A maximum likelihood method to improve faint-source flux and color estimates

Flux estimates for faint sources or transients are systematically biased high because there are far more truly faint sources than bright. Corrections that account for this effect are presented as a function of signal-to-noise ratio and the (true) slope of the faint-source number-flux relation. The corrections depend on the source being originally identified in the image in which it is being photometered. If a source has been identified in other data, the corrections are different; a prescription for calculating the corrections is presented. Implications of these corrections for analyses of surveys are discussed; the most important is that sources identified at signal-to-noise ratios of 4 or less are practically useless.