A design method is proposed to generate smooth freeform illumination optics for a point light source based on the L-2 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 eta over 0.87 (Fresnel loss considered) and the relative standard deviation (RSD) of the simulated illumination distribution less than 0.051 simultaneously. (C) 2017 Optical Society of America