Confusion Errors in Astrometry and Counterpart Association

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Abstract
In very crowded fields, the modulation of the background by the sea of unresolved faint sources induces centroid shifts. The errors increase with the number of sources per beam. Even the most optimistic simulations of imaging data show that position errors can become severe (on the order of the beam size) at flux levels at which images contain 1/50 to 1/15 sources per beam, depending on the slope of the number-flux relation d log N/d log S. These problems are expected to be significant for recent observations of faint submillimeter sources and may be the reason that some sources appear to lack optical counterparts.