General method to derive the relationship between two sets of Zernike coefficients corresponding to different aperture sizes.

Zernike polynomials have been widely used to describe the aberrations in wavefront sensing of the eye. The Zernike coefficients are often computed under different aperture sizes. For the sake of comparison, the same aperture diameter is required. Since no standard aperture size is available for reporting the results, it is important to develop a technique for converting the Zernike coefficients obtained from one aperture size to another size. By investigating the properties of Zernike polynomials, we propose a general method for establishing the relationship between two sets of Zernike coefficients computed with different aperture sizes.

[1]  Chee-Way Chong,et al.  A comparative analysis of algorithms for fast computation of Zernike moments , 2003, Pattern Recognit..

[2]  Mandyam D. Srinath,et al.  Orthogonal Moment Features for Use With Parametric and Non-Parametric Classifiers , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[3]  Joris Coppens,et al.  Corneal surface reconstruction algorithm that uses Zernike polynomial representation. , 2004, Journal of the Optical Society of America. A, Optics, image science, and vision.

[4]  J. M. Miller,et al.  Representation of videokeratoscopic height data with Zernike polynomials. , 1995, Journal of the Optical Society of America. A, Optics, image science, and vision.

[5]  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.

[6]  M. Teague.  Image analysis via the general theory of moments , 1980 .

[7]  Mark R. Morelande,et al.  Modeling of corneal surfaces with radial polynomials , 2002, IEEE Transactions on Biomedical Engineering.

[8]  D. R. Iskander,et al.  Optimal modeling of corneal surfaces with Zernike polynomials , 2001, IEEE Transactions on Biomedical Engineering.

[9]  S A Burns,et al.  Measurement of the wave-front aberration of the eye by a fast psychophysical procedure. , 1998, Journal of the Optical Society of America. A, Optics, image science, and vision.

[10]  J. Schwiegerling.  Scaling Zernike expansion coefficients to different pupil sizes. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[11]  Huazhong Shu,et al.  A novel algorithm for fast computation of Zernike moments , 2002, Pattern Recognit..

[12]  J. Y. Wang,et al.  Wave-front interpretation with Zernike polynomials. , 1980, Applied optics.

[13]  C. Campbell.  Matrix method to find a new set of Zernike coefficients from an original set when the aperture radius is changed. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[14]  Majid Ahmadi,et al.  Efficient algorithm for fast computation of Zernike moments , 1996 .

[15]  J P Carroll,et al.  A Method To Describe Corneal Topography , 1994, Optometry and vision science : official publication of the American Academy of Optometry.

[16]  Chee-Way Chong,et al.  An Efficient Algorithm for Fast computation of Zernike Moments , 2002, Joint Conference on Information Sciences.