On the design of reflectors that produce a cut-off line with a given anisotropic source of light

G. Kloos

doi:10.1117/12.679038

12 September 2006 On the design of reflectors that produce a cut-off line with a given anisotropic source of light

G. Kloos

Proceedings Volume 6338, Nonimaging Optics and Efficient Illumination Systems III; 63380B (2006) https://doi.org/10.1117/12.679038
Event: SPIE Optics + Photonics, 2006, San Diego, California, United States

Abstract

The problem of generating a cut-off line with a carefully calculated reflector contour has been treated in detail by Spencer et al. for the case of a cylindrical source of light mounted perpendicular to the optic axis. Because this geometry does not properly represent the geometry in which standard light sources are used in the illumination systems which we study, the attempt was made to extend this theory to anisotropic light sources. This case of lower symmetry is closer to the geometry of light sources encountered in headlamp design. Spencer et al. were able to obtain an implicit algebraic equation for the problem of high symmetry that they analyzed. After adopting their method to the problem under investigation, the method of analysis used was different insofar as an algebraic equation was not obtained and the corresponding ordinary differential equation and the corresponding initial-value problem were solved instead and the solutions are visualized with the aid of a computer-algebra system. In this context, the concept of a so-called polar line or surface proved helpful. This describes a set of points that connect the tangent lines that link a given point of the reflector contour to a given extended lightsource of low symmetry. The extension of the lightsource is assumed to be elliptical in the plane that contains the optic axis and the plane perpendicular to the cut-off line. The analysis extended to the anisotropic case gave some insight into the underlying scaling laws and geometrical constraints.

Citation Download Citation

G. Kloos "On the design of reflectors that produce a cut-off line with a given anisotropic source of light", Proc. SPIE 6338, Nonimaging Optics and Efficient Illumination Systems III, 63380B (12 September 2006); https://doi.org/10.1117/12.679038

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KEYWORDS

Reflectors

Light sources

Light

Ordinary differential equations

Differential equations

Mirrors

Reflector design

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