The inverse problem of diffuse transmission in transport theory

We consider a linear problem of transfer of radiation or elementary particles in a homogeneous plane layer, in the absence of internal energy sources. Let the medium on the side of one (conditionally-left) boundary be stationary illuminated by radiation of intensity $ J_0 $. Then the radiation of intensity $ J_1 = TJ_0 $ emerges from the right boundary. Some methods for constructing a linear transmission operator $ T $ are described. The existence and effective construction of the inverse operator $ T ^ {- 1} $ are considered. Knowing $ T ^ {- 1} $ allows to restore $ J_0 $ using the results from the measurement $ J_1 $ . This inverse problem adjoins [1]. Its solution has various applications.