On optical surface reconstruction from a prescribed source-target mapping

A new optical surface reconstruction technique in the source-target mapping method is proposed. The technique is based on the representation of the surface as an envelope of a parametric family of paraboloids (ellipsoids). Using such a representation, the calculation of the optical surface is reduced to solving a complete differential equation without regard for the coordinate system. By way of illustration, mirrors that generate uniform intensity distributions in a square region are designed. Simulation of the design examples shows high performance of the proposed technique: it allows us to obtain good-quality intensity distributions even with violation of the integrability condition.