Freeform surface estimation by the combination of numerical orthogonal polynomials and overlapping averaging method.

A combination method using numerical orthogonal polynomials and overlapping averaging is presented for freeform surface estimation. The whole effective aperture of freeform surface is decomposed into multiple overlapped subapertures. The corresponding local surface over each subaperture is reconstructed by numerical orthogonal polynomials suited for general shaped aperture. Then, the whole freeform surface is obtained by overlapping averaging approach from multiple local surfaces. The performance of the presented combination method is discussed and demonstrated by examples and further verified by an experiment. The results show that the combination method could reach nanometer accuracy. Meanwhile, the local deformations of freeform surface can be characterized finely. [ABSTRACT FROM AUTHOR]