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Proceedings Paper

A Different Approach to Lighting and Imaging: Formulas for Flux Density, Exact Lens and Mirror Equations and Caustic Surfaces in Terms of the Differential Geometry of Surfaces
Author(s): Donald G. Burkhard; David L. Shealy
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Paper Abstract

A formula is derived for the flux density associated with each ray traced through an optical system. The formula involves the ratio of the products of the principal curvatures of the wave front as it approaches and leaves each refracting surface. As input to the flux equation, a new and simplified derivation of the general lens equations is given. The general lens equations yield the normal curvatures and torsion of normal curves in the refracted wave front at each surface; these in turn, are related to the corresponding quantities for the incident wave front and the refracting surface. As an application, the flux equation and the generalized lens equations are specialized to meridional rays. The flux density and the caustic surfaces, that is, the loci of wave front principal curvatures, are then computed for a singlet lens. In a second application the flux density for skew rays is calculated over a receiver plane perpendicular to the symmetry axis when light from an off axis point source is reflected from a paraboloid.

Paper Details

Date Published: 23 February 1987
PDF: 25 pages
Proc. SPIE 0692, Materials and Optics for Solar Energy Conversion and Advanced Lightning Technology, (23 February 1987); doi: 10.1117/12.936713
Show Author Affiliations
Donald G. Burkhard, University of Georgia (United States)
David L. Shealy, University of Alabama at Birmingham (United States)

Published in SPIE Proceedings Vol. 0692:
Materials and Optics for Solar Energy Conversion and Advanced Lightning Technology
Sandor Holly; Carl M. Lampert, Editor(s)

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