Prescribed irradiance distributions with freeform gradient-index optics

Generating a prescribed irradiance distribution given a source distribution is an inverse problem that sits at the heart of illumination design. The growing prevalence of freeform optics has inspired several design methods for obtaining a prescribed irradiance distribution possessing no symmetry. Up to now, these methods have relied exclusively on freeform optical surfaces for generating freeform irradiances. This paper presents a design method that, for the first time, applies gradient-index (GRIN) optics to solving this inverse problem. Using a piecewise-continuous freeform gradient-index (F-GRIN) profile, a single optic with two planar surfaces can be designed to produce a far-field prescribed irradiance distribution from a point source. The design process is herein presented along with two design examples which demonstrate some of the unique properties of F-GRIN illumination optics.