Limitations of Reconstructing Pentacam Rabbit Corneal Tomography by Zernike Polynomials

Abstract

The study aims to investigate the likelihood of Zernike polynomial being used for reconstructing rabbit corneal surfaces as scanned by the Pentacam segment tomographer, and hence evaluate the accuracy of corneal power maps calculated from such Zernike fitted surfaces. The study utilised a data set of both eyes of 21 rabbits using a reverse engineering approach for deductive reasoning. Pentacam raw elevation data were fitted to Zernike polynomials of orders 2 to 20. The surface fitting process to Zernike polynomials was carried out using randomly selected 80% of the corneal surface data points, and the root means squared fitting error (RMS) was determined for the other 20% of the surface data following the Pareto principle. The process was carried out for both the anterior and posterior surfaces of the corneal surfaces that were measured via Pentacam scans. Raw elevation data and the fitted corneal surfaces were then used to determine corneal axial and tangential curvature maps. For reconstructed surfaces calculated using the Zernike fitted surfaces, the mean and standard deviation of the error incurred by the fitting were calculated. For power maps computed using the raw elevation data, different levels of discrete cosine transform (DCT) smoothing were employed to infer the smoothing level utilised by the Pentacam device. The RMS error was not significantly improved for Zernike polynomial orders above 12 and 10 when fitting the anterior and posterior surfaces of the cornea, respectively. This was noted by the statistically non-significant increase in accuracy when the order was increased beyond these values. The corneal curvature calculations suggest that a smoothing process is employed in the corneal curvature maps outputted by the Pentacam device; however, the exact smoothing method is unknown. Additionally, the results suggest that fitting corneal surfaces to high-order Zernike polynomials will incur a clinical error in the calculation of axial and tangential corneal curvature of at least 0.16 ± 01 D and 0.36 ± 0.02 D, respectively. Rabbit corneal anterior and posterior surfaces scanned via the Pentacam were optimally fitted to orders 12 and 10 Zernike polynomials. This is essential to get stable values of high-order aberrations that are not affected by Zernike polynomial fittings, such as comas for Intracorneal Ring Segments (ICRS) adjustments or spherical aberration for pre-cataract operations. Smoothing was necessary to replicate the corneal curvature maps outputted by the Pentacam tomographer, and fitting corneal surfaces to Zernike polynomials introduces errors in the calculation of both the axial and tangential corneal curvatures.