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Michael K. Smolek, Stephen D. Klyce; Zernike Polynomial Fitting Fails to Represent All Visually Significant Corneal Aberrations. Invest. Ophthalmol. Vis. Sci. 2003;44(11):4676-4681. doi: 10.1167/iovs.03-0190.
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purpose. It is assumed that wavefront error data arising from aberrometry are adequately described by a Zernike polynomial function, although this assumption has not been extensively tested. Inaccuracies in wavefront error may compromise clinical testing and refractive correction procedures. The current retrospective study correlates visual acuity with corneal wavefront error and with the residual surface elevation error after fitting with the Zernike method.
methods. Corneal topography maps were obtained from 32 keratoconus cases, 27 postoperative penetrating keratoplasty cases, and 29 postoperative conductive keratoplasty cases (88 total). The best spectacle-corrected visual acuity (BSCVA) for each case ranged from −0.2 to 1.3 logarithm of the minimum angle of resolution (logMAR) units (20/12.5–20/400). Topography was analyzed to determine wavefront error and the elevation fit error for a 4-mm optical zone. The 4th and 10th expansion series were analyzed with the 0th-order (piston) and 1st order (tip and tilt) removed. Linear regression analysis was performed. The difference in root mean square (RMS) error between the 4th- and 10th-order analyses was assessed for both wavefront and elevation fit error.
results. The correlation of BSCVA to wavefront error for 4th-order terms was moderately strong and significant (R 2 = 0.581; P < 0.001). The 10th-order correlation for wavefront error had a similar result (R 2 = 0.565; P < 0.001), but the regression was not significantly different from the 4th-order result. The correlation of BSCVA to the elevation fit error was strong and significant for the 4th order (R 2 = 0.658; P < 0.001). The 10th-order data had a similar result (R 2 = 0.509; P < 0.001), and there was no significant difference between the two regressions. Only 72% of the cases showed a shift toward increased wavefront error with the 10th-order series, whereas 18% lost wavefront error. All cases showed a shift toward improved elevation fit with the 10th-order expansion.
conclusions. The wavefront error correlation to acuity was moderately strong, but the corneal elevation fit error also strongly correlated with visual acuity, indicating that Zernike polynomials do not fully characterize the surface shape features that influence vision and that exist in postsurgical or pathologic eyes. In addition, the change in wavefront error when using a larger expansion series was found to increase or diminish somewhat unpredictably. The authors conclude that Zernike polynomials fail to model all the information that influences visual acuity, which may confound clinical diagnosis and treatment.
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