Transformation of Zernike coefficients: scaled, translated, and rotated wavefronts with circular and elliptical pupils
JOSA A, Vol. 24, Issue 3, pp. 569-577 (2007)
http://dx.doi.org/10.1364/JOSAA.24.000569
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Abstract
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
History
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
Citation
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)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-3-569
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