Multiple scattering in clouds

This report develops an analytic model for the propagation of an optical pulse through a multiple scattering medium. Such a model is needed to investigate the effect of clouds on optical communications from a satellite to a submarine. A key initial result is the derivation of simple expressions for the first two spatial and angular moments of the radiance distribution for a narrow delta-function source immersed in an infinite scattering medium. The moments support a diffusion approximation for the transport process in an infinite plane-parallel cloud. First the radiance is calculated at the cloud exit and on a plane an arbitrary distance below the cloud, then power collected by a finite receiver located on this plane is computed. The model is validated by comparing its results with computer simulation curve fits for optically thick clouds (i.e., tau = 15). The model is capable of duplicating nearly all the simulation results but at significantly lower cost. Furthermore, detailed calculations impractical to simulate are readily computed.