### Abstract

Original language | English |
---|---|

Article number | 034001 |

Number of pages | 16 |

Journal | JPhys Photonics |

Volume | 1 |

DOIs | |

Publication status | Published - 2019 |

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### Keywords

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

### Cite this

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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.

Research output: Contribution to journal › Article › Academic › peer-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

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 -