Solving Inverse Illumination Problems with Liouville’s Equation

  • Bart S. van Lith
  • Jan H. M. ten Thije Boonkamp
  • Wilbert L. IJzerman
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)


We aim to solve inverse problems in illumination optics by means of optimal control theory. This is done by first formulating geometric optics in terms of Liouville’s equation, which governs the evolution of light distributions on phase space. Choosing a metric that measures how close one distribution is to another, the formal Lagrange method can be applied. We show that this approach has great potential by a simple numerical example of an ideal lens.



B.S. van Lith wishes to thank J.H.M. ten Thije Boonkkamp for presenting the work in Norway in his stead.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Bart S. van Lith
    • 1
  • Jan H. M. ten Thije Boonkamp
    • 1
  • Wilbert L. IJzerman
    • 1
    • 2
  1. 1.Eindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Philips LightingHigh Tech Campus 7EindhovenThe Netherlands

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