A least-squares method for the design of two-reflector optical systems

Nitin Yadav; Lotte Romijn; Jan ten Thije Boonkkamp; Wilbert IJzerman

doi:10.1088/2515-7647/ab2db3

A least-squares method for the design of two-reflector optical systems

Nitin Yadav, Lotte Romijn, Jan ten Thije Boonkkamp (Corresponding author), Wilbert IJzerman

Center for Analysis, Scientific Computing and Applications

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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.

Original language	English
Article number	034001
Number of pages	16
Journal	JPhys Photonics
Volume	1
Issue number	3
DOIs	https://doi.org/10.1088/2515-7647/ab2db3
Publication status	Published - 16 Jul 2019

Keywords

Freeform optics
Inverse reflector problem
Least-squares method
Monge–Ampère equation

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Cite this

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title = "A least-squares method for the design of two-reflector optical systems",

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–Amp{\`e}re (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.",

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A least-squares method for the design of two-reflector optical systems

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