Design of a smooth freeform illumination system for a point light source based on polar-type optimal transport mapping

optimal transport (LOT) mapping. In this method, the LOT mapping between an assumed circular planar source and a prescribed target is first obtained by solving a polar-type LOT problem. Then, the mapping calculated for the circular source is applied for a point light source. Finally, the freeform optical surface is generated by a geometric construction method to realize the ray mapping. As examples, a series of smooth-surface freeform lenses are designed for a point light source to form uniform and complex illumination patterns on rectangular targets. The ray-tracing results show that all the designs achieve excellent performance with the light utilization efficiency η over 0.87 (Fresnel loss considered) and the relative standard deviation (RSD) of the simulated illumination distribution less than 0.051 simultaneously.