A previously proposed modified form of diffusion theory [Phys. Rev. 100, 517 (1955)] is applied to problems involving point sources and plane clouds over an absorbing ground. A general but formal solution is first presented. Some analytic results are then obtained for a point source at the edge of a semi-infinite (half-space) cloud; specific formulas are given for the photon density at the edge of the cloud and for the net photon current there; asymptotic results are obtained for large distances inside the cloud along the source axis. Finally, numerical results are presented for the photon density at the mid-plane of an infinite plane cloud with thickness equal to two (transport) mean free paths and a point source at the center. An appendix summarizes analytic results of the modified theory for: a point source in an infinite medium, a point source at the center of a finite sphere, the albedo and transmission of an infinite plane slab with parallel (";solar";) illumination at an arbitrary angle, the albedo of the combination of a plane cloud over a ground plane with arbitrary albedo, and a rough analysis of ambient light levels in the ocean.
PAUL I. RICHARDS, "Scattering from a Point Source in Plane Clouds," J. Opt. Soc. Am. 46, 927-932 (1956)