Journal of Refractive Surgery

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Original Article 

Comparison of Zernike and Fourier Wavefront Reconstruction Algorithms in Representing Corneal Aberration of Normal and Abnormal Eyes

Geunyoung Yoon, PhD; Seth Pantanelli, MS; Scott MacRae, MD

Abstract

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 IIz) 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 µm. 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-meansquare (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. [J Refract Surg. 2008;24:582-590.]

ABOUT THE AUTHORS

From the Department of Ophthalmology (Yoon, MacRae), School of Medicine and Dentistry (Yoon, Pantanelli), University of Rochester, Rochester, NY.

This research was funded by grants from the NIH (R01-EY014999) and Research to Prevent Blindness Inc, New York, NY.

The authors have no proprietary interest in the materials presented herein.

Correspondence: Seth Pantanelli, MS, 261 Meliora Hall, Center for Visual Science, University of Rochester, Rochester, NY 14627. Tel: 203.948.3443; Fax: 585.271.3043; E-mail: seth_pantanelli@urmc.rochester.edu

Received: January 24, 2007

Accepted: June 15, 2007

Posted online: December 28, 2007

Abstract

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 IIz) 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 µm. 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-meansquare (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. [J Refract Surg. 2008;24:582-590.]

ABOUT THE AUTHORS

From the Department of Ophthalmology (Yoon, MacRae), School of Medicine and Dentistry (Yoon, Pantanelli), University of Rochester, Rochester, NY.

This research was funded by grants from the NIH (R01-EY014999) and Research to Prevent Blindness Inc, New York, NY.

The authors have no proprietary interest in the materials presented herein.

Correspondence: Seth Pantanelli, MS, 261 Meliora Hall, Center for Visual Science, University of Rochester, Rochester, NY 14627. Tel: 203.948.3443; Fax: 585.271.3043; E-mail: seth_pantanelli@urmc.rochester.edu

Received: January 24, 2007

Accepted: June 15, 2007

Posted online: December 28, 2007

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10.3928/1081597X-20080601-06

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