Measuring the photon distribution by ON/OFF photodectors
  Reconstruction of photon statistics of optical states provide fundamental information on the nature of any optical field and find various relevant applications. Nevertheless, no detector that can reliably discriminate the number of incident photons is available. On the other hand the alternative of reconstructing density matrix by quantum tomography leads to various technical difficulties that are particular severe in the pulsed regime (where mode matching between signal an local oscillator is very challenging). Even if on/off detectors, as usual avalanche PhotoDiodes operating in Geiger mode, seem useless as photocounters, recently it was shown how reconstruction of photon statistics is possible by considering a variable quantum efficiency. Here we present experimental reconstructions of photon number distributions of both continuous-wave and pulsed light beams in a scheme based on on/off avalanche photodetection assisted by maximum-likelihood estimation. Reconstructions of the distribution for both semiclassical and quantum states of light (as single photon, coherent, pseudothermal and multithermal states) are reported for single-mode as well as for multimode beams. The stability and good accuracy obtained in the reconstruction of these states clearly demonstrate the interesting potentialities of this simple technique. 
M. Genovese, M. Gramegna, G. Brida, M. Bondani, G. Zambra, A.   Andreoni, A. R. Rossi, M. G. A. Paris