title: A novel low-order method for recovery of the corneal shape.
abstract: OBJECTIVE
  To describe a novel low-order method for the recovery of the corneal height from videokeratographically obtained images. The method uses an iterative cubic approach with implicit continuous curvature. Convergence is easily established for a particular videokeratograph. The effect of skew rays is treated in a postprocessing step.
  
  
  METHODS
  Four simulated model corneas are tested: (1) an asphere; (2) an ellipsoid; (3) a radially keratotomized cornea; and (4) a simulation of photorefractive keratectomy (PRK). The corneal height, slope, and tilt are compared against theory and a 2nd order Taylor series method using root mean square error measures. The effect of lateral and axial shifts (up to 0.1 mm) is examined. The two methods are tested (experimentally) on an 8-mm spherical calibration ball, in which the image data are processed using a least-squares calibration procedure.
  
  
  RESULTS
  The lowest height errors are found for the asphere and PRK models (4.5 x 10 microm and 3.6 x 10 microm). The maximum height error is 0.38 microm (ellipsoid), with 0.14 microm average overall error and 0.45 microm error for the 8-mm calibration ball. The comparison method has an average error of 0.92 microm, with maximum error of 1.5 microm (PRK) and 0.55 microm error for the 8-mm calibration ball. Shift induces larger (approximately 200 microm/mm) height errors than axial shift (approximately 2 microm/mm), but the errors are similar between methods. A demonstration on additional ellipsoids suggests the new algorithm (without skew ray compensation) is not as effective as the comparison method for increasingly nonspherical surfaces. The method has a short completion time of 2.3 s in seven iterations using MATLAB version 5.0 (The MathWorks, Inc., Natick, MA), running on a Pentium III 667-MHz processor with 128 MB RAM, and running the Windows 2000 operating system (Microsoft, Redmond, WA).
  
  
  CONCLUSIONS
  An accurate, simple, robust, iteratively stable and fast method for estimating the corneal shape is described. A recovery with continuous curvature and skew ray compensation suggests a potential improvement within the context of current standard corneal shape recovery algorithms.
authors.affiliation: Department of Physics and Electronic Engineering, University of Waikato, Hamilton, New Zealand. j.turuwhenua@auckland.ac.nz
authors.forename: Jason
authors.initials: J
authors.lastname: Turuwhenua
authors.forename: Jon
authors.initials: J
authors.lastname: Henderson
mesh_terms: D000465:Algorithms; D002138:Calibration; D003198:Computer Simulation; D003315:Cornea / Q000033:anatomy & histology* / Q000601:surgery; D019781:Corneal Topography; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000592:standards; D007646:Keratotomy, Radial; D054018:Lasers, Excimer; D008953:Models, Anatomic; D018903:Photorefractive Keratectomy