We demonstrate a two-window heterodyne method for measuring the <i>x</i>–<i>p</i> cross correlation, 〈Έ<sup>*</sup>(<i>x</i>)Έ (<i>p</i>)〉, of an optical field Έ for transverse position x and transverse momentum <i>p</i>. This scheme permits independent control of the <i>x</i> and <i>p</i> resolution. A simple linear transform of the <i>x</i>–<i>p</i> 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 <i>x</i>–<i>p</i> correlation measurements for classical-wave and quantum fields.
© 1999 Optical Society of America
(000.1600) General : Classical and quantum physics
(030.1640) Coherence and statistical optics : Coherence
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(270.6570) Quantum optics : Squeezed states
K. F. Lee, F. Reil, S. Bali, A. Wax, and J. E. Thomas, "Heterodyne measurement of Wigner distributions for classical optical fields," Opt. Lett. 24, 1370-1372 (1999)