Wigner function of pulsed fields reconstructed by direct detection

We present the experimental reconstruction of the Wigner function of some optical states. The method is based on direct intensity measurements by non-ideal photodetectors operated in the linear regime. The signal state is mixed at a beam-splitter with a set of coherent probes of known complex amplitudes and the probability distribution of the detected photons is measured. The Wigner function is given by a suitable sum of these probability distributions measured for di®erent values of the probe. For comparison, the same data are analyzed to obtain the number distributions and the Wigner functions for photons.