We suggest a method for measuring the photon number distribution and the de
nsity matrix of a single-mode radiation field. The setup consists of a chai
n of active ring cavities, each fed by a strong coherent probe and coupled
to the signal through cross-Kerr phase modulation. Each cavity is set at re
sonance by a different Fock component of the signal, so that the detection
probability at the cavities output is proportional to the signal photon sta
tistics. The off-diagonal elements of the density matrix can be evaluated b
y measuring the photon statistics of a set of displaced signal states. The
suggested setup allows a reliable state measurement even with low quantum e
fficiency at detectors.