Approximate theory of photon migration in a two-layer medium.

We recently examined properties of the surface emission profiles of particles (photons) injected into a turbid medium consisting of two layers [R. Nossal, J. Kiefer, G. H. Weiss, R. F. Bonner, H. Taitelbaum, and S. Havlin, "Photon Migration in Layered Media," Appl. Opt. 27, 3382-3391 (1988)]. The two layers differ in the coefficient that appears when internal absorption is modeled in terms of Beer's law. The model relates to the injection of laser radiation into tissue for diagnostic or therapeutic purposes. Results of our earlier work were derived from extensive computer simulations. In the present paper we discuss a simple analytical approximation to the surface intensity profile valid when the absorptivity of the upper layer is greater than that of the lower.