Multiple scattering corrections to the Beer-Lambert law are analyzed by means of a rigorous small-angle solution to the radiative transfer equation. Transmission functions for predicting the received radiant power—a directly measured quantity in contrast to the spectral radiance in the Beer-Lambert law—are derived. Numerical algorithms and results relating to the multiple scattering effects for laser propagation in fog, cloud, and rain are presented.
W. G. Tam and A. Zardecki, "Multiple scattering corrections to the Beer-Lambert law. 1: Open detector," Appl. Opt. 21, 2405-2412 (1982)