Redistribution of light from a given source in order to create a prescribed intensity pattern on a given set in 3D space is a task arising in numerous applications. Designing optical systems with capabilities to perform such tasks reliably in a wide variety of applications is the overall goal of much of research in optics. In many important practical cases the a priori requirement of radial symmetry should not be imposed neither on the input/output radiances nor on the geometry of the input/output beams. Such cases include the “laser beam shaping problem” requiring transformation of a Gaussian beam from a laser into a beam with “flat top” intensity profile and “picture” generation or creation of illumination patterns on flat, tilted and curved surfaces with non-uniform input/output distributions. In all such cases utilization of freeform optical surfaces is a must. The “Supporting Quadric Method (SQM) was developed to solve problems of this kind. It provides physically motivated and mathematically rigorous theoretical and computational tools for dealing with such design problems.
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