The geometric-optics relation between surface slope error and reflected ray error in solar concentrators

• A rigorous relation between surface slope error and reflected ray error is introduced from light scattering theory.
• The fundamental difference between the rigorous relation and the conventional relation is explained.
• The implementation of the rigorous relation in the Monte Carlo ray-tracing is illustrated.
• Its effect on the concentrated solar flux distribution is investigated with an exemplary case of dish concentrators.

In typical reflection-based solar concentrators, surface slope error mainly causes the reflected ray to deviate from the specular reflection direction and eventually from a target. Hence a fundamental understanding of the relation between surface slope error and reflected ray error is important for evaluating optical performance of solar concentrators. It has been widely accepted that when surface slope error follows the Rayleigh distribution, reflected ray error also follows. However, including this conventional relation, the relevant studies to date relied on purely geometric calculations and overlooked features of light scattering. In this study, the bidirectional reflectivity from geometric optics in light scattering theory is employed to derive a more rigorous distribution of reflected ray error. For the reflector surface without refraction, the geometric-optics relation demonstrates that the conventional relation holds only at normal incidence and becomes more and more incorrect as the incidence angle increases because of diminishing scattering effects. As a result, the conventional relation underestimates the peak flux produced by solar concentrators and their optical performance. The treatment that is able to account for scattering features and thereby overcome the limitations of the conventional relation is suggested in the use of the Monte Carlo ray-tracing method.