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L.R. Stark, J. Hartley, P.B. Kruger; Extrapolation of Zernike Coefficients on the Assumption of Circular, Symmetrically Dilating Pupils . Invest. Ophthalmol. Vis. Sci. 2005;46(13):1992.
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Purpose: To determine whether Zernike ocular wavefront coefficients referenced to a particular pupil size may be extrapolated safely to larger pupil sizes, thus assisting in comparisons between eyes and between studies. Methods: Ocular aberration measures were made in the uncorrected left eyes of 28 normal young participants (23–35 yr) using the COAS aberrometer (Wavefront Sciences, Albuquerque, NM). Participants viewed an internal target while the aberrometer adjusted target vergence in attempt to relax accommodation. Lenslet data were analyzed for 1.5, 2, 2.5 and 3–mm radii by discarding lenslet points outside the given radii. Aberrations were expressed as OSA Zernike coefficients through the 6th order. For any given pupil radius r2, coefficients interpolated from the 3–mm radius data were taken as the gold standard against which extrapolated–from–r1 coefficients could be compared; where r1<=r2<=3 mm. Schwiegerling's equations [J Opt Soc Am A 2002;19:1937–45] were used. Upper and lower Bland–Altman limits of agreement (LA) were calculated in the group to represent the difference of the extrapolated coefficient from gold standard. Threshold for safe extrapolation was taken as the pupil radius r2 for which both LA differed by no more than 10% from the (appropriately–scaled) baseline LA. Results: If there are k orders available in the Zernike expansion, then LA are contained within the defined threshold for extrapolation of terms in orders k and k–1. However, errors can be large for even small extrapolations in orders k–2 and lower. Conclusions: Extrapolation of Zernike coefficients to larger pupil sizes is prone to substantial error for orders k–2 and lower. This limits the usefulness of the Zernike expansion as a descriptor of ocular aberrations, particularly where pharmacological or luminance–induced dilation of the pupil would compromise a study's experimental design.
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