Solving inverse illumination problems with Liouville's equation

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Abstract

We aim to solve inverse problems in illumination optics by means of optimal control theory. This is done by first formulating geometric optics in terms of Liouville’s equation, which governs the evolution of light distributions on phase space. Choosing a metric that measures how close one distribution is to another, the formal Lagrange method can be applied. We show that this approach has great potential by a simple numerical example of an ideal lens.
Original languageEnglish
Title of host publicationNumerical Mathematics and Advanced Applications ENUMATH 2017
EditorsFlorin Adrian Radu, Kundan Kumar, Inga Berre, Jan Martin Nordbotten, Iuliu Sorin Pop
Place of PublicationCham
PublisherSpringer
Pages311-319
Number of pages9
ISBN (Electronic)978-3-319-96415-7
ISBN (Print)978-3-319-96414-0
DOIs
Publication statusPublished - 2019
EventEuropean Conference on Numerical Mathematics and Advanced Applications 2017 -
Duration: 25 Sep 201729 Sep 2017

Publication series

NameLecture Notes in Computational Science and Engineering
Volume126
ISSN (Print)1439-7358

Conference

ConferenceEuropean Conference on Numerical Mathematics and Advanced Applications 2017
Abbreviated titleENUMATH 2017
Period25/09/1729/09/17

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    van Lith, B. S., ten Thije Boonkkamp, J. H. M., & IJzerman, W. L. (2019). Solving inverse illumination problems with Liouville's equation. In F. A. Radu, K. Kumar, I. Berre, J. M. Nordbotten, & I. S. Pop (Eds.), Numerical Mathematics and Advanced Applications ENUMATH 2017 (pp. 311-319). (Lecture Notes in Computational Science and Engineering; Vol. 126). Springer. https://doi.org/10.1007/978-3-319-96415-7_27