Average distribution function ﹩\rho (f)﹩ of the fractional photon flux f from a point source in a given pixel. The solid and dashed red lines depict the distribution function for the effective detector PSF for two different pixel sizes: a HEALPix grid with resolution parameter ﹩\kappa =6﹩ (solid) and ﹩\kappa =7﹩ (dashed); see Section 3 for details. The dot-dotted blue line depicts the ﹩\kappa =6﹩ distribution function for a Gaussian PSF with a 68% containment radius resembling the one of the actual effective PSF. The average distributions have been derived from Monte Carlo simulations of ﹩5\times {10}^{4}﹩ fiducial point sources at random positions on the sky. The numerical resolution is ﹩{\rm{\Delta }}f=0.01.﹩