title: Extrapolation of central corneal topography into the periphery.
abstract: OBJECTIVE
  To investigate the errors associated with extrapolating the topography of the central cornea into the peripheral cornea.
  
  
  METHODS
  Corneal topography data previously acquired from 92 young adult subjects was used. These data were collected and analyzed by using a method that allows central and peripheral maps to be combined to produce an extended corneal topography map that reaches close to the limbus. By using the central 5-, 6-, and 7-mm corneal topography that would normally be acquired in a single measurement, various mathematical techniques were applied to extrapolate the central topography into the periphery. These mathematical techniques included the use of simple conics, generalized conics, cosine hyperbolic functions, and a set of fourth, sixth, and eighth radial order polynomials. The root-mean-square error between the extrapolated topography and true extended topography at various diameters was then compared.
  
  
  RESULTS
  The root-mean-square errors in the outer extrapolated region ranged from 30 to 220 microm, depending on the fit function used. The lowest errors were achieved with the conic fits, cosine hyperbolic functions, and fourth and sixth radial order polynomials, with root-mean-square error levels of approximately 30 to 40 microm. The variables of global versus meridional fitting, centering the data on the geometric center versus vertex normal, the regional quadrant, and the diameter of the central topography used had relatively little influence on the fit errors.
  
  
  CONCLUSIONS
  Extrapolation from central corneal topography into the periphery by using radial polynomials of the fourth order provides the lowest levels of fit errors for normal corneas.
authors.affiliation: Contact Lens and Visual Optics Laboratory, School of Optometry, Queensland University of Technology, Victoria Park Road, Kelvin Grove 4059, Brisbane, Australia. d.iskander@qut.edu.au
authors.forename: D Robert
authors.initials: DR
authors.lastname: Iskander
authors.forename: Michael J
authors.initials: MJ
authors.lastname: Collins
authors.forename: Scott A
authors.initials: SA
authors.lastname: Read
mesh_terms: D000328:Adult; D019781:Corneal Topography; D006801:Humans; D008954:Models, Biological; D012016:Reference Values