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Given the basic parameters of a cosmic shear weak lensing survey, how wellcan systematic errors due to anisotropy in the point spread function (PSF) becorrected? The largest source of error in this correction to date has been theinterpolation of the PSF to the locations of the galaxies. To address thiserror, we separate the PSF patterns into components that recur in multipleexposures/pointings and those that vary randomly between different exposures(such as those due to the atmosphere). In an earlier study we developed aprincipal component approach to correct the recurring PSF patterns (Jarvis andJain 2004). In this paper we show how randomly varying PSF patterns can also becircumvented in the measurement of shear correlations. For the two-pointcorrelation function this is done by simply using pairs of galaxy shapesmeasured in different exposures. Combining the two techniques allows us totackle generic combinations of PSF anisotropy patterns. The second goal of thispaper is to give a formalism for quantifying residual systematic errors due toPSF patterns. We show how the main PSF corrections improve with increasingsurvey area (and thus can stay below the reduced statistical errors), and weidentify the residual errors which do not scale with survey area. Our formalismcan be applied both to planned lensing surveys to optimize instrumental andsurvey parameters and to actual lensing data to quantify residual errors.Comment: 18 pages, 1 figure; revised submission with minor edit

PSF anisotropy and systematic errors in weak lensing surveys