<title>Automated mirror design for an extended light source</title>

Abstract

A computer package, Automated Mirror Design, has been developed by us to automate the design of luminaire reflectors. In this paper, new improvements to the algorithm for Automated Mirror Design are presented. We have previously reported a study on a series of point-light source luminaire problems. We now report on the operation of Automated Mirror Design for non-trivial light sources. In particular, reflector designs are presented for an extended light source, which produce limited Lambertian output and return no radiation to the source. Finally, the operation of differential evolution relies on the use of an appropriate merit function to determine the quality of proposed mirror designs. Merit functions specific to the Lambertian output design problem are discussed.

A Survey of Inverse Surface Design From Light Transport Behavior Specification

“…We have also seen that almost all works use a local illumination approach, with the further restrictions of using pure specular surfaces and the highly restrictive condition that no inter-reflections occur, with the only exception in the works by Doyle et al [46][47][48], which use global illumination with a perfect specular BRDF model with a threshold based stopping criteria, and [49], in which a more generic global illumination algorithm is used.…”

“…[45] uses a modified Newtoniteration method. On the other hand, Doyle et al [46][47][48] use a Genetic Algorithm for the optimization, and [49] uses a custom global 'Brute Force' algorithm. To the authors' knowledge, choosing one optimization method or another is quite arbitrary, and no method has proven to be the best for this sort of optimization problem.…”

“…As [45] None front-surf with const dist form back-surf Error functional that describes the aberrations in a progressive lens Bi-cubic tensor product of NURBS, took 66.5 secs in a SGI Onix w/R10000. [46][47][48] None Random Initial Population Diff between target and resultant distrib at obj region plus lost rays plus difference between reflected and desired power [48] 2D: parabolic & elliptic reflectors [49] None Generic Initial Refl Least squares error between the current light distribution from the reflector and the desired distribution.…”

“…Doyle et al present [46][47][48] an evolution strategy (a variation on the Genetic Algorithm) for 2D luminary design with point [46] and extended [47] light sources, later completed with a careful analysis of the objective function [48] (called Merit Function in the papers). As such, they defined a threeterm objective function consisting of a term that represents the absolute element-wise difference between the target and resultant distributions in an objective region, and a term representing a penalty for the rays that lie outside the desired region, plus a third term that represents a measure of the difference between the reflected and the desired light power.…”

Freeform optical element for uniform illumination

“…Approximately, there are two ways to design them. One is by trial and error method, which always takes a lot of time [1,2]. The other is to construct the freeform optical element by solving a set of differential equations [3][4][5][6][7][8].…”