Implications of complete coherence in the space-frequency domain

It was shown not long ago that complete spatial coherence of light at a pair of points in the space-time domain may be interpreted as a manifestation of so-called "statistical similarity" between the fluctuating field at the two points. In this Letter, we consider complete spatial coherence at a pair of points in the space-frequency domain and derive a condition that the field at those points must obey. We illustrate the usefulness of the condition by an example.