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Mathematical Aspects of Design of Beam Shaping Surfaces in Geometrical Optics

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Trends in Nonlinear Analysis

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.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Mathematics and Sciences Center, Emory University, Suite W401, 400 Dowman Drive, Atlanta, Georgia, 30322, USA

    Vladimir Oliker

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  1. Vladimir Oliker
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Editors and Affiliations

  1. Mathematics Department and Center for Scientific Computing, University of Warwick, CV4 7AL, Coventry, UK

    Markus Kirkilionis

  2. Institute of Scientific Computing, University of Heidelberg, Im Neuheimer Feld 368, 69120, Heidelberg, Germany

    Susanne Krömker

  3. Institute of Applied Mathematics, University of Heidelberg, Im Neuheimer Feld 293, 69120, Heidelberg, Germany

    Rolf Rannacher

  4. Department of Mathematics, University of Heidelberg, Im Neuheimer Feld 288, 69120, Heidelberg, Germany

    Friedrich Tomi

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Oliker, V. (2003). Mathematical Aspects of Design of Beam Shaping Surfaces in Geometrical Optics. In: Kirkilionis, M., Krömker, S., Rannacher, R., Tomi, F. (eds) Trends in Nonlinear Analysis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05281-5_4

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  • DOI: https://doi.org/10.1007/978-3-662-05281-5_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-07916-0

  • Online ISBN: 978-3-662-05281-5

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