Through the flux characterization of a high flux solar simulator, all directional information of the flux distribution is lost. Therefore, an experimental approach is necessary to restore the directional information. In this study, 13 heat flux maps were experimentally obtained from a 10 kWe Xenon arc solar simulator through an indirect flux mapping technique, implementing the use of one Lambertian target. The formulation of the inverse problem of experimentally determining the intensity distribution at the focal plane is presented. In addition, a Monte Carlo ray tracing in-house code modeling the Xenon arc is developed and used to generate the experimentally obtained flux maps and intensity at the focal plane to be used as a reference. Two intensity interpolation schemes were examined; a zeroth and first-order schemes. It is shown that a first order interpolation unnecessary complicates the inverse problem. The percentage error reduced from 90.9% to 82.6% when changing the interpolation scheme from a first to zeroth-order, in addition to a five times reduction in computational time. Furthermore, a new approach of constraining the formulated system of equations with an equality constraint that works by eliminating some of the intensity values that cannot be traced back to the ellipsoidal reflector is proposed. Therefore, it can be used as a technique to change the ill-conditioned problem to a well-conditioned one, without depending heavily on Tikhonov regularization methods. This new approach provided intensity values at the focal plane with a reduced percentage error from 52.2% to 30.4% for the zeroth-order interpolation scheme.