Tip–tilt compensation for astronomical imaging

We present a performance analysis of tip–tilt-compensation systems that use natural stars as tilt references. Taking into account properties of the atmosphere and of the galactic stellar populations, we optimize the system operating parameters to determine performance limits for several varieties of tip–tilt-compensation system operating on a 10-m telescope on Mauna Kea, Hawaii. We find that, for systems that use a single tilt reference star, if the image of the star is uncorrected, a one-axis root-mean-square tilt residual of less than 190 nrad can be obtained for at least 99% of all astronomical objects, whereas if the image of the tilt reference star is fully corrected this limit drops to 90 nrad. For systems that use two tilt reference stars the limits drop to 160 nrad if the images of the stars are uncorrected and to 60 nrad if the images of the stars are fully corrected. These residual tilt levels would permit V-band images with long-exposure resolution of 8.5, 4.2, 7.3, and 2.9 times the diffraction limit, respectively, where the diffraction-limited resolution in the V band is 0.011 arcsec. These results may be compared with the typical seeing of 0.75 arcsec.