Radiative transfer on curved surfaces

Abstract

After a review of appropriate concepts in local surface geometry, a formally exact solution of the radiative transfer equation is constructed, for transfer from one surface of arbitrary shape to another. The solution is obtained from repeated application of the linear interaction principle to form a path integral over paths that cross many intermediate surfaces. Invariant imbedding in general geometries is presented and found to be manifest in the path integral solution as an invariance under local coordinate transformations of the intermediate surfaces. Aspects of possible numerical implementations of this geometrical approach are discussed.