  The effects of anisoplanatism on the adaptive optics point spread function
are investigated. A model is derived that combines observations of the guide
star with an analytic formulation of anisoplanatism to generate predictions for
the adaptive optics point spread function at arbitrary locations within the
field of view. The analytic formulation captures the dependencies of
anisoplanatism on aperture diameter, observing wavelength, angular offset,
zenith angle and turbulence profile. The predictions of this model are compared
to narrowband 2.12 um and 1.65 um images of a 21 arcsec binary (mV=7.3, 7.6)
acquired with the Palomar Adaptive Optics System on the Hale 5 meter telescope.
Contemporaneous measurements of the turbulence profile made with a DIMM/MASS
unit are used together with images of the primary to predict the point spread
function of the binary companion. Predicted companion Strehl ratios are shown
to match measurements to within a few percent, whereas predictions based on the
isoplanatic angle approximation are highly discrepant. The predicted companion
point spread functions are shown to agree with observations to 10%. These
predictions are used to measure the differential photometry between binary
members to an accuracy of 1 part in 10^{3}, and the differential astrometry to
an accuracy of 1 mas. Errors in the differential astrometry are shown to be
dominated by differential atmospheric tilt jitter. These results are compared
to other techniques that have been employed for photometry, astrometry, and
high contrast imaging.
