A Least-Squares Method for a Monge-Ampère Equation with Non-quadratic Cost Function Applied to Optical Design

  • N. K. Yadav
  • J. H. M. ten Thije Boonkkamp
  • W. L. IJzerman
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)


Freeform optical surfaces can transfer a given light distribution of the source into a desired distribution at the target. Freeform optical design problems can be formulated as a Monge-Ampère type differential equation with transport boundary condition, using properties of geometrical optics, conservation of energy, and the theory of optimal mass transport. We present a least-squares method to compute freeform lens surfaces corresponding to a non-quadratic cost function. The numerical algorithm is capable to compute both convex and concave surfaces.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • N. K. Yadav
    • 1
  • J. H. M. ten Thije Boonkkamp
    • 1
  • W. L. IJzerman
    • 1
    • 2
  1. 1.Department of Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Philips LightingPhilips ResearchEindhovenThe Netherlands

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