Construction of freeforms in illumination systems via generalized Cartesian oval representation

Abstract

Freeforms in illumination systems are directly constructed by adapting some ideas of Oliker and co-workers [1]. The freeform is created by a set of primitive surface elements which are generalized Cartesian ovals including the optical response of the residual system. Hamiltonian theory of ray optics can be used to determine the family of primitives which is in particular a simple task if the freeform is the exit surface of the illumination system. For simple optical systems an analytical description of the primitives is possible. Contrarily, for more complex optics a conventional raytracer is additionally utilized to determine the required system's information, like the optical path lengths or mixed characteristics. To this end a discrete set of rays is traced through the residual systems and the required relations are interpolated to obtain a quasi-analytic representation of the primitives. The potential of this approach is demonstrated by some examples, e.g. freeform optics including collimating or deflection elements.