Inverse Analysis of Radiative Flux Maps for the Characterization of High Flux Sources

Abstract

The reconstruction of the angular and spatial intensity distribution from radiative flux maps measured in high flux solar simulators (HFSS) or optical concentrators is an ill-posed inverse problem requiring special solution strategies. We aimed at providing a solution strategy for the determination of intensity distributions of arbitrarily complicated concentrating facilities. The approach consists of the inverse reconstruction of the intensities from multiple radiative flux maps recorded at various positions around the focal plane. The approach was validated by three test cases including uniform spatial, Gaussian spatial, and uniform angular distributions for which we successfully predicted the intensity for a square-shaped target with edge length of 0.5 m and for a displacement range spanning ±1.5 m at a resolution of 3.2 × 106 elements, yielding relative errors between 19.8–26.4% and 15.7–25.6% when using Tikhonov regularization and the conjugate gradient least square (CGLS) method, respectively. The latter method showed superior performance and was used at a resolution of 2.35 × 107 elements to analyze EPFL's HFSS comprising 18 lamps. The inverse solution for a single lamp retrieved from experimentally measured and simulated radiative flux maps showed peak intensities of 13.7 MW/m2/sr and 16.0 MW/m2/sr, respectively, with a relative error of 81.1%. The inverse reconstruction of the entire simulator by superimposing the single lamp intensities retrieved from simulated flux maps resulted in a maximum intensity of 18.8 MW/m2/sr with a relative error of 80%. The inverse method proved to provide reasonable intensity predictions with limited resolution of details imposed by the high gradients in the radiative flux maps.