We present a study of the effect of crowding on stellar photometry. We develop an analytical model through which we are able to predict the error in magnitude and color for a given star for any combination of telescope resolution, stellar luminosity function, background surface brightness, and distance. We test our predictions with Monte Carlo simulations of the LMC globular cluster NGC 1835, for resolutions corresponding to a seeing-limited telescope, the $HST$, and an AO-corrected 30-m (near diffraction limited) telescope. Our analytically predicted magnitude errors agree with the simulation results to within $sim$20%. The analytical model also predicts that errors in color are strongly affected by the correlation of crowding--induced photometric errors between bands as is seen in the simulations. Using additional Monte Carlo simulations and our analytical crowding model, we investigate the photometric accuracy which 30-m and 100-m Extremely Large Telescopes (ELTs) will be able to achieve at distances extending to the Virgo cluster. We argue that for stellar populations work, ELTs quickly become crowding-limited, suggesting that low--Strehl AO systems may be sufficient for this type of science.
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