Solving inverse illumination problems with Liouville's equation

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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.
LanguageEnglish
Title of host publicationNumerical Mathematics and Advanced Applications ENUMATH 2017
EditorsF.A. Radu, K. Kumar, I. Berre, J.M. Nordbotten, I.S. 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
StatePublished - 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
PublisherSpringer
Volume126

Conference

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

Fingerprint

Liouville equations
illumination
optics
control theory
optimal control
lenses

Cite this

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). Cham: Springer. DOI: 10.1007/978-3-319-96415-7_27
van Lith, B.S. ; ten Thije Boonkkamp, J.H.M. ; IJzerman, W.L./ Solving inverse illumination problems with Liouville's equation. Numerical Mathematics and Advanced Applications ENUMATH 2017. editor / F.A. Radu ; K. Kumar ; I. Berre ; J.M. Nordbotten ; I.S. Pop. Cham : Springer, 2019. pp. 311-319 (Lecture Notes in Computational Science and Engineering).
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van Lith, BS, ten Thije Boonkkamp, JHM & IJzerman, WL 2019, Solving inverse illumination problems with Liouville's equation. in FA Radu, K Kumar, I Berre, JM Nordbotten & IS Pop (eds), Numerical Mathematics and Advanced Applications ENUMATH 2017. Lecture Notes in Computational Science and Engineering, vol. 126, Springer, Cham, pp. 311-319, European Conference on Numerical Mathematics and Advanced Applications 2017, 25/09/17. DOI: 10.1007/978-3-319-96415-7_27

Solving inverse illumination problems with Liouville's equation. / van Lith, B.S.; ten Thije Boonkkamp, J.H.M.; IJzerman, W.L.

Numerical Mathematics and Advanced Applications ENUMATH 2017. ed. / F.A. Radu; K. Kumar; I. Berre; J.M. Nordbotten; I.S. Pop. Cham : Springer, 2019. p. 311-319 (Lecture Notes in Computational Science and Engineering; Vol. 126).

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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van Lith BS, ten Thije Boonkkamp JHM, IJzerman WL. Solving inverse illumination problems with Liouville's equation. In Radu FA, Kumar K, Berre I, Nordbotten JM, Pop IS, editors, Numerical Mathematics and Advanced Applications ENUMATH 2017. Cham: Springer. 2019. p. 311-319. (Lecture Notes in Computational Science and Engineering). Available from, DOI: 10.1007/978-3-319-96415-7_27