A method for dealing with inverse problems in transport and filter theory

For a plane parallel atmosphere, the inverse problem of radiative transfer treated here utilizes the results of an experiment which measures the total angle dependent column density of the specific intensity for determination of the phase function (or angular differential cross section) and the albedo for single scattering. A generalization of this technique is presented to deal with the multi-dimensional problems in which the atmosphere is contained in a volume bounded by any arbitrary convex surface. We use two methods of mathematical approach for the solutions of appropriate integral equations of the Fredholm type. One, the spherical harmonic expansion method, and two, a maximal variational principle. We also demonstrate the use of the maximal variational principle to deal with the linear filter matrix equation of the Wiener-Hopf type.