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

N.K. Yadav; J.H.M. ten Thije Boonkkamp; W.L. IJzerman

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

N.K. Yadav, J.H.M. ten Thije Boonkkamp, W.L. IJzerman

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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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-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.

Original language	English
Title of host publication	Numerical Mathematics and Advanced Applications ENUMATH 2017
Editors	Florin Adrian Radu, Kundan Kumar, Inga Berre, Jan Martin Nordbotten, Iuliu Sorin Pop
Place of Publication	Cham
Publisher	Springer
Pages	301-309
Number of pages	9
ISBN (Electronic)	978-3-319-96415-7
ISBN (Print)	978-3-319-96414-0
DOIs	https://doi.org/10.1007/978-3-319-96415-7_26
Publication status	Published - 1 Jan 2019
Event	European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017 - Voss, Norway Duration: 25 Sep 2017 → 29 Sep 2017

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	126
ISSN (Print)	1439-7358

Conference

Conference	European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017
Country	Norway
City	Voss
Period	25/09/17 → 29/09/17

Access to Document

10.1007/978-3-319-96415-7_26

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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. 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. 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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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 (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. 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. 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 proceeding › Conference contribution › Academic › peer-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). https://doi.org/10.1007/978-3-319-96415-7_26