Detection of atoms in a beam: filtering of the atomic shot noise and velocity dispersion contribution

We calculate the contribution of the atomic shot noise in the detection of the laser-induced fluorescence signal emitted by atoms in a beam. We point out a filtering of such a contribution which is the consequence of the finite transit time of the atoms through the laser beam. Moreover, we demonstrate that the distribution of the atomic velocities in the beam induces an extra noise which degrades the measured signal-to-noise ratio and modifies the observed statistics of the fluorescence photons emitted by the whole interaction zone.