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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 16 — Aug. 12, 2013
  • pp: 19061–19081

Fitting freeform shapes with orthogonal bases

G. W. Forbes  »View Author Affiliations


Optics Express, Vol. 21, Issue 16, pp. 19061-19081 (2013)
http://dx.doi.org/10.1364/OE.21.019061


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Abstract

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.

© 2013 OSA

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(220.1250) Optical design and fabrication : Aspherics
(220.4610) Optical design and fabrication : Optical fabrication
(220.4830) Optical design and fabrication : Systems design
(220.4840) Optical design and fabrication : Testing

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: June 11, 2013
Manuscript Accepted: July 19, 2013
Published: August 2, 2013

Citation
G. W. Forbes, "Fitting freeform shapes with orthogonal bases," Opt. Express 21, 19061-19081 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-16-19061


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References

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