Generalized Monge–Ampère Equations for Freeform Optical System Design

Jan H.M. ten Thije Boonkkamp; Lotte B. Romijn; Wilbert L. IJzerman

doi:10.1007/978-3-030-55874-1_98

Generalized Monge–Ampère Equations for Freeform Optical System Design

Jan H.M. ten Thije Boonkkamp, Lotte B. Romijn, Wilbert L. IJzerman

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

Samenvatting

We present the derivation of the generalized Monge–Ampère equation for two optical systems, viz. a freeform lens with parallel incident and refracted light rays, which transforms a source emittance into a desired target illuminance, and a freeform reflector converting the intensity of a point source into a far-field distribution. The derivations are based on Hamilton’s characteristic functions. We outline a least-squares solution method and apply it to a test problem from laser beam shaping.

Originele taal-2	Engels
Titel	Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference
Redacteuren	Fred J. Vermolen, Cornelis Vuik
Uitgeverij	Springer
Pagina's	991-999
Aantal pagina's	9
Volume	139
ISBN van geprinte versie	9783030558734
DOI's	https://doi.org/10.1007/978-3-030-55874-1_98
Status	Gepubliceerd - 2021
Evenement	European Conference on Numerical Mathematics and Advanced Applications: ENUMATH 2019 - Hotel Zuiderduin, Egmond aan Zee, Nederland Duur: 30 sep. 2019 → 4 okt. 2019 https://www.enumath2019.eu/

Publicatie series

Naam	Lecture Notes in Computational Science and Engineering
Volume	139
ISSN van geprinte versie	1439-7358
ISSN van elektronische versie	2197-7100

Congres

Congres	European Conference on Numerical Mathematics and Advanced Applications
Verkorte titel	ENUMATH 2019
Land/Regio	Nederland
Stad	Egmond aan Zee
Periode	30/09/19 → 4/10/19
Internet adres	https://www.enumath2019.eu/

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10.1007/978-3-030-55874-1_98

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ten Thije Boonkkamp, J. H. M., Romijn, L. B., & IJzerman, W. L. (2021). Generalized Monge–Ampère Equations for Freeform Optical System Design. In F. J. Vermolen, & C. Vuik (editors), Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference (Vol. 139, blz. 991-999). (Lecture Notes in Computational Science and Engineering; Vol. 139). Springer. https://doi.org/10.1007/978-3-030-55874-1_98

ten Thije Boonkkamp, Jan H.M. ; Romijn, Lotte B. ; IJzerman, Wilbert L. / Generalized Monge–Ampère Equations for Freeform Optical System Design. Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. redacteur / Fred J. Vermolen ; Cornelis Vuik. Vol. 139 Springer, 2021. blz. 991-999 (Lecture Notes in Computational Science and Engineering).

@inproceedings{45931260894b49d0a0959385a6a02b34,

title = "Generalized Monge–Amp{\`e}re Equations for Freeform Optical System Design",

abstract = "We present the derivation of the generalized Monge–Amp{\`e}re equation for two optical systems, viz. a freeform lens with parallel incident and refracted light rays, which transforms a source emittance into a desired target illuminance, and a freeform reflector converting the intensity of a point source into a far-field distribution. The derivations are based on Hamilton{\textquoteright}s characteristic functions. We outline a least-squares solution method and apply it to a test problem from laser beam shaping.",

author = "{ten Thije Boonkkamp}, {Jan H.M.} and Romijn, {Lotte B.} and IJzerman, {Wilbert L.}",

year = "2021",

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booktitle = "Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference",

address = "Germany",

note = "European Conference on Numerical Mathematics and Advanced Applications : ENUMATH 2019, ENUMATH 2019 ; Conference date: 30-09-2019 Through 04-10-2019",

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ten Thije Boonkkamp, JHM, Romijn, LB & IJzerman, WL 2021, Generalized Monge–Ampère Equations for Freeform Optical System Design. in FJ Vermolen & C Vuik (uitgave), Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. vol. 139, Lecture Notes in Computational Science and Engineering, vol. 139, Springer, blz. 991-999, European Conference on Numerical Mathematics and Advanced Applications, Egmond aan Zee, Nederland, 30/09/19. https://doi.org/10.1007/978-3-030-55874-1_98

Generalized Monge–Ampère Equations for Freeform Optical System Design. / ten Thije Boonkkamp, Jan H.M.; Romijn, Lotte B.; IJzerman, Wilbert L.
Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. uitgave / Fred J. Vermolen; Cornelis Vuik. Vol. 139 Springer, 2021. blz. 991-999 (Lecture Notes in Computational Science and Engineering; Vol. 139).

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

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AB - We present the derivation of the generalized Monge–Ampère equation for two optical systems, viz. a freeform lens with parallel incident and refracted light rays, which transforms a source emittance into a desired target illuminance, and a freeform reflector converting the intensity of a point source into a far-field distribution. The derivations are based on Hamilton’s characteristic functions. We outline a least-squares solution method and apply it to a test problem from laser beam shaping.

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ten Thije Boonkkamp JHM, Romijn LB, IJzerman WL. Generalized Monge–Ampère Equations for Freeform Optical System Design. In Vermolen FJ, Vuik C, redacteurs, Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. Vol. 139. Springer. 2021. blz. 991-999. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-030-55874-1_98

Generalized Monge–Ampère Equations for Freeform Optical System Design

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