Wigner function for nonparaxial wave fields

The generalized optical transfer function and the spectral correlation function are investigated for nonparaxial two-dimensional wave fields. The angle-impact marginal of the four-dimensional Wigner function is derived directly. For focused wave fields of semiangle greater than 90 degrees, the spectral correlation function exhibits overlapping and interference. For focused wave fields for which the semiangle is known to be less than 180 degrees, the magnitude and phase can be recovered directly from knowledge of the intensity in the focal region.