  Even though the technology of adaptive optics (AO) is rapidly maturing,
calibration of the resulting images remains a major challenge. The AO
point-spread function (PSF) changes quickly both in time and position on the
sky. In a typical observation the star used for guiding will be separated from
the scientific target by 10" to 30". This is sufficient separation to render
images of the guide star by themselves nearly useless in characterizing the PSF
at the off-axis target position. A semi-empirical technique is described that
improves the determination of the AO off-axis PSF. The method uses calibration
images of dense star fields to determine the change in PSF with field position.
It then uses this information to correct contemporaneous images of the guide
star to produce a PSF that is more accurate for both the target position and
the time of a scientific observation. We report on tests of the method using
natural-guide-star AO systems on the Canada-France-Hawaii Telescope and Lick
Observatory Shane Telescope, augmented by simple atmospheric computer
simulations. At 25" off-axis, predicting the PSF full width at half maximum
using only information about the guide star results in an error of 60%. Using
an image of a dense star field lowers this error to 33%, and our method, which
also folds in information about the on-axis PSF, further decreases the error to
19%.
