ORIGINAL RESEARCH article

Front. Phys.

Sec. Optics and Photonics

Volume 13 - 2025 | doi: 10.3389/fphy.2025.1518660

This article is part of the Research TopicFreeform Optics: From Theory to ApplicationsView all 5 articles

Inverse methods for freeform optical design

Provisionally accepted
Jan  Ten Thije BoonkkampJan Ten Thije Boonkkamp1*K  MitraK Mitra1M  AnthonissenM Anthonissen1L  KuschL Kusch1P  BraamP Braam1W  IJzermanW IJzerman2
  • 1Eindhoven University of Technology, Eindhoven, Netherlands
  • 2Signify Research, Eindhoven, Netherlands

The final, formatted version of the article will be published soon.

We present a systematic derivation of three mathematical models of increasing complexity for optical design, based on Hamilton's characteristic functions and conservation of luminous flux, and briefly explain the connection with the mathematical theory of optimal transport. We outline several iterative least-squares solvers for our models and demonstrate their performance for a few challenging problems.

Keywords: geometrical optics, Hamilton's characteristic functions, Optimal transport, optical map, conservation of luminous flux, inverse methods, least-squares methods

Received: 28 Oct 2024; Accepted: 24 Jan 2025.

Copyright: © 2025 Ten Thije Boonkkamp, Mitra, Anthonissen, Kusch, Braam and IJzerman. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Jan Ten Thije Boonkkamp, Eindhoven University of Technology, Eindhoven, Netherlands

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