Inverse identification of intensity distributions from multiple flux maps in concentrating solar applications

Abstract

Radiative flux measurements at the focal plane of solar concentrators are typically performed using digital cameras in conjunction with Lambertian targets. To accurately predict flux distributions on arbitrary receiver geometries directional information about the radiation is required. Currently, the directional characteristics of solar concentrating systems are predicted via ray tracing simulations. No direct experimental technique to determine intensities of concentrating solar systems is available. In the current paper, multiple parallel flux measurements at varying distances from the focal plane together with a linear inverse method and Tikhonov regularization are used to identify the directional and spatial intensity distribution at the solution plane. The directional binning feature of an in-house Monte Carlo ray tracing program is used to provide a reference solution. The method has been successfully applied to two-dimensional concentrators, namely parabolic troughs and elliptical troughs using forward Monte Carlo ray tracing simulations that provide the flux maps as well as consistent, associated intensity distribution for validation. In the two-dimensional case, intensity distributions obtained from the inverse method approach the Monte Carlo forward solution. In contrast, the method has not been successful for three dimensional and circular symmetric concentrator geometries.