Inverse reflector design for a point source and far-field target

Lotte B. Romijn; Jan H.M. ten Thije Boonkkamp; Wilbert L. IJzerman

doi:10.1016/j.jcp.2020.109283

Inverse reflector design for a point source and far-field target

Lotte B. Romijn (Corresponding author)
, Jan H.M. ten Thije Boonkkamp
, Wilbert L. IJzerman

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

30 Citaten (Scopus)

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Samenvatting

We present a method for the design of a single freeform reflector that converts the light distribution of a point source to a desired light distribution in the far field. Using the geometrical-optics law of reflection and requiring energy conservation, this optical design problem can be represented by a generalized Monge–Ampère equation for the shape of the reflector with transport boundary condition. We use a generalized least-squares algorithm that can handle a logarithmic cost function in the corresponding optimal transport problem. The algorithm first computes the optical map and subsequently constructs the optical surface. We demonstrate that the algorithm can generate reflector surfaces for a number of complicated target distributions.

Originele taal-2	Engels
Artikelnummer	109283
Aantal pagina's	23
Tijdschrift	Journal of Computational Physics
Volume	408
DOI's	https://doi.org/10.1016/j.jcp.2020.109283
Status	Gepubliceerd - 1 mei 2020

Bibliografische nota

Funding Information:
This work is part of the research program NWO-TTW Perspectief with project number P15-36 , which is (partly) financed by the Netherlands Organisation for Scientific Research (NWO).

Publisher Copyright:
© 2020 Elsevier Inc.

Financiering

This work is part of the research program NWO-TTW Perspectief with project number P15-36 , which is (partly) financed by the Netherlands Organisation for Scientific Research (NWO).

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title = "Inverse reflector design for a point source and far-field target",

abstract = "We present a method for the design of a single freeform reflector that converts the light distribution of a point source to a desired light distribution in the far field. Using the geometrical-optics law of reflection and requiring energy conservation, this optical design problem can be represented by a generalized Monge–Amp{\`e}re equation for the shape of the reflector with transport boundary condition. We use a generalized least-squares algorithm that can handle a logarithmic cost function in the corresponding optimal transport problem. The algorithm first computes the optical map and subsequently constructs the optical surface. We demonstrate that the algorithm can generate reflector surfaces for a number of complicated target distributions.",

keywords = "Generalized Monge–Amp{\`e}re equation, Geometrical optics, Least-squares method, Logarithmic cost function, Optimal mass transport, Stereographic coordinates",

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note = "Funding Information: This work is part of the research program NWO-TTW Perspectief with project number P15-36 , which is (partly) financed by the Netherlands Organisation for Scientific Research (NWO). Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

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AU - IJzerman, Wilbert L.

N1 - Funding Information: This work is part of the research program NWO-TTW Perspectief with project number P15-36 , which is (partly) financed by the Netherlands Organisation for Scientific Research (NWO). Publisher Copyright: © 2020 Elsevier Inc.

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AB - We present a method for the design of a single freeform reflector that converts the light distribution of a point source to a desired light distribution in the far field. Using the geometrical-optics law of reflection and requiring energy conservation, this optical design problem can be represented by a generalized Monge–Ampère equation for the shape of the reflector with transport boundary condition. We use a generalized least-squares algorithm that can handle a logarithmic cost function in the corresponding optimal transport problem. The algorithm first computes the optical map and subsequently constructs the optical surface. We demonstrate that the algorithm can generate reflector surfaces for a number of complicated target distributions.

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KW - Logarithmic cost function

KW - Optimal mass transport

KW - Stereographic coordinates

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Inverse reflector design for a point source and far-field target

Samenvatting

Bibliografische nota

Financiering

Duurzame ontwikkelingsdoelstellingen van de VN

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