Extended object wavefront sensing based on the correlation spectrum phase

In this paper we investigate the performance of a Fourier based algorithm for fast subpixel shift determination of two mutually shifted images subjected to noise. The algorithm will be used for Shack-Hartmann based adaptive optics correction of images of an extended object subjected to dynamical atmospheric fluctuations. The performance of the algorithm is investigated both analytically and by Monte Carlo simulations. Good agreement is achieved in relation to how the precision of the shift estimate depends on image parameters such as contrast, photon counts and readout noise, as well as the dependence on sampling format, zero-padding and field of view. Compared to the conventional method for extended object wavefront sensing, a reduction of the computational cost is gained at a marginal expense of precision.