Fourier analysis of video-keratographic data A tool for separation of spherical, regular astigmatic and irregular astigmatic corneal power components

Abstract

Topographic analysis of the cornea and computation of changes in corneal topography is difficult because of the lack of a standardized concept for analysing topographic information. We have used Fourier series harmonic analysis to decompose the often very complex information given in topographic images (TMS-1 video-keratograph). The polar data values arising from each mire were separated into spherical (average power), regular astigmatic (2' harmonic) and non-regular astigmatic components. The non-regular astigmatic components were further divided into a decentration component (1' harmonic) and a higher order irregular refractive component (root mean square (r.m.s.) of the residual between original data and the sum of spherical, 1' and 2' order components). Algorithms for utilizing the Fourier analysis technique on subjective refractive and on keratometric changes in regular astigmatism were also derived. Averages of the separate refractive components were calculated for groups of normal (right and left eye of 25 patients), keratoconic (13 eyes), and transplanted eyes (20 eyes), and average topographic maps were reconstructed and imaged. Changes in the separate topographic refractive components were compared with subjective refractive changes in eyes that had undergone combined myopic-astigmatic excimer laser ablation (8 eyes). Fourier series analysis was found superior to conventional keratometry in predicting spherical and regular astigmatic changes in subjective refraction. Fourier series analysis seems to be a powerful tool to decompose the information of complex topographic corneal images into rational optical components.

Optical System Design for Noncontact, Normal Incidence, THz Imaging of in vivo Human Cornea

“…In particular, Videokeratography [20] can be used to construct dioptric power maps from corneal surface height data, which can be further fitted to a parametric surface to analyze higher-order surface features from disease or refractive surgery [21]. However, despite the maturity of topology mapping technology, there is no standardized method for analyzing topographic information [22]. Therefore, the following analysis is performed to characterize physiologic variations of anterior corneal surface.…”

“…Corneal surface data is decomposed to into a set of concentric rings centered at the corneal apex. Fourier decomposition analysis was utilized to explore the deviations between average human cornea topology and an ideal sphere [22, 23]. The fundamental mode (first term in the Fourier series expansion) is attributed to de-centration (Figure 1(a)), and the second term is attributed to “regular” astigmatism (Figure 1(b)).…”

“…In [22], corneal surface curvature measurements are reported as diopters (D) across the meridian cross-section as a function of radial distance from the center of the cornea and the meridian angle. The diopter values are averaged and converted to an expected RoC deviation using equation (1) where P typical is the focusing power of a cornea representative of typical population ( P typical = 44D), P measured is the data from [22], n is the refractive index of the cornea ( n = 1.376), and Δ r is the resulting standard deviation in the RoC.…”

“…The average RoC deviation from the first term in the series (decentration), the second term in the series (astigmatism) and the higher order terms are displayed in Figure 2 for healthy eyes (N=25), Keratoconic eyes (N=13), and grafted cornea (N=20) [22]. The format represents the expected geometric variation from an ideal sphere.…”

“…Average corneal RoC variation (Δr, equation (1)) for healthy cornea (left), Keratoconus (middle), and Grafted cornea (right). The contribution to overall RoC variation is decomposed into decentration, regular Astigmatism, and higher order irregularities [22]. The maximum RoC variation is less than 1λ @ 650 GHz.…”