A Monge-Ampère Least-Squares Solver for the Design of a Freeform Lens

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

doi:10.1007/978-3-030-55874-1_82

A Monge-Ampère Least-Squares Solver for the Design of a Freeform Lens

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

Samenvatting

Designing freeform optical surfaces that control the redistribution of light from a particular source distribution to a target irradiance poses challenging problems in the field of illumination optics. There exists a wide variety of strategies in academia and industry, and there is an interesting link with optimal transport theory. Many freeform optical design problems can be formulated as a generalized Monge-Ampère equation. In this paper, we consider the design of a single freeform lens that converts the light from an ideal point source into a far-field target. We derive the generalized Monge-Ampère equation and numerically solve it using a generalized least-squares algorithm. The algorithm first computes the optical map and subsequently constructs the optical surface. We show that the numerical algorithm is capable of computing a lens surface that produces a projection of a painting on a screen in the far field.

Originele taal-2	Engels
Titel	Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference
Redacteuren	Fred J. Vermolen, Cornelis Vuik
Plaats van productie	Cham
Uitgeverij	Springer
Pagina's	833-840
Aantal pagina's	8
ISBN van elektronische versie	978-3-030-55874-1
ISBN van geprinte versie	9783030558734
DOI's	https://doi.org/10.1007/978-3-030-55874-1_82
Status	Gepubliceerd - 3 mei 2021
Evenement	European Conference on Numerical Mathematics and Advanced Applications: ENUMATH 2019 - Hotel Zuiderduin, Egmond aan Zee, Nederland Duur: 30 sep. 2019 → 4 okt. 2019 https://www.enumath2019.eu/

Publicatie series

Naam	Lecture Notes in Computational Science and Engineering
Volume	139
ISSN van geprinte versie	1439-7358
ISSN van elektronische versie	2197-7100

Congres

Congres	European Conference on Numerical Mathematics and Advanced Applications
Verkorte titel	ENUMATH 2019
Land/Regio	Nederland
Stad	Egmond aan Zee
Periode	30/09/19 → 4/10/19
Internet adres	https://www.enumath2019.eu/

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:
© 2021, Springer Nature Switzerland AG.

Financiering

Acknowledgments 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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Romijn, L. B., .ten Thije Boonkkamp, J. H. M., & IJzerman, W. L. (2021). A Monge-Ampère Least-Squares Solver for the Design of a Freeform Lens. In F. J. Vermolen, & C. Vuik (editors), Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference (blz. 833-840). (Lecture Notes in Computational Science and Engineering; Vol. 139). Springer. https://doi.org/10.1007/978-3-030-55874-1_82

Romijn, Lotte B. ; .ten Thije Boonkkamp, Jan H.M. ; IJzerman, Wilbert L. / A Monge-Ampère Least-Squares Solver for the Design of a Freeform Lens. Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. redacteur / Fred J. Vermolen ; Cornelis Vuik. Cham : Springer, 2021. blz. 833-840 (Lecture Notes in Computational Science and Engineering).

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title = "A Monge-Amp{\`e}re Least-Squares Solver for the Design of a Freeform Lens",

abstract = "Designing freeform optical surfaces that control the redistribution of light from a particular source distribution to a target irradiance poses challenging problems in the field of illumination optics. There exists a wide variety of strategies in academia and industry, and there is an interesting link with optimal transport theory. Many freeform optical design problems can be formulated as a generalized Monge-Amp{\`e}re equation. In this paper, we consider the design of a single freeform lens that converts the light from an ideal point source into a far-field target. We derive the generalized Monge-Amp{\`e}re equation and numerically solve it using a generalized least-squares algorithm. The algorithm first computes the optical map and subsequently constructs the optical surface. We show that the numerical algorithm is capable of computing a lens surface that produces a projection of a painting on a screen in the far field.",

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Romijn, LB, .ten Thije Boonkkamp, JHM & IJzerman, WL 2021, A Monge-Ampère Least-Squares Solver for the Design of a Freeform Lens. in FJ Vermolen & C Vuik (uitgave), Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. Lecture Notes in Computational Science and Engineering, vol. 139, Springer, Cham, blz. 833-840, European Conference on Numerical Mathematics and Advanced Applications, Egmond aan Zee, Nederland, 30/09/19. https://doi.org/10.1007/978-3-030-55874-1_82

A Monge-Ampère Least-Squares Solver for the Design of a Freeform Lens. / Romijn, Lotte B.; .ten Thije Boonkkamp, Jan H.M.; IJzerman, Wilbert L.
Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. uitgave / Fred J. Vermolen; Cornelis Vuik. Cham: Springer, 2021. blz. 833-840 (Lecture Notes in Computational Science and Engineering; Vol. 139).

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

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Romijn LB, .ten Thije Boonkkamp JHM , IJzerman WL. A Monge-Ampère Least-Squares Solver for the Design of a Freeform Lens. In Vermolen FJ, Vuik C, redacteurs, Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. Cham: Springer. 2021. blz. 833-840. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-030-55874-1_82

A Monge-Ampère Least-Squares Solver for the Design of a Freeform Lens

Samenvatting

Publicatie series

Congres

Bibliografische nota

Financiering

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