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Mathematical Aspects of Design of Beam Shaping Surfaces in Geometrical Optics

In: Trends in Nonlinear Analysis

Author

Listed:
  • Vladimir Oliker

    (Emory University, Department of Mathematics and Computer Science, Mathematics and Sciences Center)

Abstract

Numerous optical and electromagnetic applications require synthesis of reflecting and refracting surfaces capable of reshaping the energy radiation intensity of a given source into a prescribed output irradiance distribution. Determination of such surfaces requires investigation of nonlinear, second order partial differential equations of Monge-Ampère type and development of computational algorithms for constructing their numerical solutions. These equations are very far from being standard and it is quite remarkable that geometric ideas not only provide natural means for their analysis but also means for computing solutions numerically. In this paper we survey some of these problems and describe the current progress in their study.

Suggested Citation

  • Vladimir Oliker, 2003. "Mathematical Aspects of Design of Beam Shaping Surfaces in Geometrical Optics," Springer Books, in: Markus Kirkilionis & Susanne Krömker & Rolf Rannacher & Friedrich Tomi (ed.), Trends in Nonlinear Analysis, chapter 4, pages 193-224, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-05281-5_4
    DOI: 10.1007/978-3-662-05281-5_4
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