Determination of Density Matrices from Field Distributions and Quasiprobabilities

It is shown that the density matrix elements of a radiation mode in a chosen field strength representation can be obtained from the field strength distributions (with the phase being varied in a π interval) by a twofold Fourier transformation, and from the quasiprobability distributions P(α; s) (s < 0) by a threefold one. The method also applies, in principle, to the smoothed distributions observed in balanced homodyne (four-port and eight-port) detections with detector efficiencies less than unity.