  Properties of weak spatio-spectral twin beams in paraxial approximation are
analyzed using the decomposition into appropriate paired modes. Numbers of
paired modes as well as numbers of modes in the signal (or idler) field in the
transverse wave-vector and spectral domains are analyzed as functions of
pump-beam parameters. Spatial and spectral coherence of weak twin beams is
described by auto- and cross-correlation functions. Relation between the
numbers of modes and coherence is discussed.
