Heterodyne measurement of Wigner distributions for classical optical fields

We demonstrate a two-window heterodyne method for measuring the x-p cross correlation, ??(*)(x)? (p)?, of an optical field ? for transverse position x and transverse momentum p. This scheme permits independent control of the x and p resolution. A simple linear transform of the x-p correlation function yields the Wigner phase-space distribution. This technique is useful for both coherent and low-coherence light sources and may permit new biological imaging techniques based on transverse coherence measurement with time gating. We point out an interesting analogy between x-p correlation measurements for classical-wave and quantum fields.