Abstract
The purpose of this paper is to present a method for the design of two-reflector optical systems that transfer a given energy density of the source to a desired energy density at the target. It is known that the two-reflector design problem gives rise to a Monge–Ampère (MA) equation with transport boundary condition. We solve this boundary value problem using a recently developed least-squares algorithm (Prins et al 2015 J. Sci. Comput. 37 B937–61). It is one of the few numerical algorithms capable to solve these type of problems efficiently. The least-squares algorithm can provide two solutions of the MA problem, one is concave and the other one is convex. The reflectors are validated for several numerical examples by a ray-tracer based on Monte-Carlo simulation.
Highlights
The optical design problem can be formulated as an inverse problem: determine an optical system consisting of reflectors and/or lenses that converts a given light distribution of the source into a desired target light distribution
Solution methods for inverse problems, in short inverse methods, can significantly speed up the design process, and even provide designs that could realistically never be achieved without these methods [1, 2]
We have presented a geometrical formulation for a two-reflector optical system which is based on the principle of equal optical path length
Summary
The optical design problem can be formulated as an inverse problem: determine an optical system consisting of reflectors and/or lenses that converts a given light distribution of the source into a desired target light distribution. We can consider the forward problem: given a light source and an optical system, compute the resulting target light distribution. The prototypical solution method for this problem is Monte-Carlo ray tracing [3]. In this method, a large collection of rays is traced through an optical system until they hit a target receiver. From the distribution of target rays one can compute an estimate of the light output. Optical design by ray tracing is a slow process, all the more since the resulting light output is most likely not equal to the desired output. Ray tracing can be used to validate the optical design computed by an inverse method
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