Solving inverse illumination problems with Liouville's equation

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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.
Originele taal-2Engels
TitelNumerical Mathematics and Advanced Applications ENUMATH 2017
RedacteurenFlorin Adrian Radu, Kundan Kumar, Inga Berre, Jan Martin Nordbotten, Iuliu Sorin Pop
Plaats van productieCham
UitgeverijSpringer
Pagina's311-319
Aantal pagina's9
ISBN van elektronische versie978-3-319-96415-7
ISBN van geprinte versie978-3-319-96414-0
DOI's
StatusGepubliceerd - 2019
EvenementEuropean Conference on Numerical Mathematics and Advanced Applications 2017 -
Duur: 25 sep 201729 sep 2017

Publicatie series

NaamLecture Notes in Computational Science and Engineering
Volume126
ISSN van geprinte versie1439-7358

Congres

CongresEuropean Conference on Numerical Mathematics and Advanced Applications 2017
Verkorte titelENUMATH 2017
Periode25/09/1729/09/17

Vingerafdruk

Liouville equations
illumination
optics
control theory
optimal control
lenses

Citeer dit

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 (editors), Numerical Mathematics and Advanced Applications ENUMATH 2017 (blz. 311-319). (Lecture Notes in Computational Science and Engineering; Vol. 126). Cham: Springer. https://doi.org/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. redacteur / Florin Adrian Radu ; Kundan Kumar ; Inga Berre ; Jan Martin Nordbotten ; Iuliu Sorin Pop. Cham : Springer, 2019. blz. 311-319 (Lecture Notes in Computational Science and Engineering).
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title = "Solving inverse illumination problems with Liouville's equation",
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.",
author = "{van Lith}, B.S. and {ten Thije Boonkkamp}, J.H.M. and W.L. IJzerman",
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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 (redactie), Numerical Mathematics and Advanced Applications ENUMATH 2017. Lecture Notes in Computational Science and Engineering, vol. 126, Springer, Cham, blz. 311-319, European Conference on Numerical Mathematics and Advanced Applications 2017, 25/09/17. https://doi.org/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. redactie / Florin Adrian Radu; Kundan Kumar; Inga Berre; Jan Martin Nordbotten; Iuliu Sorin Pop. Cham : Springer, 2019. blz. 311-319 (Lecture Notes in Computational Science and Engineering; Vol. 126).

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

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AB - 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.

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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, redacteurs, Numerical Mathematics and Advanced Applications ENUMATH 2017. Cham: Springer. 2019. blz. 311-319. (Lecture Notes in Computational Science and Engineering). https://doi.org/10.1007/978-3-319-96415-7_27