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 (Corresponderende auteur)
, Lotte B. Romijn
, Wilbert L. IJzerman

Computational Illumination Optics

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

30 Downloads (Pure)

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
Subtitel	European Conference, Egmond aan Zee, The Netherlands, September 30 - October 4
Redacteuren	Fred J. Vermolen, Cornelis Vuik
Plaats van productie	Cham
Uitgeverij	Springer
Pagina's	991-999
Aantal pagina's	9
ISBN van elektronische versie	978-3-030-55874-1
ISBN van geprinte versie	978-3-030-55873-4, 978-3-030-55876-5
DOI's	https://doi.org/10.1007/978-3-030-55874-1_98
Status	Gepubliceerd - 22 aug. 2020
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 (LNCSE)
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/

Toegang tot document

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

pdfDefinitieve gepubliceerde versie, 314 KBLicentie: TAVERNE

Andere bestanden en links

Link naar publicatie in Scopus

Citeer dit

ten Thije Boonkkamp, J. H. M., Romijn, L. B., & IJzerman, W. L. (2020). 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, Egmond aan Zee, The Netherlands, September 30 - October 4 (blz. 991-999). (Lecture Notes in Computational Science and Engineering (LNCSE); 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, Egmond aan Zee, The Netherlands, September 30 - October 4. redacteur / Fred J. Vermolen ; Cornelis Vuik. Cham : Springer, 2020. blz. 991-999 (Lecture Notes in Computational Science and Engineering (LNCSE)).

@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 = "2020",

month = aug,

day = "22",

doi = "10.1007/978-3-030-55874-1\_98",

language = "English",

isbn = "978-3-030-55873-4",

series = "Lecture Notes in Computational Science and Engineering (LNCSE)",

publisher = "Springer",

pages = "991--999",

editor = "Vermolen, \{Fred J.\} and Cornelis Vuik",

booktitle = "Numerical Mathematics and Advanced Applications : ENUMATH 2019",

address = "Germany",

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

url = "https://www.enumath2019.eu/",

}

ten Thije Boonkkamp, JHM, Romijn, LB & IJzerman, WL 2020, Generalized Monge–Ampère Equations for Freeform Optical System Design. in FJ Vermolen & C Vuik (reds.), Numerical Mathematics and Advanced Applications : ENUMATH 2019: European Conference, Egmond aan Zee, The Netherlands, September 30 - October 4. Lecture Notes in Computational Science and Engineering (LNCSE), vol. 139, Springer, Cham, 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. (Corresponderende auteur); Romijn, Lotte B.; IJzerman, Wilbert L.
Numerical Mathematics and Advanced Applications : ENUMATH 2019: European Conference, Egmond aan Zee, The Netherlands, September 30 - October 4. reds. / Fred J. Vermolen; Cornelis Vuik. Cham: Springer, 2020. blz. 991-999 (Lecture Notes in Computational Science and Engineering (LNCSE); Vol. 139).

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

TY - GEN

T1 - Generalized Monge–Ampère Equations for Freeform Optical System Design

AU - ten Thije Boonkkamp, Jan H.M.

AU - Romijn, Lotte B.

AU - IJzerman, Wilbert L.

PY - 2020/8/22

Y1 - 2020/8/22

N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/85106401558

U2 - 10.1007/978-3-030-55874-1_98

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

M3 - Conference contribution

AN - SCOPUS:85106401558

SN - 978-3-030-55873-4

SN - 978-3-030-55876-5

T3 - Lecture Notes in Computational Science and Engineering (LNCSE)

SP - 991

EP - 999

BT - Numerical Mathematics and Advanced Applications : ENUMATH 2019

A2 - Vermolen, Fred J.

A2 - Vuik, Cornelis

PB - Springer

CY - Cham

T2 - European Conference on Numerical Mathematics and Advanced Applications

Y2 - 30 September 2019 through 4 October 2019

ER -

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, Egmond aan Zee, The Netherlands, September 30 - October 4. Cham: Springer. 2020. blz. 991-999. (Lecture Notes in Computational Science and Engineering (LNCSE)). doi: 10.1007/978-3-030-55874-1_98

Generalized Monge–Ampère Equations for Freeform Optical System Design

Samenvatting

Publicatie series

Congres

Toegang tot document

Andere bestanden en links

Vingerafdruk

Citeer dit