The steady state inverse radiative transfer problem in one-dimensional participating media is studied as an example of application of the new methodology presented in a accompanying paper by the authors [2]. Spectral methods are used for the appropriate analysis of the direct transport problem. For the inverse problem, we present a matrix that involves only values of the flux intensities at the boundary of the medium. Its columns are built with a set of linearly independent solutions for the system, which is formed when angular half-range prescribed boundary values and the complementary measured half-range boundary values are coupled. The final inverse albedo problem is treated as a full range two point boundary value problem. Test cases results are presented. Mathematical subject classification: 80A23, 15A29.

In the present work the inverse problem of identification of radiative properties, the total extinction and scattering coefficients, is analyzed and explicitly formulated based in an elementary semi-group theory. The Chandrasekhar discrete ordinates finite dimensional approximation of the angular variables is used for the direct problem representation with the stationary Linear Transport (Boltzmann) Equation in absorbing and scattering media in matrix form. For the inverse problem we suppose known the albedo operator from measured intensities at the boundaries of the medium. Here we analize the inverse problem for an N-dimensional medium and from the solution of the transmission problem we present an explicit form for the matrix that contains the total extinction and scattering coefficients. Mathematical subject classification: 80A23, 15A29.