Multichannel unbalanced homodyning is proposed for measuring the densi
ty matrix of a single-mode optical field in the photon-number represen
tation. Combining the signal beam and the local oscillator by a high-t
ransmittance beam splitter, the interfering field is detected using mu
ltichannel photocounting. The density matrix is determined by direct s
tatistical sampling of the coincident events recorded for various valu
es of the local-oscillator phase. The usefulness of the method is demo
nstrated by computer simulations of measurements including error estim
ations.