An explicit formulation for the inverse transport problem using only external detectors: Part II: Application to one-dimensional homogeneous and heterogeneous participating media

Abstract

Abstract. 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.

An explicit formulation for the inverse transport problem using only external detectors: Part I: computational modelling

“…In an accompanying article [2] we apply this formulation for a one-dimensional inverse radiative transfer problem. We will show the derivation of the explicit equation for matrix A and the strategy developed to extract the total extinction and scattering coefficients contained in it from albedo operator information.…”

“…As an example of the new methodology application we present the study of the one-dimensional stationary problem in an accompanying article [2].…”