Tailoring freeform lenses for illumination

The general problem to find the shape of a refractive surface such as to produce a desired brightness distribution on a given target surface from a known point source leads to a boundary value problem with an elliptic partial differential equation of the Monge-Ampere type. This equation has been described and analyzed in the literature. The purpose of our contribution is to present a venue for a numerical solution as well as several solved examples. The essence of our algorithm for a numerical solution appears to be the explicit incorporation of the condition for the existence of a pseudopotential for a normal vector field.