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

    4 Citations (Scopus)
    88 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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