Inverse freeform design in non-imaging optics: Hamilton’s theory of geometrical optics, optimal transport, and least-squares solvers

J.H.M. ten Thije Boonkkamp; K. Mitra; M.J.H. Anthonissen; L. Kusch; P.A. Braam; W.L. IJzerman

doi:10.3389/fphy.2025.1518660

Inverse freeform design in non-imaging optics: Hamilton’s theory of geometrical optics, optimal transport, and least-squares solvers

J.H.M. ten Thije Boonkkamp (Corresponding author), K. Mitra, M.J.H. Anthonissen, L. Kusch, P.A. Braam, W.L. IJzerman

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Abstract

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.

Original language	English
Article number	1518660
Number of pages	17
Journal	Frontiers in Physics
Volume	13
DOIs	https://doi.org/10.3389/fphy.2025.1518660
Publication status	Published - 2025

Bibliographical note

Publisher Copyright:
Copyright © 2025 Ten Thije Boonkkamp, Mitra, Anthonissen, Kusch, Braam and IJzerman.

Keywords

conservation of luminous flux
geometrical optics
Hamilton’s characteristic functions
inverse methods
least-squares methods
optical map
optimal transport

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10.3389/fphy.2025.1518660

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abstract = "We present a systematic derivation of three mathematical models of increasing complexity for optical design, based on Hamilton{\textquoteright}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.",

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AU - Mitra, K.

AU - Anthonissen, M.J.H.

AU - Kusch, L.

AU - Braam, P.A.

AU - IJzerman, W.L.

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KW - geometrical optics

KW - Hamilton’s characteristic functions

KW - inverse methods

KW - least-squares methods

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Inverse freeform design in non-imaging optics: Hamilton’s theory of geometrical optics, optimal transport, and least-squares solvers

Abstract

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Keywords

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