Key words: inverse problem, Levenberg-Marquardt, optical thickness, sensitivity analysis.

Abstract: An inverse radiation problem was considered to estimate the optical thickness for a one-dimensional cylindrical model of a semi-transparent, gray and isotropically scattering medium. The radiative transfer equation is solved using the finite volume method and the temperature is determined according to the dimension of the semi-transparent medium. In order to find the points which give us more information about the optical thickness using the measured temperatures, we carried out a sensitivity analysis. The solution of the inverse problem is obtained with the Levenberg-Marquardt method. The identification results were analyzed with respect to the number of measurements and the initial estimate of the unknown radiative property. The effect of the parameter of the LM method on the stability of the solution, in particular in the vicinity of the initial estimate, was also investigated.