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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 9 — Apr. 28, 2008
  • pp: 6586–6591

Orthonormal vector polynomials in a unit circle, Part II : completing the basis set

Chunyu Zhao and James H. Burge  »View Author Affiliations


Optics Express, Vol. 16, Issue 9, pp. 6586-6591 (2008)
http://dx.doi.org/10.1364/OE.16.006586


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Abstract

Zernike polynomials provide a well known, orthogonal set of scalar functions over a circular domain, and are commonly used to represent wavefront phase or surface irregularity. A related set of orthogonal functions is given here which represent vector quantities, such as mapping distortion or wavefront gradient. Previously, we have developed a basis of functions generated from gradients of Zernike polynomials. Here, we complete the basis by adding a complementary set of functions with zero divergence – those which are defined locally as a rotation or curl.

© 2008 Optical Society of America

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(080.1010) Geometric optics : Aberrations (global)
(220.4840) Optical design and fabrication : Testing

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: February 19, 2008
Revised Manuscript: April 18, 2008
Manuscript Accepted: April 19, 2008
Published: April 24, 2008

Virtual Issues
Vol. 3, Iss. 5 Virtual Journal for Biomedical Optics

Citation
Chunyu Zhao and James H. Burge, "Orthonormal vector polynomials in a unit circle, Part II : completing the basis set," Opt. Express 16, 6586-6591 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-9-6586


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References

  1. C. Zhao and J. H. Burge, "Orthonormal vector polynomials in a unit circle, Part I: basis set derived from gradients of Zernike polynomials," Opt. Express 15, 18014-18024 (2007). [CrossRef] [PubMed]
  2. C. Zhao,  et al, "Figure measurement of a large optical flat with a Fizeau interferometer and stitching technique," Proc. SPIE 6293, 62930k (2006). [CrossRef]
  3. R. J. Noll, "Zernike polynomials and atmospheric turbulence," J. Opt. Soc. Am. 66, 207-211(1976). [CrossRef]
  4. H. F. Davis and A. D. Snider, Introduction to Vector Analysis, (Wm. C. Brown Publisher, 1986).

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