Biased estimators and object-spectrum estimation in the method of deconvolution from wave-front sensing.

The method of deconvolution from wave-front sensing (DWFS), which is a method for improving the quality of astronomical images measured through atmospheric turbulence, uses simultaneous shortexposure measurements of both an image and the output of a wave-front sensor exposed to an image of the telescope pupil. The wave-front sensor measurements are used to reconstruct an estimate of the instantaneous generalized pupil function of the telescope, which is used to compute an estimate of the instantaneous optical transfer function (OTF). This estimate of the OTF is then used in a deconvolution procedure. We point out the existence and origin of an unnoticed bias in the estimator for the DWFS method. This bias leads to nonrandom errors in the estimated object spectrum beyond those expected to arise by virtue of low-pass filtering and noise, including the possibility of an overall system transfer function greater than unity at some spatial frequencies. An alternative measurement and postprocessing scheme to overco e this source of error is suggested.