Simultaneous estimation of extinction coefficient distribution, scattering albedo and phase function of a two-dimensional medium

In this work, we develop a scheme based on solving the general integro-differential equation of radiation transport to estimate simultaneously the distribution of the extinction coefficient, the scattering albedo and the phase function of a two-dimensional inhomogeneous medium with less diffusive radiation. The forward problem for a cylindrical medium subjected to collimated incident radiation is solved by the discrete-ordinate method. The inverse radiation problem is formulated as a least square problem that minimizes the discrepancy between the measured and the calculated leaving radiative fluxes. The Levenberg-Marquardt algorithm is applied to the least square problems for a variety of cases. The results obtained show that this scheme can reconstruct accurate enough results for most of the cases considered. Comparisons of the results show that the accuracy of the estimated results decreases with the increase of the scattering albedo and we need more discrete ordinates to generate accurate enough estimated results for an optically thin case. The estimated results obtained from the measurement data with moderate errors are still acceptable.