Comparison of Zernike and Fourier wavefront reconstruction algorithms in representing corneal aberration of normal and abnormal eyes.

PURPOSE To investigate the accuracy of Zernike and Fourier reconstruction algorithms in describing simulated wavefront data from corneal topography of normal and abnormal eyes. METHODS Corneal topography (Orbscan Ilz) was collected on 87 normal, 27 keratoconus, 9 penetrating keratoplasty (PKP), and 20 postoperative LASIK symptomatic eyes over a 6-mm pupil. Raw data from slit images were converted into elevation maps, which were then resampled at resolutions of 100, 300, and 500 microm. Differences in elevation between adjacent pixels were used to generate simulated wavefront slope data. Both conventional Zernike and iterative Fourier algorithms were used to reconstruct the elevation map from the same slope information. The difference between the reconstructed and original maps was used to evaluate reconstruction performance, quantified by the residual root-mean-square (RMS) error. RESULTS When using the Zernike-based method, residual RMS error decreased substantially as the number of modes used in the reconstruction increased up to approximately the 10th order. Both Zernike and Fourier algorithms performed best when reconstructing simulated wavefronts from normal eyes and worst with PKP eyes. Using a large number of Zernike modes to reconstruct simulated wavefronts of low spatial resolution lead to inaccurate reconstructions. The Fourier method had better reconstruction reliability in the center of the pupil than peripherally. Only 2nd through 5th order Zernike modes were required to produce less residual RMS error than the Fourier method. CONCLUSIONS For all conditions tested, the Zernike method outperformed the Fourier method when representing simulated wavefront data from topography maps. Even 2nd through 5th order Zernike polynomials were enough to outperform the Fourier method in all populations. Up to 9th order Zernike modes may be required to accurately describe the simulated wavefronts in some abnormal eyes.

[1]  F Roddier,et al.  Wavefront reconstruction using iterative Fourier transforms. , 1991, Applied optics.

[2]  P Mierdel,et al.  Principles of Tscherning aberrometry. , 2000, Journal of refractive surgery.

[3]  Mark R. Morelande,et al.  A refined bootstrap method for estimating the Zernike polynomial model order for corneal surfaces , 2004, IEEE Transactions on Biomedical Engineering.

[4]  M S SMIRNOV,et al.  [Measurement of the wave aberration of the human eye]. , 1961, Biofizika.

[5]  W N Charman,et al.  Objective technique for the determination of monochromatic aberrations of the human eye. , 1984, Journal of the Optical Society of America. A, Optics and image science.

[6]  Geunyoung Yoon,et al.  Changes in aberrations and retinal image quality due to tear film dynamics. , 2006, Optics express.

[7]  L. Thibos,et al.  Standards for reporting the optical aberrations of eyes. , 2002, Journal of refractive surgery.

[8]  S. Klyce,et al.  Zernike polynomial fitting fails to represent all visually significant corneal aberrations. , 2003, Investigative ophthalmology & visual science.

[9]  Michael D Karon,et al.  Advantages and disadvantages of the Zernike expansion for representing wave aberration of the normal and aberrated eye. , 2004, Journal of refractive surgery.

[10]  Guang-Ming Dai,et al.  Comparison of wavefront reconstructions with Zernike polynomials and Fourier transforms. , 2006, Journal of refractive surgery.

[11]  Junzhong Liang,et al.  Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor. , 1994, Journal of the Optical Society of America. A, Optics, image science, and vision.

[12]  W. Southwell.  Wave-front estimation from wave-front slope measurements , 1980 .

[13]  E. H. Linfoot.  Principles of Optics , 1961 .

[14]  William H. Press,et al.  Numerical Recipes in Fortran 77: The Art of Scientific Computing 2nd Editionn - Volume 1 of Fortran Numerical Recipes , 1992 .

[15]  Luis Alberto Carvalho,et al.  Accuracy of Zernike polynomials in characterizing optical aberrations and the corneal surface of the eye. , 2005, Investigative ophthalmology & visual science.

[16]  D. Williams,et al.  Monochromatic aberrations of the human eye in a large population. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.