Exact and approximate analytical solutions of the two- und three-dimensional radiative transfer equation

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The radiative transfer equation (RTE) is the fundamental equation for describing light propagation in scattering media in the mesoscopic and macroscopic scales such as in biological media, in plastics, in paints, in stones, in soils, in the atmosphere or in the interstellar space. Usually, the RTE is solved by numerical approaches like the Monte Carlo method. Recently, however we succeeded in deriving analytical solutions to the RTE for different geometries and to some of its extensions, e.g. for the generalized RTE. The aim of the project is to derive further important analytical solutions to the RTE for a variety of geometries in all spatial frequency domains and in all spatial domains considering also the solutions for discrete numbers of scattering interactions. Furthermore, analytical solutions will be derived for the correlation RTE and the diffusion equation, an often used approximation of the RTE. The new analytical solutions will be validated with or compared to Monte Carlo simulations. Analytical solutions of the RTE will be combined to solutions of the heat conduction equation, to which also analytical solutions will be derived for different geometries. In addition, the new analytical solutions will be efficiently implemented, first, to study important applications in different technical and medical fields and, second, to make the solutions available to the interested user.