  Random optical fields with two widely different correlation lengths generate
far field speckle spots that are themselves highly speckled. We call such
patterns speckled speckle, and study their critical points (singularities and
stationary points) using analytical theory and computer simulations. We find
anomalous spatial arrangements of the critical points and orders of magnitude
anomalies in their relative number densities, and in the densities of the
associated zero crossings.
