  Interference of randomly scattered classical waves naturally leads to
familiar speckle patterns, where the wave intensity follows an exponential
distribution while the wave field itself is described by a circularly symmetric
complex normal distribution. In the It\^o-Schr\"odinger paraxial model of wave
beam propagation, we demonstrate how a deterministic incident beam transitions
to such a fully developed speckle pattern over long distances in the so-called
scintillation (weak-coupling) regime.
