Identification of Scattering Media from Reflected Flows

An inverse problem of linear transport theory is investigated. Using an approach closely related to the well-known invariant imbedding techniques, an equation is derived relating the time distribution of reflected flows at one end of a slab $[0,1]$ to the density distribution of the scattering medium in the interior. Criteria for the wellposedness of the inverse problem of identifying the medium from the reflected flow are formulated and a numerical scheme is proposed.