  We propose a general method for measuring an arbitrary observable of a
multimode electromagnetic field using homodyne detection with a single local
oscillator. In this method the local oscillator scans over all possible linear
combinations of the modes. The case of two modes is analyzed in detail and the
feasibility of the measurement is studied on the basis of Monte-Carlo
simulations. We also provide an application of this method in tomographic
testing of the GHZ state.
