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Optics Letters

Optics Letters

| RAPID, SHORT PUBLICATIONS ON THE LATEST IN OPTICAL DISCOVERIES

  • Editor: Anthony J. Campillo
  • Vol. 31, Iss. 16 — Aug. 15, 2006
  • pp: 2462–2464

Orthonormal polynomials for hexagonal pupils

Virendra N. Mahajan and Guang-ming Dai  »View Author Affiliations


Optics Letters, Vol. 31, Issue 16, pp. 2462-2464 (2006)
http://dx.doi.org/10.1364/OL.31.002462


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Abstract

The problem of determining the orthonormal polynomials for hexagonal pupils by the Gram–Schmidt orthogonalization of Zernike circle polynomials is revisited, and closed-form expressions for the hexagonal polynomials are given. We show how the orthonormal coefficients are related to the corresponding Zernike coefficients for a hexagonal pupil and emphasize that it is the former that should be used for any quantitative wavefront analysis for such a pupil.

© 2006 Optical Society of America

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(080.1010) Geometric optics : Aberrations (global)
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(220.4840) Optical design and fabrication : Testing

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: March 27, 2006
Revised Manuscript: May 18, 2006
Manuscript Accepted: May 21, 2006
Published: July 25, 2006

Virtual Issues
Vol. 1, Iss. 9 Virtual Journal for Biomedical Optics

Citation
Virendra N. Mahajan and Guang-ming Dai, "Orthonormal polynomials for hexagonal pupils," Opt. Lett. 31, 2462-2464 (2006)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-31-16-2462

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