Freeform optical surfaces offer additional degrees of freedom for designing imaging systems without rotational symmetry. This allows for a reduction in the number of optical elements, leading to more compact and lightweight systems, while at the same time improving the image quality. This also enables new areas of application. Commonly used representations for freeform surfaces are x-y-polynomials, Zernike polynomials and NURBS. Radial basis functions (RBF) have been used for many years e.g. in artificial neural networks and functional approximation and can also be used to describe optical surfaces. In this contribution we investigate properties specific to RBF-based optical surfaces and compare the performance of RBF-based surfaces to other representations in selected optical imaging systems. Interesting aspects include the dependency on the number of RBF that are summed to form the surface, the locality structure and its effects on optimization.
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