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

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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.

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's301-309
Aantal pagina's9
ISBN van elektronische versie978-3-319-96415-7
ISBN van geprinte versie978-3-319-96414-0
DOI's
StatusGepubliceerd - 1 jan 2019
EvenementEuropean Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017 - Voss, Noorwegen
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, ENUMATH 2017
LandNoorwegen
StadVoss
Periode25/09/1729/09/17

Vingerafdruk

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

Citeer dit

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 (editors), Numerical Mathematics and Advanced Applications ENUMATH 2017 (blz. 301-309). (Lecture Notes in Computational Science and Engineering; Vol. 126). Cham: Springer. https://doi.org/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. redacteur / Florin Adrian Radu ; Kundan Kumar ; Inga Berre ; Jan Martin Nordbotten ; Iuliu Sorin Pop. Cham : Springer, 2019. blz. 301-309 (Lecture Notes in Computational Science and Engineering).
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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-Amp{\`e}re 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.",
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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 (redactie), Numerical Mathematics and Advanced Applications ENUMATH 2017. Lecture Notes in Computational Science and Engineering, vol. 126, Springer, Cham, blz. 301-309, European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017, Voss, Noorwegen, 25/09/17. https://doi.org/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. redactie / Florin Adrian Radu; Kundan Kumar; Inga Berre; Jan Martin Nordbotten; Iuliu Sorin Pop. Cham : Springer, 2019. blz. 301-309 (Lecture Notes in Computational Science and Engineering; Vol. 126).

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer 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, redacteurs, Numerical Mathematics and Advanced Applications ENUMATH 2017. Cham: Springer. 2019. blz. 301-309. (Lecture Notes in Computational Science and Engineering). https://doi.org/10.1007/978-3-319-96415-7_26