A Monge–Ampère problem with non-quadratic cost function to compute freeform lens surfaces

N.K. Yadav (Corresponding author), J.H.M. ten Thije Boonkkamp, W.L. IJzerman

Research output: Contribution to journalArticleAcademicpeer-review

11 Citations (Scopus)
125 Downloads (Pure)

Abstract

In this article, we present a least-squares method to compute freeform surfaces of a lens with parallel incoming and outgoing light rays, which is a transport problem corresponding to a non-quadratic cost function. The lens can transfer a given emittance of the source into a desired illuminance at the target. The freeform lens design problem can be formulated as a Monge–Ampère type differential equation with transport boundary condition, expressing conservation of energy combined with the law of refraction. Our least-squares algorithm is capable to handle a non-quadratic cost function, and provides two solutions corresponding to either convex or concave lens surfaces.

Original languageEnglish
Pages (from-to)475-499
Number of pages25
JournalJournal of Scientific Computing
Volume80
Issue number1
Early online date27 Mar 2019
DOIs
Publication statusPublished - 15 Jul 2019

Keywords

  • Freeform lens surfaces
  • Inverse problem
  • Least-squares method
  • Monge–Ampère equation
  • Non-quadratic cost function
  • Optical design
  • Transport boundary conditions

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