Getting lucky with adaptive optics: diffraction-limited resolution in the visible with current AO systems on large and small telescopes

We have recently demonstrated diffraction-limited resolution imaging in the visible on the 5m Palomar Hale telescope. The new LAMP instrument is a Lucky Imaging backend camera for the Palomar AO system. Typical resolutions of 35-40 mas with Strehls of 10-20% were achieved at 700nm, and at 500nm the FWHM resolution was as small as 42 milliarcseconds. In this paper we discuss the capabilities and design challenges of such a system used with current and near future AO systems on a variety of telescopes. In particular, we describe the designs of two planned Lucky Imaging + AO instruments: a facility instrument for the Palomar 200" AO system and its PALM3K upgrade, and a visible-light imager for the CAMERA low-cost LGS AO system planned for the Palomar 60" telescope. We introduce a Monte Carlo simulation setup that reproduces the observed PSF variability behind an adaptive optics system, and apply it to predict the performance of 888Cam and CAMERA. CAMERA is predicted to achieve diffraction-limited resolution at wavelengths as short as 350 nm. In addition to on-axis resolution improvements we discuss the results of frame selection with the aim of improving other image parameters such as isoplanatic patch sizes, showing that useful improvements in image quality can be made by Lucky+AO even with very temporally and spatially undersampled data.