Freeform LED lens design for uniform rectangular illumination using a new source-target mapping

We proposed an approach to design a freeform LED lens for forming uniform rectangular illumination from a point Lambertian source based on a new source-target mapping. The new source-target mapping we present can be obtained analytically and the system geometry allows separation of variables. According to the Snell´s law and the source-target mapping, we can get a first-order partial differential equation set. The freeform lens then can be constructed by solving these PDEs numerically. The simulated results showed that we can get a good uniformity of illumination, and a good rectangular target illumination shape can be realized by our freeform lens.