A least-squares method for the design of two-reflector optical systems

Nitin Yadav, Lotte Romijn, Jan ten Thije Boonkkamp (Corresponding author), Wilbert IJzerman

Research output: Contribution to journalArticleAcademicpeer-review

11 Citations (Scopus)
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The purpose of this paper is to present a method for the design of two-reflector optical systems that transfer a given energy density of the source to a desired energy density at the target. It is known that the two-reflector design problem gives rise to a Monge-Amp`\{e}re equation with transport boundary condition. We solve this boundary value problem using a recently developed least-squares algorithm [1]. It is one of the few numerical algorithms capable to solve these type of problems efficiently. The least-squares algorithm can provide two solutions of the Monge-Amp`\{e}re problem, one is concave and the other one is convex. The reflectors are validated for several numerical examples by a ray-tracer based on Monte-Carlo simulation.
Original languageEnglish
Article number034001
Number of pages16
JournalJPhys Photonics
Issue number3
Publication statusPublished - 16 Jul 2019


  • least-squares method, Monge-Amp\`{e}re equation, inverse problem, transport boundary conditions, optical design, freeform optics, ray tracing
  • Inverse reflector problem
  • Least-squares method
  • Monge–Ampère equation
  • Freeform optics


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