Fast Fourier and wavelet transforms for wavefront reconstruction in adaptive optics

Wavefront reconstruction techniques using the least-squares estimators are computationally quite expensive. We compare wavelet and Fourier transforms techniques in addressing the computation issues of wavefront reconstruction in adaptive optics. It is shown that because the Fourier approach is not simply a numerical approximation technique unlike the wavelet method, the Fourier approach might have advantages in terms of numerical accuracy. To optimize the wavelet method, a statistical study might be necessary to use the best basis functions or 'approximation tree.'