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ABBAS OMMANI, Natalie Hutchings, Damber Thapa, Vasudevan Lakshminarayanan; Validating Theoretical Pupil Size Scaling Formula For The Estimation Of Ocular Wavefront Aberrations. Invest. Ophthalmol. Vis. Sci. 2012;53(14):145.
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To validate the mathematical pupil size scaling formula by comparing the estimates of the Zernike coefficients with corresponding clinical measurements obtained at different pupil sizes.
The iProfiler aberometer (Carl Zeiss, Germany) was used to measure the wavefront aberrations and it provides Zernike coefficients for two pupil sizes (3mm and the maximum natural pupil size). 81 eyes (40 OD, 41 OS) of 49 visually normal subjects (mean age 57±7 yrs) whose maximum pupil size was ≥4.8mm were enrolled. For those subjects with pupil size >4.8mm, Zernike coefficients were recalculated from the measured data for a pupil size of 4.8mm.1 To validate a scaling procedure, Zernike coefficients were estimated for a 4.8mm pupil size using the measured data for the 3mm pupil size. The conversion matrix [C] derived by Lundstrom and Unsbo2 was used to generate the estimated Zernike coefficients. MATLAB software version (R2010b) was used to code the procedure. The estimated coefficients were then compared with the measured data for the 4.8mm pupil size. The procedure was repeated to estimate Zernike coefficients for a 3mm pupil size from the measured data of the 4.8mm pupil size. Third and fourth orders Zernike coefficients were used for the analysis.
Repeated measures ANOVA (Factor: Method, Coefficients) was used to evaluate differences between estimated and theoretical Zernike coefficients. No significant differences (all p>0.05) were found between the estimated and measured coefficients overall. Paired t-tests between the estimated and measured individual coefficients were not significant (Tukey; all p>0.05). Correlation coefficients were at the lowest of r=0.87, (p<0.001). A Bland-Altman analysis was used to determine any systematic and spread differences between the estimated and measured Zernike coefficients for each pupil. The limits of agreement (LOA: mean±95% CI) ranged between +0.033 and -0.043 for scaling up to 4.8mm, and +0.128 and -0.124 for scaling down to 3.0mm. In all cases, the differences were distributed symmetrically around the mean difference.
The differences between the estimated and measured values were not significantly different over the range of pupils examined, irrespective if the estimates were made when scaling up from a small pupil or the converse. Scaling to a larger pupil size had larger LOAs than scaling to a smaller pupil size.1. Lakshminarayanan V, Fleck A. J Modern Optics. 2011;58(7):545-561.2. L. Lundström and P. Unsbo. J. Opt. Soc. Am. A. 2007; 24(3):556-577
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