Gram-Charlier matched filter for Shack-Hartmann sensing at low light levels

A study has been made of a Gram-Charlier matched filter for Shack-Hartmann sensing of wave-front slopes. The method is based on modeling the point-spread function by an expansion in terms of Gauss-Hermite polynomials. We present results for several subapertureycoherence area sizes both with and without CCD read noise. A more accurate estimation of the local slopes can be achieved at low light levels in this way than with the standard first-moment estimator.