The source-count distribution as a function of their flux , \mathrm { d } N / \mathrm { d } S , is one of the main quantities characterizing gamma-ray source populations .
We employ statistical properties of the Fermi Large Area Telescope ( LAT ) photon counts map to measure the composition of the extragalactic gamma-ray sky at high latitudes ( |b| \geq 30 ^ { \circ } ) between 1 GeV and 10 GeV .
We present a new method , generalizing the use of standard pixel-count statistics , to decompose the total observed gamma-ray emission into ( a ) point-source contributions , ( b ) the Galactic foreground contribution , and ( c ) a truly diffuse isotropic background contribution .
Using the 6-year Fermi -LAT data set ( P7REP ) , we show that the \mathrm { d } N / \mathrm { d } S distribution in the regime of so far undetected point sources can be consistently described with a power law of index between 1.9 and 2.0 .
We measure \mathrm { d } N / \mathrm { d } S down to an integral flux of \sim 2 \times 10 ^ { -11 } \mathrm { cm } ^ { -2 } \mathrm { s } ^ { -1 } , improving beyond the 3FGL catalog detection limit by about one order of magnitude .
The overall \mathrm { d } N / \mathrm { d } S distribution is consistent with a broken power law , with a break at 2.1 ^ { +1.0 } _ { -1.3 } \times 10 ^ { -8 } \mathrm { cm } ^ { -2 } \mathrm { s } ^ { -1 } .
The power-law index n _ { 1 } = 3.1 ^ { +0.7 } _ { -0.5 } for bright sources above the break hardens to n _ { 2 } = 1.97 \pm 0.03 for fainter sources below the break .
A possible second break of the \mathrm { d } N / \mathrm { d } S distribution is constrained to be at fluxes below 6.4 \times 10 ^ { -11 } \mathrm { cm } ^ { -2 } \mathrm { s } ^ { -1 } at 95 % confidence level .
The high-latitude gamma-ray sky between 1 GeV and 10 GeV is shown to be composed of \sim 25 % point sources , \sim 69.3 % diffuse Galactic foreground emission , and \sim 6 % isotropic diffuse background .