1 September 1996 General near-zone light source model and its application to computer-automated reflector design
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The goal of this work is to develop a general light source model that is physically accurate, intuitively descriptive, computationally convenient, and applicable to real sources. It solves two major problems in illumination optics: near zone general extended light source characterization for accurate image rendering and ray tracing, and computerautomated reflector design using the resulting near-zone model. The main approach is to combine measurements with Fourier analysis, using judiciously chosen coordinate systems and orthogonal fitting functions. This has several advantages over standard ray tracing: it provides for natural data compression and interpolation; it bypasses the problem of computing the radiance distribution of a real source by using actual pinhole CCD camera measurements; and it eliminates the computationally intensive ray-filament intersection problem by transforming the source into an equivalent nonuniform spherical radiator. A method for treating the occlusion of rays by the extended filament, with only spherical intersection calculations, is also discussed. The application of the method is illustrated by the problem of designing a smooth specular reflector to cast a desired intensity distribution on a distant screen for a given source. The problem becomes a straightforward numerical optimization of the perturbations to a base reflector shape. An algorithm to provide a first guess for the perturbations based on the shape of the image perimeter is also described.
Mel Siegel, Robert D. Stock, "General near-zone light source model and its application to computer-automated reflector design," Optical Engineering 35(9), (1 September 1996). https://doi.org/10.1117/1.600832

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