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

Donald G. Burkhard; David L. Shealy

doi:10.1117/12.936713

23 February 1987 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

Donald G. Burkhard, David L. Shealy

Author Affiliations +

Proceedings Volume 0692, Materials and Optics for Solar Energy Conversion and Advanced Lightning Technology; (1987) https://doi.org/10.1117/12.936713
Event: 30th Annual Technical Symposium, 1986, San Diego, United States

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.

Citation Download Citation

Donald G. Burkhard and David L. Shealy "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", Proc. SPIE 0692, Materials and Optics for Solar Energy Conversion and Advanced Lightning Technology, (23 February 1987); https://doi.org/10.1117/12.936713

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