Abstract

We use the radiative transfer equation to study a laser beam propagating through a turbid medium. During the propagation, we view the beam as first scattering into a narrow forward cone, and then into a diffuse pattern. To describe this process, we propose a systematic and practical method to combine the small-angle approximation with the diffusion approximation. The method works when the scattering cross section describing scattering from aerosols can be written as the sum of a Gaussian σ_s to describe scattering into small angles and a smooth term σ_d to describe scattering into large/diffuse angles. We use a Green's function formalism to perform partial resummations and set up a hierarchy of approximations in the form of coupled radiative transfer equations to describe the scattering of radiation from small angles into large angles. The adjoint operator formalism then provides a simple way to obtain the net flux received by an open detector. Our approximations may be described rigorously as a power series expansion in σ₀^d/σ₀^s, the ratio of the diffusion and the forward scattering cross sections.

© 1986 Optical Society of America