title: Modal reconstruction methods with Zernike polynomials.
abstract: OBJECTIVE
  To compare the advantages and disadvantages of different techniques for fitting Zernike polynomials to surfaces.
  
  
  METHODS
  Two different methods, Orthogonal Projection and Gram-Schmidt orthogonalization, are compared in terms of speed and performance at fitting a complex object.
  
  
  RESULTS
  Orthogonal Projection provides an extremely rapid fitting of a surface, but leaves residual high frequency noise. The Gram-Schmidt technique provides a more accurate fit of the original object, but consumes much more computing time. Orthogonal Projection, and its associated noise, may be tolerated in classifying corneal topography.
  
  
  CONCLUSIONS
  Orthogonal Projection has a distinct advantage in calculation time over other methods for fitting surfaces. This advantage may be exploited in cases where accurate surface fitting is not necessary, but only general features need to be extracted for classification. If fit accuracy is needed, then slower fitting techniques, such as Gram-Schmidt, should be used.
authors.affiliation: Department of Ophthalmology & Vision Science, University of Arizona, Tucson, Arizona, USA. jschwieg@u.arizona.edu
authors.forename: Jim
authors.initials: J
authors.lastname: Schwiegerling
mesh_terms: D003315:Cornea / Q000473:pathology* / Q000601:surgery; D019781:Corneal Topography; D006801:Humans; D007640:Keratoconus / Q000473:pathology* / Q000601:surgery; D008433:Mathematics; D015233:Models, Statistical; D055095:Optics and Photonics; D012030:Refractive Errors / Q000175:diagnosis*