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.
|Title of host publication||Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference|
|Editors||Fred J. Vermolen, Cornelis Vuik|
|Publisher||Springer Science and Business Media Deutschland GmbH|
|Number of pages||9|
|Publication status||Published - 2021|
|Event||European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019 - Egmond aan Zee, Netherlands|
Duration: 30 Sep 2019 → 4 Oct 2019
|Name||Lecture Notes in Computational Science and Engineering|
|Conference||European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019|
|City||Egmond aan Zee|
|Period||30/09/19 → 4/10/19|
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