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Proceedings Paper

Geometric and variational methods in optical design of reflecting surfaces with prescribed irradiance properties
Author(s): Vladimir Oliker
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Paper Abstract

Numerous optical and electromagnetic applications require numerical design of reflecting surfaces in 3D with capabilities to redirect the input energy flow and reshape the energy radiation intensity of a source into a prescribed output irradiance distribution over a specified target surface. In the geometrical optics approximation, a systematic application of the ray tracing equations and energy conservation law reduces the problem, in many cases, to finding numerical solutions to nonlinear, second order partial differential equations. If the severe limitation of rotational symmetry is not assumed then the resulting equations are very far from being standard and require significant efforts for their theoretical investigation and reliable numerical solution. In recent years a quite general approach combining geometric techniques with methods from calculus of variations has been developed and applied to a rigorous and unified investigation of several classes of such equations. Moreover, this approach allows implementations in provably convergent numerical algorithms. In this paper I outline this approach in the problem of designing a reflecting surface capable of redirecting the energy flow from a point source so that the reflected rays have directions specified in advance as a subset on the far-sphere and the output irradiance density is also pre-specified in advance as a function of the reflected direction. A numerical example illustrating the solution is also presented.

Paper Details

Date Published: 2 September 2005
PDF: 12 pages
Proc. SPIE 5942, Nonimaging Optics and Efficient Illumination Systems II, 594207 (2 September 2005); doi: 10.1117/12.615973
Show Author Affiliations
Vladimir Oliker, Emory Univ. (United States)

Published in SPIE Proceedings Vol. 5942:
Nonimaging Optics and Efficient Illumination Systems II
Roland Winston; R. John Koshel, Editor(s)

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