Statistical Model of Ocular Wavefronts With Accommodation

The purpose of this study was to determine the minimum number of orthonormal basis functions, applying Principal Component Analysis (PCA), to represent the most wavefront aberrations at different accommodation stages. The study also aims to generate synthetic wavefront data using these functions.

Monocular wavefront data from 191 subjects (26.15 ± 5.56 years old) were measured with a Hartmann-Shack aberrometer, simulating accommodation from 0 diopters (D) to 5 D in 1 D steps. The wavefronts for each accommodative demand were rescaled for different pupil sizes: 4.66, 4.76, 4.40, 4.09, 4.07, and 3.68 mm. PCA was applied to 150 wavefront parameters (25 Zernike coefficients × 6 accommodation levels) to obtain eigenvectors for dimensional reduction. A total of 49 eigenvectors were modeled as a sum of 2 multivariate Gaussians, from which 1000 synthetic data sets were generated.

The first 49 eigenvectors preserved 99.97% of the original data variability. No significant differences were observed between the mean values and standard deviation of the generated and original 49 eigenvectors (two one-sided test [TOST], P > 0.05/49) and (F-test, P > 0.05/49), both with Bonferroni correction. The mean values of the generated parameters (1000) were statistically equal to those of the original data (TOST, P > 0.05/150). The variability of the generated data was similar to the original data for the most important Zernike coefficients (F-test, P > 0.05/150).

PCA significantly reduces the dimensionality of wavefront aberration data across 6 accommodative demands, reducing the variable space by over 66%. The synthetic data generated by the proposed wavefront model for accommodation closely resemble the original clinical data.