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 . 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.