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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: Franco Gori
  • Vol. 30, Iss. 4 — Apr. 1, 2013
  • pp: 726–732

Transformation of Zernike coefficients: a Fourier-based method for scaled, translated, and rotated wavefront apertures

Eric Tatulli  »View Author Affiliations


JOSA A, Vol. 30, Issue 4, pp. 726-732 (2013)
http://dx.doi.org/10.1364/JOSAA.30.000726


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Abstract

This paper studies the effects on Zernike coefficients of aperture scaling, translation, and rotation, when a given aberrated wavefront is described on the Zernike polynomial basis. It proposes an analytical method for computing the matrix that enables the building of transformed Zernike coefficients from the original ones. The technique is based on the properties of Zernike polynomials and Fourier transform, and, in the case of a full aperture without central obstruction, the coefficients of the matrix are given in terms of integrals of Bessel functions. The integral formulas are exact and do not depend on any specific ordering of the polynomials.

© 2013 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(330.4460) Vision, color, and visual optics : Ophthalmic optics and devices
(350.1260) Other areas of optics : Astronomical optics

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: December 3, 2012
Revised Manuscript: February 25, 2013
Manuscript Accepted: February 25, 2013
Published: March 26, 2013

Citation
Eric Tatulli, "Transformation of Zernike coefficients: a Fourier-based method for scaled, translated, and rotated wavefront apertures," J. Opt. Soc. Am. A 30, 726-732 (2013)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-4-726

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