  We introduce a new algorithm for interpolating measurements of the
point-spread function (PSF) using stars from many exposures. The principal
components of the variation in the PSF pattern from multiple exposures are used
to solve for better fits for each individual exposure. These improved fits are
then used to correct the weak lensing shapes. Since we expect some degree of
correlation in the PSF anisotropy across exposures, using information from
stars in all exposures leads to a significant gain in the accuracy of the
estimated PSF. It means that in general, the accuracy of PSF reconstruction is
limited not by the number density of stars per exposure, but by the stacked
number density across all exposures in a given survey. This technique is
applied to the 75 square degree CTIO lensing survey, and we find that the PSF
variation is well described by a small number of components. There is a
significant improvement in the lensing measurements: the residual stellar PSF
correlations are reduced by several orders of magnitude, and the measured
B-mode in the two-point correlation is consistent with zero down to 1
arcminute. We also discuss the applications of the PCA technique to future
surveys.
