Generalized Monge–Ampère Equations for Freeform Optical System Design

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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.

Original languageEnglish
Title of host publicationNumerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference
EditorsFred J. Vermolen, Cornelis Vuik
Number of pages9
ISBN (Print)9783030558734
Publication statusPublished - 2021
EventEuropean Conference on Numerical Mathematics and Advanced Applications: ENUMATH 2019 - Hotel Zuiderduin, Egmond aan Zee, Netherlands
Duration: 30 Sep 20194 Oct 2019

Publication series

NameLecture Notes in Computational Science and Engineering
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100


ConferenceEuropean Conference on Numerical Mathematics and Advanced Applications
Abbreviated titleENUMATH 2019
CityEgmond aan Zee
Internet address

Bibliographical note

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.


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