Comparison of wavefront reconstructions with Zernike polynomials and Fourier transforms

To make a direct comparison between Fourier and Zernike reconstructions of ocular wavefronts using a newly available analytical theory by which Fourier coefficients can be converted to Zernike coefficients and vice versa.

Noise-free random wavefronts were simulated with up to the 15th order of Zernike polynomials. For each case, 100 random wavefronts were simulated separately. These wavefronts were smoothed with a low-pass Gaussian filter to remove edge effects. Wavefront slopes were calculated, and normally distributed random noise was added within the circular area to simulate realistic Shack-Hartmann spot patterns. Three wavefront reconstruction methods were performed. The wavefront surface error was calculated as the percentage of the input wavefront root mean square.

Fourier full reconstruction was more accurate than Zernike reconstruction from the 6th to the 10th orders for low-to-moderate noise levels. Fourier reconstruction was found to be approximately 100 times faster than Zernike reconstruction. Fourier reconstruction always makes optimal use of information. For Zernike reconstruction, however, the optimal number of orders must be chosen manually. The optimal Zernike order for Zernike reconstruction is lower for smaller pupils than larger pupils.

Fourier full reconstruction is faster and more accurate than Zernike reconstruction, makes optimal use of slope information, and better represents ocular aberrations of highly aberrated eyes.