Abstract
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.
Highlights
Within the last ten years adaptive optics (AO) correction of astronomical images has become a standard technique on many observatories
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
Summary
Within the last ten years adaptive optics (AO) correction of astronomical images has become a standard technique on many observatories. If the reference object is a point source, the position of the center of intensity in the subimage defines a vectorial shift that is proportional to the average wavefront gradient over the corresponding lenslet. These vectorial shifts serve as sensor signals for controlling the actuators on a deformable mirror counteracting the wavefront error. An analytical model for the photon and readout noise induced RMS error to the shift estimate is derived. Analytical predictions of how the RMS error depends on object contrast, photon counts and readout noise are verified by simulations, as are the dependencies on sampling format, zero-padding and field of view (FoV). The reduction of computational cost for this method compared to the conventional method, based on the localization of the cross correlation peak [6], is discussed
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