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.
© 1956 Optical Society of AmericaFull Article | PDF Article
OSA Recommended Articles
Appl. Opt. 3(2) 197-202 (1964)
David A. de Wolf, Herman W. J. Russchenberg, and Leo P. Ligthart
Appl. Opt. 38(3) 585-593 (1999)
S. Menon, Q. Su, and R. Grobe
Opt. Lett. 30(12) 1542-1544 (2005)