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For sources with a pronounced extension and ray divergence, e.g. an LED with a small source-freeform-distance, the image points are blurred and the blurred patterns might be different between different points. Besides, due to Fresnel losses and vignetting, the relationship between light intensity of image points and area of freeform surface elements becomes complicated. These individual light distributions of each freeform element are taken into account in a mapping algorithm. To this end the method of steepest decent procedures are used to adapt the mapping goal. A structured target pattern for a optics system with an ideal source is computed applying corresponding linear optimization matrices. Special weighting factor and smoothing factor are included in the procedures to achieve certain edge conditions and to ensure the manufacturability of the freefrom surface. The corresponding linear optimization matrices, which are the lighting distribution patterns of each of the freeform surface elements, are gained by conventional raytracing with a realistic source. Nontrivial source geometries, like LED-irregularities due to bonding or source fine structures, and a complex ray divergence behavior can be easily considered. Additionally, Fresnel losses, vignetting and even stray light are taken into account. After optimization iterations, with a realistic source, the initial mapping goal can be achieved by the optics system providing a structured target pattern with an ideal source.
The algorithm is applied to several design examples. A few simple tasks are presented to discussed the ability and limitation of the this mothed. It is also presented that a homogeneous LED-illumination system design, in where, with a strongly tilted incident direction, a homogeneous distribution is achieved with a rather compact optics system and short working distance applying a relatively large LED source. It is shown that the lighting distribution patterns from the freeform surface elements can be significantly different from the others. The generation of a structured target pattern, applying weighting factor and smoothing factor, are discussed. Finally, freeform designs for much more complex sources like clusters of LED-sources are presented.
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