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

Ophthalmic Physiol Opt. 1995 May;15(3):171-85.


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.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Algorithms
  • Anthropometry
  • Astigmatism / pathology
  • Cornea / pathology*
  • Corneal Transplantation
  • Fourier Analysis
  • Humans
  • Keratoconus / pathology*
  • Keratoconus / surgery
  • Refraction, Ocular