  We show that the full statistics of the two detectors outputs in a balanced
homodyne detection setup involving a local oscillator in an ideal coherent
state is experimentally accessible despite the excess noise existing in actual
laser sources. This possibility is illustrated using phase randomized coherent
states signals from which the statistics of Fock states can accurately be
obtained. The experimental verification of the recently predicted [K\"{u}hn and
Vogel, Phys. Rev. A, \textbf{98}, 013832 (2018)] two-detector correlation
probability for Fock states is presented for states $\vert 1 \rangle$ and
$\vert 2 \rangle$.
