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Study of reflectors for illumination via conformal maps

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Abstract

We present an approach for the study and design of reflectors with rotational or translational symmetry that redirect light from a point source into any desired radiant intensity distribution. This method is based on a simple conformal map that transforms the reflector’s shape into a curve that describes light’s direction after reflection. Both segmented reflectors and continuous reflectors are discussed, illustrating how certain reflector characteristics become apparent under this transformation. This method can also be used to study extended sources via translations.

© 2019 Optical Society of America

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Supplementary Material (3)

NameDescription
Visualization 1       Design of a piecewise parabolic reflector from its light curve. Same source range, but three different geometries: convergent, divergent, mixed. (Left) Light curve consists of simple straight-line segments.
Visualization 2       (a) Circular reflector, in solid black line, used as a collimator at different positions away from the ideal paraxial collimating location. It is compared with a parabola in dashed line. Rays are shown in light blue.
Visualization 3       (Left) CPC (in solid, black) and rays (dashed, grey lines) corresponding to different source points along the extended source/colector. (Right) Light curves for the corresponding points.

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