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

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

### Uittreksel

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-2 Engels 034001 16 JPhys Photonics 1 https://doi.org/10.1088/2515-7647/ab2db3 Gepubliceerd - 2019

### Vingerafdruk

Optical systems
Boundary value problems
Boundary conditions
Monte Carlo simulation

### Citeer dit

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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 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.",
keywords = "least-squares method, Monge-Amp\`{e}re equation, inverse problem, transport boundary conditions, optical design, freeform optics, ray tracing",
author = "Nitin Yadav and Lotte Romijn and {ten Thije Boonkkamp}, Jan and Wilbert IJzerman",
year = "2019",
doi = "10.1088/2515-7647/ab2db3",
language = "English",
volume = "1",
journal = "JPhys Photonics",
issn = "2515-7647",
publisher = "Institute of Physics",

}

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

TY - JOUR

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

AU - Romijn, Lotte

AU - ten Thije Boonkkamp, Jan

AU - IJzerman, Wilbert

PY - 2019

Y1 - 2019

N2 - 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.

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

U2 - 10.1088/2515-7647/ab2db3

DO - 10.1088/2515-7647/ab2db3

M3 - Article

VL - 1

JO - JPhys Photonics

JF - JPhys Photonics

SN - 2515-7647

M1 - 034001

ER -