Four different views of the heliostat flux density integral

Abstract The image due to a single heliostat is represented by its flux density, which can be formulated as an integral over the solid angle of the incoming rays. The initial formulation is transformed into three alternative representations, each having some particular utility. The incoming ray formulation leads to analytic results for flat heliostats with polygonal boundaries. The mirror plane formulation leads to a numerical integration over the mirror plane which can be used to study effects due to distortions of the mirror. The pin-hole view leads to an approximate expression for the flux density integral as a convolution of the image due to a point Sun with respect to the brightness distribution of the real Sun. This formulation allows us to treat the Sun size as though it were a source of guidance errors or alternatively, we can introduce a degraded Sun which includes the guidance errors.