Theoretical formulation of scattering for a layered atmosphere is presented in this paper. This theory is a generalization of previous formulation based on the small-angle approximation of the radiative transfer equation for laser beams propagating through spherical aerosols. Relative contribution to the beam irradiance from the various orders of scattering are presented for the case of laser beam propagating in successive layers of clouds. Numerical data on broadening as a function of optical depth is presented.
Usamah O Farrukh,
"Multiple Scattering For Laser Beams Propagating In A Layered Atmosphere", Proc. SPIE 0663, Laser Radar Technology and Applications I, (6 October 1986); doi: 10.1117/12.938654; https://doi.org/10.1117/12.938654