Aperture Photometry Uncertainties assuming Priors and Correlated Noise

We derive a general formula for the noise variance in the flux of a source estimated from aperture photometry assuming (i) prior pixel-flux uncertainties are available for the image (e.g., computed a priori from a noise model), and (ii) noise is correlated amongst pixels. Correlated noise usually occurs in re-sampled and interpolated images (e.g., mosaics), with the degree of correlation depending on the size of the interpolation kernel. The smoothing kernel moves noise-power from high to low spatial frequencies and therefore needs to be recaptured to properly quantify the uncertainty in the flux summed over a region. Ignorance of correlated-noise will lead to an underestimate of the final aperture-flux uncertainty. The 1-σ uncertainty is given by the square root of the variance expression below. A formalism for estimating uncertainties when one does not have access to priors and is content on ignoring correlated-noise is described in: http://web.ipac.caltech.edu/staff/fmasci/home/wise/ApPhotUncert.pdf