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

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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 languageEnglish
Title of host publicationNumerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference
EditorsFred J. Vermolen, Cornelis Vuik
Place of PublicationCham
Number of pages8
ISBN (Electronic)978-3-030-55874-1
ISBN (Print)9783030558734
Publication statusPublished - 3 May 2021
EventEuropean Conference on Numerical Mathematics and Advanced Applications: ENUMATH 2019 - Hotel Zuiderduin, Egmond aan Zee, Netherlands
Duration: 30 Sept 20194 Oct 2019

Publication series

NameLecture Notes in Computational Science and Engineering
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100


ConferenceEuropean Conference on Numerical Mathematics and Advanced Applications
Abbreviated titleENUMATH 2019
CityEgmond aan Zee
Internet address

Bibliographical note

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.


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