Reflector design from radiance distributions

Abstract

This paper proposes a technique for the design of reflector shapes from prescribed optical properties (far field radiance distribution) and geometrical constraints, which is of high importance in the field of Lighting Engineering, more specifically for Luminaire Design. The reflector shape to be found is just a part of a set of pieces of what is known in lighting engineering as an optical set, and is composed of a lamp (light source), a reflector, a holding case and a glass that protects the system from dust and other environmental phenomena. Thus, we aim at the design and development of a system capable of generating a reflector shape in a way such that the optical set emits a given, user defined, far field radiance distribution. This problem can be put in the mathematical context of inverse problems, which refer to all the problems where, contrary to what happens with traditional direct problems, several aspects of the scene are unknown. Then, the algorithm is allowed to work backwards to establish the missing parameters. In order to do so, light propagation inside and outside the optical set must be computed and the resulting radiance distribution compared to the desired one. Finally, constraints on the shape imposed by industry needs must be taken into account, bounding the set of possible shape definitions. The general approach taken is based on a minimization procedure on the space of possible reflector shapes. The algorithm moves towards minimizing the distance, in the I2 metric, between the resulting illumination far from the reflector and a prescribed, ideal optical radiance distribution specified at the far field by the user.