  We suggest an iterative, maximum-likelihood-based, method to reconstruct the
photon number distribution of the steady state cavity field of a micromaser
starting from the statistics of the atoms leaving the cavity after the
interaction. The scheme is based on measuring the atomic populations of probe
atoms for different interaction times and works effectively using a small
number of atoms and a limited sampling of the interaction times. The method has
been tested by numerically simulated experiments showing that it may be
reliably used in any micromaser regime leading to high-fidelity reconstructions
for single-peaked distributions as well as for double-peaked ones and for
trapping states.
