Beam propagation through slab scattering media in the small angle approximation

Abstract

A general solution to the radiative transfer equation applicable to beam propagation in scattering media in which scattering takes place principally in extreme forward direction was obtained by H. S. Snider and W. T. Scott [Phys. Rev. 76, 220 (1949)] and discussed by R. L. Fante [IEEE Trans. Antennas Propag. AP-21, 750 (1973)]. This solution is applicable to media in which the aerosol number densities are nonuniformly distributed in space. Subsequently, W. G. Tam and A. Zardecki [Appl. Opt. 21, 2405 (1982)] obtained a specific solution applicable to those cases in which the beam width and angular spread as well as the aerosol phase function can be approximated by a Gaussian. Their solution is restricted to uniform or step function shaped media in which the detector is in the scattering medium. The present work shows that the Tam and Zardecki approach can be applied to the inhomogeneous case. Specifically, a solution is obtained for a slab shaped scattering medium. The results are compared with those obtained by use of a Monte Carlo simulation and to experimental data.