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

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

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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 equation with transport boundary condition. We solve this boundary value problem using a recently developed least-squares algorithm [1]. 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 Monge-Amp`\{e}re 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.
Originele taal-2Engels
Artikelnummer034001
Aantal pagina's16
TijdschriftJPhys Photonics
Volume1
DOI's
StatusGepubliceerd - 2019

Vingerafdruk

Optical systems
Boundary value problems
Boundary conditions
Monte Carlo simulation

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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-Amp`\{e}re equation with transport boundary condition. We solve this boundary value problem using a recently developed least-squares algorithm [1]. 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 Monge-Amp`\{e}re 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. / Yadav, Nitin; Romijn, Lotte; ten Thije Boonkkamp, Jan (Corresponding author); IJzerman, Wilbert.

In: JPhys Photonics, Vol. 1, 034001, 2019.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

TY - JOUR

T1 - A least-squares method for the design of two-reflector optical systems

AU - Yadav, Nitin

AU - Romijn, Lotte

AU - ten Thije Boonkkamp, Jan

AU - IJzerman, Wilbert

PY - 2019

Y1 - 2019

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AB - 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 equation with transport boundary condition. We solve this boundary value problem using a recently developed least-squares algorithm [1]. 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 Monge-Amp`\{e}re 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.

KW - least-squares method, Monge-Amp\`{e}re equation, inverse problem, transport boundary conditions, optical design, freeform optics, ray tracing

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DO - 10.1088/2515-7647/ab2db3

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JO - JPhys Photonics

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