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.
|Title of host publication||Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference|
|Editors||Fred J. Vermolen, Cornelis Vuik|
|Place of Publication||Cham|
|Number of pages||8|
|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 Sep 2019 → 4 Oct 2019
|Name||Lecture Notes in Computational Science and Engineering|
|Conference||European Conference on Numerical Mathematics and Advanced Applications|
|Abbreviated title||ENUMATH 2019|
|City||Egmond aan Zee|
|Period||30/09/19 → 4/10/19|
Bibliographical notePublisher Copyright:
© 2021, Springer Nature Switzerland AG.