Theory of light pulse propagation through thick clouds

Abstract

In the previous paper, the diffusion equation was derived from the ordinary space-time transport equation; corresponding boundary conditions on a surface of medium discontinuity were also obtained. In this paper, the theory is applied to evaluate the reflected and transmitted wave intensities of a plane wave pulse incident upon a scattering slab and the pulse shapes are displayed for a wide range of parameters. In both cases, the pulses are found to decrease exponentially with time t in the asymptotic domain, even when the scatterers have no absorption. This forms a marked contrast to the case of semi-infinite or infinite scattering media where the intensities decrease by the factor t3/2. An expression for average pulse width is obtained analytically for the pulses transmitted through the scattering slab and is given as a function of the mean cosine of the scattering angle, the optical thickness, and the absorption cross section. The expression obtained for pulse width, with a reasonable value of absorption cross section, seems to show good agreement with the experimental results of Bucher and Lerner concerning optical pulse propagation through thick clouds.