Intensity critical point correlation functions in random wave fields

Correlations at critical points of the intensity are studied in gaussian random wave fields. Speckle spots are shown to be congruent, i.e. to have a shape and width that is substantially independent of the peak intensity. Unusual correlations between the real and imaginary parts of the wave function and between their derivatives are found at speckle spot maxima. These correlations are identically zero when averaged over the whole wave field.