Open AccessFitting freeform shapes with orthogonal bases
Author(s) -
G. W. Forbes
Publication year - 2013
Publication title -
optics express
Language(s) - Uncategorized
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.21.019061
Subject(s) - orthogonality , quadrature (astronomy) , simple (philosophy) , gaussian , orthogonal polynomials , gaussian quadrature , computer science , spatial filter , polynomial , spatial frequency , optics , algorithm , mathematics , geometry , mathematical analysis , physics , nyström method , philosophy , epistemology , quantum mechanics , integral equation
Orthogonality is exploited for fitting analytically-specified freeform shapes in terms of orthogonal polynomials. The end result is expressed in terms of FFTs coupled to a simple explicit form of Gaussian quadrature. Its efficiency opens the possibilities for proceeding to arbitrary numbers of polynomial terms. This is shown to create promising options for quantifying and filtering the mid-spatial frequency structure within circular domains from measurements of as-built parts.