  Spatio-spectral properties of twin beams at their transition from low to high
intensities are analyzed in parametric and paraxial approximations using the
decomposition into paired spatial and spectral modes. Intensity auto- and
cross-correlation functions are determined and compared in the spectral and
temporal domains as well as the transverse wave-vector and crystal output
planes. Whereas the spectral, temporal and transverse wave-vector coherence
increases with the increasing pump intensity, coherence in the crystal output
plane is practically independent on the pump intensity owing to the mode
structure in this plane. The corresponding auto- and cross-correlation
functions approach each other for larger pump intensities. Entanglement
dimensionality of a twin beam is determined comparing several approaches.
