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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 7 — Jul. 1, 2006
  • pp: 1657–1668

Wavefront expansion basis functions and their relationships

Guang-ming Dai  »View Author Affiliations


JOSA A, Vol. 23, Issue 7, pp. 1657-1668 (2006)
http://dx.doi.org/10.1364/JOSAA.23.001657


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Abstract

Wavefront expansion basis functions are important in representing ocular aberrations and phase perturbations due to atmospheric turbulence. A general discussion is presented for the conversions of the coefficients between any two sets of basis functions. Several popular sets of basis functions, namely, Zernike polynomials, Fourier series, and Taylor monomials, are discussed and the conversion matrices between any two of these basis functions are derived. Some analytical and numerical examples are given to demonstrate conversion of coefficients of different basis function sets.

© 2006 Optical Society of America

OCIS Codes
(000.3870) General : Mathematics
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(220.1010) Optical design and fabrication : Aberrations (global)
(330.4460) Vision, color, and visual optics : Ophthalmic optics and devices

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: September 30, 2005
Manuscript Accepted: January 3, 2006

Virtual Issues
Vol. 1, Iss. 8 Virtual Journal for Biomedical Optics

Citation
Guang-ming Dai, "Wavefront expansion basis functions and their relationships," J. Opt. Soc. Am. A 23, 1657-1668 (2006)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-7-1657

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