Limiting magnitude of reference source for Lucky Exposures

In order for the Lucky Exposures method to be successful, each short exposure must be re-centred based on an unresolved feature in a reference source which provides a measure of the PSF. If the imaging detector is limited by photon noise, the unresolved reference source must provide a few photons within the brightest speckle during one atmospheric coherence time in order for this method to be successful. This sets a limit on the faintest reference sources which can be used, which in turn limits the range of astronomical targets which can be observed. For I-band observations under good astronomical seeing conditions the limiting magnitude for high resolution observations with a $\sim2.5$ $m$ diameter telescope is in the range $I=17$ to $I=18$.