Exact formulation of multiple scattering in a three-dimensional cylindrical geometry

Exact expressions for the source function, flux, and scattered intensity normal to the surface are developed in cylindrical coordinates for a three-dimensional, absorbing, emitting, isotropically scattering medium exposed to both diffuse and collimated radiation. Simplifications of these expressions for certain important geometries and uniform loading are presented. Also, superposition of these equations and radiative equilibrium are discussed. The generalized three-dimensional equations are shown to reduce to the familiar one-dimensional results. Also, the equations for a strongly anisotropic phase function which is made up of a spike in the forward direction superimposed on an otherwise isotropic phase function are expressed in terms of the isotropic expressions.