Lucky imaging and speckle discrimination for the detection of faint companions with adaptive optics

We have analyzed the application of frame selection ("lucky imaging") to adaptive optics (AO), short-exposure observations of faint companions. We have used the instantaneous Strehl ratio as an image quality metric. The probability density function (PDF) of this quantity can be used to determine the outcome of frame selection in terms of optimizing the Strehl ratio and the peak-signal-to-noise-ratio of the shift-and-add image. In the presence of static speckles, frame selection can lead to both: improvement in resolution--as quantified by the Strehl ratio, as well as faint signal detectability--given by the peak-signal-to-noise-ratio. This theoretical prediction is confirmed with real data from AO observations using Lick Observatory's 3m Shane telescope, and the Palomar Observatory's 5m Hale telescope. In addition, we propose a novel statistics-based technique for the detection of faint companions from a sequence of AO-corrected exposures. The algorithm, which we call stochastic speckle discrimination, utilizes the "statistical signature" of the centre of the point spread function (PSF) to discriminate between faint companions and static speckles. The technique yields excellent results even for signals invisible in the shift-and-add images.