Analytic function for heliostat flux mapping with astigmatism and defocus

Off-axis incidence is inherent to sun tracking mirrors, named heliostats. Moreover, heliostat defocus takes place, provided that the focal length of the mirrors usually differs from their distance to the target. Defocus, along with high incidence angles, lead to astigmatic aberrations, that are overlooked by analytic functions based on convolution. This paper presents an analytic function on the image plane that reproduces these aberrations. As the reflection of the heliostat axes is non-orthogonal with defocus, the identification of the reflected axes plays a key role in the resulting model. In comparison with Monte Carlo Ray-Tracing, the model shows correlation coefficients above 90%, except at the tangential and sagittal foci, where the analytic function is indeterminate. An astigmatic parameter is provided to assess the model validity, which is complementary to UNIZAR at high incidence angles.This work has been supported by the Madrid Government (Comunidad de Madrid), Spain under the Multiannual Agreement with UC3M in the line of "Fostering Young Doctors Research" (VISHELIO-CM-UC3M), and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation). Funding for APC: Universidad Carlos III de Madrid (Read & Publish Agreement CRUE-CSIC 2022)