three scatterings according to Rayleigh’s law, are presented for the case of a plane-parallel, homogeneous atmosphere of finite optical thickness. They clearly show that the inclusion of the first three orders of scattering is essential even when the normal scattering optical thickness of the atmosphere is of the order of 0.2. For still higher optical thicknesses, the present step-by-step treatment is not satisfactory, as it is necessary to include several higher orders of scattering. The anisotropic nature of the scattering air molecules should also be taken into account for obtaining reliable theoretical results, especially when the optical thickness is small.
J. V. DAVE, "Importance of Higher Order Scattering in a Molecular Atmosphere," J. Opt. Soc. Am. 54, 307-314 (1964)