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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 24, Iss. 3 — Mar. 1, 2007
  • pp: 569–577

Transformation of Zernike coefficients: scaled, translated, and rotated wavefronts with circular and elliptical pupils

Linda Lundström and Peter Unsbo  »View Author Affiliations

JOSA A, Vol. 24, Issue 3, pp. 569-577 (2007)

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Zernike polynomials and their associated coefficients are commonly used to quantify the wavefront aberrations of the eye. When the aberrations of different eyes, pupil sizes, or corrections are compared or averaged, it is important that the Zernike coefficients have been calculated for the correct size, position, orientation, and shape of the pupil. We present the first complete theory to transform Zernike coefficients analytically with regard to concentric scaling, translation of pupil center, and rotation. The transformations are described both for circular and elliptical pupils. The algorithm has been implemented in MATLAB, for which the code is given in an appendix.

© 2007 Optical Society of America

OCIS Codes
(000.3870) General : Mathematics
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(220.1010) Optical design and fabrication : Aberrations (global)
(330.4460) Vision, color, and visual optics : Ophthalmic optics and devices

ToC Category:
Vision, Color, and Visual Optics

Original Manuscript: June 15, 2006
Revised Manuscript: September 4, 2006
Manuscript Accepted: September 25, 2006
Published: February 14, 2007

Virtual Issues
Vol. 2, Iss. 4 Virtual Journal for Biomedical Optics

Linda Lundström and Peter Unsbo, "Transformation of Zernike coefficients: scaled, translated, and rotated wavefronts with circular and elliptical pupils," J. Opt. Soc. Am. A 24, 569-577 (2007)

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