  For ground-based optical imaging with current CCD technology, the Poisson
fluctuations in source and sky background photon arrivals dominate the noise
budget and are readily estimated. Another component of noise, however, is the
signal from the undetected population of stars and galaxies. Using injection of
artificial galaxies into images, we demonstrate that the measured variance of
galaxy moments (used for weak gravitational lensing measurements) in Dark
Energy Survey (DES) images is significantly in excess of the Poisson
predictions, by up to 30\%, and that the background sky levels are
overestimated by current software. By cross-correlating distinct images of
"empty" sky regions, we establish that there is a significant image noise
contribution from undetected static sources (US), which on average are mildly
resolved at DES resolution. Treating these US as a stationary noise source, we
compute a correction to the moment covariance matrix expected from Poisson
noise. The corrected covariance matrix matches the moment variances measured on
the injected DES images to within 5\%. Thus we have an empirical method to
statistically account for US in weak lensing measurements, rather than
requiring extremely deep sky simulations. We also find that local sky
determinations can remove the bias in flux measurements, at a small penalty in
additional, but quantifiable, noise.
