Sunshape and Its Influence on the Flux Distribution in Imaging Solar Concentrators

Imaging solar concentrators, such as a parabolic dish, image the sun to their focal plane. Thus, the flux distribution is basically an image of the angular distribution of the direct incident solar radiation. This distribution, referred to as sunshape, is determined by solar limb darkening and by small angle scattering in the atmosphere. In this paper we present measurements of the sunshape and investigate its influence on the flux distribution in the solar furnace at Paul Scherrer Institute (PSI) and in parabolic concentrators, both experimentally and by a ray tracing procedure. Analyzing the influence of the spectral dependence of the sunshape we find that the characteristic width of the focal spot increases with longer wavelengths. In contrary, the mean concentration ratio is higher at shorter wavelengths. Although these effects are rather small, they can be important in radiometric measurement techniques to determine the emissivity and the temperature distribution of an irradiated sample as well as in designing solar pumped lasers. Comparing various sunshapes with the corresponding flux distributions in the two-stage solar furnace at PSI, we show that the influence of the circumsolar radiation on the flux distribution is usually negligible as compared to the distortion due to astigmatism. However, in more accurate optical systems, such as highly concentrating parabolic dishes, the flux distribution is a fairly accurate image of the sunshape. We find, that due to sunshape, the mean concentration ratio in a parabolic dish is decreased by about ten percent. As an example we subsequently estimate the mean annual conversion efficiency of an ideal solar converter operated in the Swiss mountains.