  Strong correlations between the signal and idler beams imprinted during their
generation dominantly determine the properties of twin beams. They are also
responsible for the waves in intensity coherence observed in the wave-vector
space of a twin beam propagating in a nonlinear crystal in the regime with pump
depletion. These waves start to develop at certain twin-beam intensity and move
from the signal and idler beam centers towards their tails. They manifest
themselves via the change of coherence volume monitored in the far field by the
measurement of local modified $ \bar{g}^{(2)} $ function, which acts as a
sensitive and stable tool for investigating field intensity coherence.
