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The first step toward doing high-precision astrometry is the measurement ofindividual stars in individual images, a step that is fraught with dangers whenthe images are undersampled. The key to avoiding systematic positional error inundersampled images is to determine an extremely accurate point-spread function(PSF). We apply the concept of the {\it effective} PSF, and show that in imagesthat consist of pixels it is the ePSF, rather than the often-used instrumentalPSF, that embodies the information from which accurate star positions andmagnitudes can be derived. We show how, in a rich star field, one can use theinformation from dithered exposures to derive an extremely accurate effectivePSF by iterating between the PSF itself and the star positions that we measurewith it. We also give a simple but effective procedure for representing spatialvariations of the HST PSF. With such attention to the PSF, we find that we areable to measure the position of a single reasonably bright star in a singleimage with a precision of 0.02 pixel (2 mas in WF frames, 1 mas in PC), butwith a systematic accuracy better than 0.002 pixel (0.2 mas in WF, 0.1 mas inPC), so that multiple observations can reliably be combined to improve theaccuracy by $\surd N$.Comment: 33 pp. text + 15 figs.; accepted by PAS

Toward High‐Precision Astrometry with WFPC2. I. Deriving an Accurate Point‐Spread Function