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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 Topic Freeform Optics: From Theory to Applications View all 5 articles

Inverse methods for freeform optical design

Provisionally accepted
Jan Ten Thije Boonkkamp Jan Ten Thije Boonkkamp 1*K Mitra K Mitra 1M Anthonissen M Anthonissen 1L Kusch L Kusch 1P Braam P Braam 1W IJzerman W IJzerman 2
  • 1 Eindhoven University of Technology, Eindhoven, Netherlands
  • 2 Signify 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

    Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.