An inverse source problem in radiative transfer for spherical media

A method is presented to identify the source term in a one-dimensional, absorbing, emitting scattering spherical medium from the knowledge of the exit radiation intensities. The inverse radiation problem is formulated as an optimization problem. The sensitivity problem and the gradient equation are derived. The conjugate gradient method is used for its solution. Although the source term is a function of the space variable, only radiation intensities exiting the outer boundary are required. Both data with and without measurement errors are used as input to identify the source term. The study shows that the estimation of the source term is more sensitive to increases in measurement errors as the optical thickness increases.