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

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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-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.

Original language	English
Title of host publication	Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference
Editors	Fred J. Vermolen, Cornelis Vuik
Place of Publication	Cham
Publisher	Springer
Pages	833-840
Number of pages	8
ISBN (Electronic)	978-3-030-55874-1
ISBN (Print)	9783030558734
DOIs	https://doi.org/10.1007/978-3-030-55874-1_82
Publication status	Published - 3 May 2021
Event	European Conference on Numerical Mathematics and Advanced Applications: ENUMATH 2019 - Hotel Zuiderduin, Egmond aan Zee, Netherlands Duration: 30 Sept 2019 → 4 Oct 2019 https://www.enumath2019.eu/

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	139
ISSN (Print)	1439-7358
ISSN (Electronic)	2197-7100

Conference

Conference	European Conference on Numerical Mathematics and Advanced Applications
Abbreviated title	ENUMATH 2019
Country/Territory	Netherlands
City	Egmond aan Zee
Period	30/09/19 → 4/10/19
Internet address	https://www.enumath2019.eu/

Bibliographical note

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.

Funding

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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10.1007/978-3-030-55874-1_82Licence: Unspecified

Cite this

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 (Eds.), Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference (pp. 833-840). (Lecture Notes in Computational Science and Engineering; Vol. 139). Springer. https://doi.org/10.1007/978-3-030-55874-1_82

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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 (eds), Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. Lecture Notes in Computational Science and Engineering, vol. 139, Springer, Cham, pp. 833-840, European Conference on Numerical Mathematics and Advanced Applications, Egmond aan Zee, Netherlands, 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. ed. / Fred J. Vermolen; Cornelis Vuik. Cham: Springer, 2021. p. 833-840 (Lecture Notes in Computational Science and Engineering; Vol. 139).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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

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