Mathematical Aspects of Design of Beam Shaping Surfaces in Geometrical Optics

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

Chapter 4 in Trends in Nonlinear Analysis, 2003, pp 193-224 from Springer

Abstract: 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.

Keywords: Weak Solution; Convex Body; Supporting Hyperplane; Order Partial Differential Equation; Asymptotic Cone (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-05281-5_4

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DOI: 10.1007/978-3-662-05281-5_4

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