Multiscattering model for propagation of narrow light beams in aerosol media

An approximation to the radiative transfer equation is derived for the propagation of narrow light beams. The main feature is the representation of the power flux in the direction normal to the propagation axis by a diffusion process. Coupled partial differential equations are obtained for the forward and backward flux densities. They are valid in the paraxial approximation. The solutions are written in general analytic formulas applicable to inhomogeneous aerosol media. Comparisons with Monte Carlo calculations and laboratory data reported in a companion paper [Appl. Opt. 27, 2485 (1988)] show very good agreement over a wide range of extinction coefficients, scattering albedos, and particle size parameters.