title: Errors in Zernike transformations and non-modal reconstruction methods.
abstract: OBJECTIVE
  Wavefront aberrometers often represent the wavefront in terms of Zernike polynomials. The fit coefficients for these polynomials are pupil-size dependent; hence it is desirable to be able to calculate polynomial coefficients at a different pupil size from the initial measurement.
  
  
  METHODS
  We developed a method for scaling the Zernike fit coefficients for different sized pupils and compared them to the coefficients calculated by reanalyzing the original data. We evaluated cases where the initial set of Zernike coefficients was an accurate representation of the data as well as cases where the Zernike polynomials fit the data poorly.
  
  
  RESULTS
  The rescaling methods work well in all cases with a good original fit (as measured by the gradient root-mean-square [RMS] fit error). Rescaling and reanalyzing also agree well over a small scaling range. However, if the original fit was poor, large errors result if the rescaling is more than approximately 25%.
  
  
  CONCLUSIONS
  Rescaling works well and is useful as long as the RMS fit error can be evaluated. The RMS difference between the zonal reconstruction and the Zernike fit is useful for determining this fit error.
authors.affiliation: WaveFront Sciences Inc, Albuquerque, NM 87123, USA. drneal@wavefrontsciences.com
authors.forename: Daniel R
authors.initials: DR
authors.lastname: Neal
authors.forename: C David
authors.initials: CD
authors.lastname: Baer
authors.forename: Daniel M
authors.initials: DM
authors.lastname: Topa
mesh_terms: D000328:Adult; D000465:Algorithms; D003315:Cornea / Q000473:pathology* / Q000601:surgery; D019781:Corneal Topography / Q000379:methods*; D005260:Female; D006801:Humans; D020731:Keratomileusis, Laser In Situ; D008297:Male; D008875:Middle Aged; D015233:Models, Statistical; D011680:Pupil / Q000502:physiology; D012030:Refractive Errors / Q000175:diagnosis*; D054140:Refractive Surgical Procedures