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Preprint-No.: <   427   >   Published in: June 2015   PDF-File: IGPM427.pdf
Title:Designing Illumination Lenses and Mirrors by the Numerical Solution of Monge-Ampère Equations
Authors:Kolja Brix, Yasemin Hafizogullari, Andreas Platen
Abstract:
We consider the inverse refractor and the inverse reflector problem. The task is to design a free-form lens or a free-form mirror that, when illuminated by a point light source, produces a given illumination pattern on a target. Both problems can be modeled by strongly nonlinear second-order partial differential equations of Monge-Ampère type. In [Math. Models Methods Appl. Sci. 25 (2015), pp. 803–837, DOI: 10.1142/S0218202515500190] the authors have proposed a B-spline collocation method which has been applied to the inverse reflector problem. Now this approach is extended to the inverse refractor problem. We explain in depth the collocation method and how to handle boundary conditions and constraints. The paper concludes with numerical results of refracting and reflecting optical surfaces and their verification via ray tracing.
Keywords:inverse refractor problem, inverse reflector problem, elliptic Monge-Ampère equation, B-spline collocation method, Picard-type iteration
DOI: 10.1364/JOSAA.32.002227
Publication:Journal of the Optical Society of America A
Volume 32, Issue 11, pp. 2227-2236, 2015
Peer reviewed article

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