title: Iteratively re-weighted bi-cubic spline representation of corneal topography and its comparison to the standard methods.
abstract: OBJECTIVE
  The aim of this study is to represent the corneal anterior surface by utilizing radius and height data extracted from a TMS-2N topographic system with three different mathematical approaches and to simulate the visual performance.
  
  
  METHODS
  An iteratively re-weighted bi-cubic spline method is introduced for the local representation of the corneal surface. For comparison, two standard mathematical global representation approaches are used: the general quadratic function and the higher order Taylor polynomial approach. First, these methods were applied in simulations using three corneal models. Then, two real eye examples were investigated: one eye with regular astigmatism, and one eye which had undergone refractive surgery. A ray-tracing program was developed to evaluate the imaging performance of these examples with each surface representation strategy at the best focus plane. A 6 mm pupil size was chosen for the simulation.
  
  
  RESULTS
  The fitting error (deviation) of the presented methods was compared. It was found that the accuracy of the topography representation was worst using the quadratic function and best with bicubic spline. The quadratic function cannot precisely describe the irregular corneal shape. In order to achieve a sub-micron fitting precision, the Taylor polynomial's order selection behaves adaptive to the corneal shape. The bi-cubic spline shows more stable performance. Considering the visual performance, the more precise the cornea representation is, the worse the visual performance is.
  
  
  CONCLUSIONS
  The re-weighted bi-cubic spline method is a reasonable and stable method for representing the anterior corneal surface in measurements using a Placido-ring-pattern-based corneal topographer.
authors.affiliation: Medical Optics at the Institute of Medical Physics, University of Erlangen-Nuremberg, Henkestr. 91, 91052 Erlangen, Germany. zhongxia.zhu@imp.uni-erlangen.de
authors.forename: Zhongxia
authors.initials: Z
authors.lastname: Zhu
authors.forename: Edgar
authors.initials: E
authors.lastname: Janunts
authors.forename: Timo
authors.initials: T
authors.lastname: Eppig
authors.forename: Tomas
authors.initials: T
authors.lastname: Sauer
authors.forename: Achim
authors.initials: A
authors.lastname: Langenbucher
mesh_terms: D001251:Astigmatism / Q000601:surgery; D003198:Computer Simulation; D003315:Cornea / Q000033:anatomy & histology / Q000601:surgery*; D006801:Humans; D008962:Models, Theoretical; D054140:Refractive Surgical Procedures; D013499:Surface Properties