Influence of the characteristics of light source and target on the Monge-Ampére equation method in freeform optics design

It was previously demonstrated in [Opt. Lett. 38, 229 (2013)] that the problem of freeform surface illumination design can be converted into a nonlinear boundary problem for the elliptic Monge–Ampére equation based on the ideal source assumption. But how the Monge–Ampére equation method is affected by the characteristics of the light source and target was not discussed there. This Letter systematically analyzes the influence of discontinuity, nonconvexity, and connectivity of light source and target on the Monge–Ampére equation method and presents some intrinsic features of this design method. These features are applied in practical examples in freeform optics design.