https://doi.org/10.1051/epjconf/202226602003
Design of optical surfaces conform the hyperbolic Monge-Ampère equation
1 CASA, Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
2 Signify Research, High Tech Campus 7, 5656 AE Eindhoven, The Netherlands
* e-mail: m.w.m.c.bertens@tue.nl
Published online: 13 October 2022
We present a method for designing freeform optical surfaces for illumination optics. By the laws of reflection, refraction and conservation of energy, a fully nonlinear PDE, the Monge-Ampere equation, is derived for the optical surface. By the edge ray principle a transport boundary condition is obtained. We solve the hyperbolic variant of the PDE using a least-squares method, resulting in optical saddle surfaces for a parallel source and far-field target.
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