title: Fitting behaviors of Fourier transform and Zernike polynomials.
abstract: OBJECTIVE
  To evaluate the residual fit errors for wavefront measurements and corneal surfaces in virgin and post-surgery eyes using the Fourier transform and Zernike 6th- and 10th-order expansions.
  
  
  METHODS
  Using MatLab (The MathWorks, Inc.) and VOLCT program (Sarver and Associates, Inc.), wavefront gradient fields derived from the Hartmann-Shack lenslet array of the CustomVue System (Visx, Inc.) and the corneal surface obtained from the Humphrey Atlas topographer (Carl Zeiss, Inc.) were fitted with the Fourier transform and Zernike 6th- and 10th-order expansions. The wavefront gradient fields and corneal surfaces reconstructed by the 3 methods were compared with original ones, and the residual fit errors were analyzed (6.0 mm pupil). Ten eyes in each of the 4 groups (virgin eyes, post-laser in situ keratomileusis (LASIK) for myopia, post-LASIK for hyperopia, and post-radial keratotomy) were included.
  
  
  RESULTS
  Wavefront gradient fields reconstructed with Fourier transform produced significantly smaller residual fit errors than Zernike 6th-order in all groups and Zernike 10th-order in all eyes except post-myopic-LASIK eyes. In all groups, wavefront gradient fields reconstructed with Zernike 10th order yielded significantly smaller residual errors than Zernike 6th order (all P<.05). Higher residual errors were produced by these 3 methods in more highly aberrated eyes. When corneal surfaces for all groups were reconstructed, the Fourier transform produced significantly lower residual fit errors than Zernike 6th order and 10th order and the Zernike 10th order yielded significantly lower residual errors than Zernike 6th order (all P<.05). As corneal higher-order aberrations increased, higher residual surface fit errors were produced by Zernike 6th-order and 10th-order expansions but not by Fourier transform.
  
  
  CONCLUSIONS
  Fourier transform reconstructed ocular wavefront and corneal topographic maps more accurately than Zernike polynomials up to the 10th order. Clinical implications require further study.
authors.affiliation: Department of Ophthalmology, Baylor College of Medicine, 6565 Fannin, Houston, TX 77030, USA.
authors.forename: Li
authors.initials: L
authors.lastname: Wang
authors.forename: Dimitri
authors.initials: D
authors.lastname: Chernyak
authors.forename: David
authors.initials: D
authors.lastname: Yeh
authors.forename: Douglas D
authors.initials: DD
authors.lastname: Koch
mesh_terms: D000328:Adult; D003315:Cornea / Q000473:pathology*; D019781:Corneal Topography; D005583:Fourier Analysis; D006801:Humans; D006956:Hyperopia / Q000601:surgery; D020731:Keratomileusis, Laser In Situ; D007646:Keratotomy, Radial; D008875:Middle Aged; D015233:Models, Statistical; D009216:Myopia / Q000601:surgery; D012189:Retrospective Studies