  We present a rigorous description of the general problem of aperture
photometry in high energy astrophysics photon-count images, in which the
statistical noise model is Poisson, not Gaussian. We compute the full posterior
probability density function for the expected source intensity for various
cases of interest, including the important cases in which both source and
background apertures contain contributions from the source, and when multiple
source apertures partially overlap. A Bayesian approach offers the advantages
that it allows one to (a) include explicit prior information on source
intensities, (b) propagate posterior distributions as priors for future
observations, and (c) use Poisson likelihoods, making the treatment valid in
the low counts regime. Elements of this approach have been implemented in the
Chandra Source Catalog.
