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

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

JOURNAL=Frontiers in Physics

VOLUME=Volume 13 - 2025

YEAR=2025

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2025.1518660

DOI=10.3389/fphy.2025.1518660

ISSN=2296-424X

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.