Accuracy of sampling quantum phase space in a photon counting experiment

We study the accuracy of determining the phase space quasi-distribution of a single quantized light mode by a photon counting experiment. We derive an exact analytical formula for the error of the experimental outcome. This result provides an estimate of the experimental parameters, such as the number of events, required to determine the quasi-distribution with assumed precision. Our analysis also shows that it is, in general, not possible to compensate for the imperfection of the photodetector in the numerical processing of the experimental data. The discussion is illustrated with Monte Carlo simulations of the photon counting experiment for the coherent state, the one photon Fock state, and the Schrodinger cat state.