Generalized Monge-Ampère equations for illumination freeform design

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In this contribution we introduce the (generalized) Monge-Ampere equation, defining the shape/location of an optical surface. In particular, we consider a lens with one freeform surface and a freeform reflector. For the lens we consider a source emitting a parallel bundle of light and for the reflector we assume a point source emitting light radially outward. In both cases the target distribution is a far-field intensity. As numerical solution method we propose a least-squares method, which is a two-stage method. In the first stage the optical map is computed, and subsequently in the second stage, the shape of the optical surface. We demonstrate that our method can handle complicated source and target distributions.

Original languageEnglish
Title of host publicationOptical Design and Testing IX
EditorsYongtian Wang, Pablo Benitez, Osamu Matoba
Number of pages18
ISBN (Electronic)9781510630871
Publication statusPublished - 19 Nov 2019
EventOptical Design and Testing IX 2019 - Hangzhou, China
Duration: 21 Oct 201922 Oct 2019

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X


ConferenceOptical Design and Testing IX 2019


  • Energy conservation
  • Freeform optics
  • Generalized Monge-Ampère equation
  • Leastsquares method
  • Optical map
  • generalized Monge-Ampere equation
  • energy conservation
  • least-squares method
  • optical map


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