Freeform illumination optics construction following an optimal transport map

We present a modified optimal transport (OT) ray-mapping approach for designing freeform illumination optics. After mapping the source intensity into a virtual irradiance distribution under stereographic projection, we employ an advanced OT map computation method with the ability to tackle nonstandard boundary conditions. Following the computed map, we construct the freeform optical surface directly from normal vectors by requiring that the chord between two adjacent points is perpendicular to the average of the two normal vectors at these two points and enforcing this relationship with a least squares method. Examples of designing freeform lenses for LED sources show that we can produce various uniform illumination patterns with high optical efficiencies.