Iterative generalized functional method of nonimaging optical design

In a previous paper we derived a generalized functional method of nonimaging optical design, applicable in the case of axisymmetric or translationally symmetric geometries utilizing extended sources and multiple reflective and/or refractive optical surfaces. Variations of this method were described for generation of either a prescribed intensity distribution as a function of angle or a prescribed irradiance distribution as a function of position along the shape profile of an aspheric target surface. A dual-surface functional (DSF) method was described for generation of two successive optical surfaces that transform a given source distribution into either two prescribed irradiance distributions on successive target surfaces or a prescribed irradiance distribution and a prescribed intensity distribution. The RMS difference between the intensity or irradiance distribution produced by a given generalized-functional design and the corresponding prescribed distribution approaches zero in the limit as the optical characteristics of the actual source approach those of the zero-étendue extended source model used in generating the design. In the current contribution, we present an iterative algorithm that can significantly improve the beam-shaping performance of generalized functional designs for sources having non-zero étendue. Three examples are provided, including an iterative DSF design that provides both high irradiance uniformity and étendue-matched flux-transfer efficiency greater than 97%.