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Optics Letters

Optics Letters

| RAPID, SHORT PUBLICATIONS ON THE LATEST IN OPTICAL DISCOVERIES

  • Editor: Anthony J Campillo
  • Vol. 32, Iss. 1 — Jan. 1, 2007
  • pp: 74–76

Nonrecursive determination of orthonormal polynomials with matrix formulation

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


Optics Letters, Vol. 32, Issue 1, pp. 74-76 (2007)
http://dx.doi.org/10.1364/OL.32.000074


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Abstract

A general theoretical approach has been developed for the determination of orthonormal polynomials over any integrable domain, such as a hexagon. This approach is better than the classical Gram–Schmidt orthogonalization process because it is nonrecursvie and can be performed rapidly with matrix transformations. The determination of the orthonormal hexagonal polynomials is demonstrated as an example of the matrix approach.

© 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
(330.4460) Vision, color, and visual optics : Ophthalmic optics and devices

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: July 11, 2006
Revised Manuscript: July 31, 2006
Manuscript Accepted: October 5, 2006
Published: December 13, 2006

Virtual Issues
Vol. 2, Iss. 2 Virtual Journal for Biomedical Optics

Citation
Guang-ming Dai and Virendra N. Mahajan, "Nonrecursive determination of orthonormal polynomials with matrix formulation," Opt. Lett. 32, 74-76 (2007)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-32-1-74

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