TIP-TILT COMPENSATION - RESOLUTION LIMITS FOR GROUND-BASED TELESCOPES USING LASER GUIDE STAR ADAPTIVE OPTICS

The angular resolution of long-exposure images from ground-based telescopes equipped with laser guide star adaptive optics systems is fundamentally limited by the accuracy with which the tip-tilt aberrations introduced by the atmosphere can be corrected. Assuming that a natural star is used as the tilt reference, the residual error due to tilt anisoplanatism can significantly degrade the long-exposure resolution even if the tilt reference star is separated from the object being imaged by a small angle. Given the observed distribution of stars in the sky, the need to find a tilt reference star quite close to the object restricts the fraction of the sky over which long-exposure images with diffraction limited resolution can be obtained. In this paper, we present a comprehensive performance analysis of tip-tilt compensation systems that use a natural star as a tilt reference, taking into account properties of the atmosphere and of the Galactic stellar populations, and optimizing over the system operating parameters to determine the fundamental limits to the long-exposure resolution. Our results show that for a 10 m telescope on Mauna Kea, if the image of the tilt reference star is uncorrected, about half the sky can be imaged in the V band with long-exposure resolution less than 60 mas, while if the image of the tilt reference star is fully corrected, about half the sky can be imaged in the V band with long-exposure resolution less than 16 mas. Furthermore. V-band images with long-exposure resolution less than 16 mas may be obtained with a 10 m telescope on Mauna Kea for unresolved objects brighter than magnitude 22 that are fully corrected by a laser guide star adaptive optics system. This level of resolution represents approximately 70% of the diffraction limit of a 10 m telescope in the V band and is more than a factor of 45 better than the median seeing in the V band on Mauna Kea.