Fitting freeform shapes with orthogonal bases

G. W. Forbes*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

36 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)19061-19081
Number of pages21
JournalOptics Express
Issue number16
Publication statusPublished - 12 Aug 2013
Externally publishedYes


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