A least-squares method for a Monge-Ampère equation with non-quadratic cost function applied to optical design

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

Abstract

Freeform optical surfaces can transfer a given light distribution of the source into a desired distribution at the target. Freeform optical design problems can be formulated as a Monge-Ampère type differential equation with transport boundary condition, using properties of geometrical optics, conservation of energy, and the theory of optimal mass transport. We present a least-squares method to compute freeform lens surfaces corresponding to a non-quadratic cost function. The numerical algorithm is capable to compute both convex and concave surfaces.

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
Pages301-309
Number of pages9
ISBN (Electronic)978-3-319-96415-7
ISBN (Print)978-3-319-96414-0
DOIs
StatePublished - 1 Jan 2019
EventEuropean Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017 - Voss, Norway
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, ENUMATH 2017
CountryNorway
CityVoss
Period25/09/1729/09/17

Fingerprint

Monge-Ampère Equation
Optical design
Optical Design
Least Square Method
Cost functions
Cost Function
Optimal Transport
Geometrical optics
Geometrical Optics
Mass Transport
Numerical Algorithms
Lens
Conservation
Lenses
Differential equations
Mass transfer
Boundary conditions
Differential equation
Target
Energy

Cite this

Yadav, N. K., ten Thije Boonkkamp, J. H. M., & IJzerman, W. L. (2019). A least-squares method for a Monge-Ampère equation with non-quadratic cost function applied to optical design. In F. A. Radu, K. Kumar, I. Berre, J. M. Nordbotten, & I. S. Pop (Eds.), Numerical Mathematics and Advanced Applications ENUMATH 2017 (pp. 301-309). (Lecture Notes in Computational Science and Engineering; Vol. 126). Cham: Springer. DOI: 10.1007/978-3-319-96415-7_26
Yadav, N.K. ; ten Thije Boonkkamp, J.H.M. ; IJzerman, W.L./ A least-squares method for a Monge-Ampère equation with non-quadratic cost function applied to optical design. Numerical Mathematics and Advanced Applications ENUMATH 2017. editor / Florin Adrian Radu ; Kundan Kumar ; Inga Berre ; Jan Martin Nordbotten ; Iuliu Sorin Pop. Cham : Springer, 2019. pp. 301-309 (Lecture Notes in Computational Science and Engineering).
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Yadav, NK, ten Thije Boonkkamp, JHM & IJzerman, WL 2019, A least-squares method for a Monge-Ampère equation with non-quadratic cost function applied to optical design. 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. 301-309, European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017, Voss, Norway, 25/09/17. DOI: 10.1007/978-3-319-96415-7_26

A least-squares method for a Monge-Ampère equation with non-quadratic cost function applied to optical design. / Yadav, N.K.; ten Thije Boonkkamp, J.H.M.; IJzerman, W.L.

Numerical Mathematics and Advanced Applications ENUMATH 2017. ed. / Florin Adrian Radu; Kundan Kumar; Inga Berre; Jan Martin Nordbotten; Iuliu Sorin Pop. Cham : Springer, 2019. p. 301-309 (Lecture Notes in Computational Science and Engineering; Vol. 126).

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

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Yadav NK, ten Thije Boonkkamp JHM, IJzerman WL. A least-squares method for a Monge-Ampère equation with non-quadratic cost function applied to optical design. In Radu FA, Kumar K, Berre I, Nordbotten JM, Pop IS, editors, Numerical Mathematics and Advanced Applications ENUMATH 2017. Cham: Springer. 2019. p. 301-309. (Lecture Notes in Computational Science and Engineering). Available from, DOI: 10.1007/978-3-319-96415-7_26