  Photon counts statistics have recently been proven to provide a sensitive
observable for characterizing gamma-ray source populations and for measuring
the composition of the gamma-ray sky. In this work, we generalize the use of
the standard 1-point probability distribution function (1pPDF) to decompose the
high-latitude gamma-ray emission observed with Fermi-LAT into: (i) point-source
contributions, (ii) the Galactic foreground contribution, and (iii) a diffuse
isotropic background contribution. We analyze gamma-ray data in five adjacent
energy bands between 1 and 171 GeV. We measure the source-count distribution
dN/dS as a function of energy, and demonstrate that our results extend current
measurements from source catalogs to the regime of so far undetected sources.
Our method improves the sensitivity for resolving point-source populations by
about one order of magnitude in flux. The dN/dS distribution as a function of
flux is found to be compatible with a broken power law. We derive upper limits
on further possible breaks as well as the angular power of unresolved sources.
We discuss the composition of the gamma-ray sky and capabilities of the 1pPDF
method.
