  The statistics of the field structure in the vortex core surrounding phase
singularities in random wave fields are measured and calculated for diffusive
and localized waves. Excellent agreement is found between experiment and
theory. The variation of phase with geometric angle is deterministic, depending
only upon the eccentricity of elliptical intensity contours, whose probability
distribution is shown to be universal. The distribution of vorticity is shown
to reflect both the vorticity distribution in the Gaussian limit and the
mesoscopic distribution of total transmission.
