The explicit formulation of a Radial Basis Function (RBF) method, RBF7QR, to describe optical freeform surfaces is given. The method extends the use of RBFs for optical freeform surfaces to minimize the number of basis required to reach a level of accuracy. An F/1 axicon, as a convenient test case, and a freeform non-rotationally symmetric mirror were constructed by the method. The least number of RBF basis elements for freeform optical surface descriptions is determined based upon the different accuracy levels demanded by the non-imaging, precision, and lithography optics applications.
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