MEASUREMENTS OF THE ANGULAR-CORRELATION OF STELLAR CENTROID MOTION

Using a fast readout CCD camera we acquired data at frame rates of 20 Hz in order to investigate the problem of tilt anisoplanatism over scales of 1 arcmin. We find that differential image motion rises linearly between 10 arcsec and 1 arcmin. Extrapolating the conditions at the observing airmass to the zenith we find that, in order to guide to the diffraction limit of a 2.4 m telescope at 1 μ, a natural guide star must be within 39 arcsec of the target, even with perfect guiding and very bright guide stars. We performed simulations of a Kolmogorov spectrum phase error with a large outer scale length to compare guiding strategies. We find that the centroid and the median of a stellar image start differing significantly when the ratio of the telescope diameter to Fried's parameter describing the turbulence, D/r0, exceeds ∼25. With these simulations we examine the effects of guiding on the centroid, the median, and the brightest speckle. Guiding on the brightest speckle produces better central intensities, though using the centroid produces a stellar profile with less power in the wings. Application of cross-correlation techniques to the 20 Hz data shows that there is some evidence for persistent, detectable pattern motion at speeds up to 10 min of arc per second across the field of view, but these results are not interpretable in the context of a single pattern moving at a fixed velocity across the focal plane. We elucidate the differences between the G tilt and the Z tilt, and illustrate this with an algorithm for wave front reconstruction using a natural guide star for sensing tilt and a laser beacon for the higher-order wave front deformations. We show that in this case the centroid (i.e., the G tilt) is the easiest estimator of position to use with any hardware that measures local tilts of the wave front in subapertures. With this approach, detecting a coma in the guide star wave front and correcting for it becomes unnecessary. © 1995 American Astronomical Society.