Spatial and spectral coherence of high-intensity twin-beam states propagating from the near-field to the far-field configurations is experimentally investigated by measuring intensity auto- and cross-correlation functions. The experimental setup includes a moving crystal and an iCCD camera placed at the output plane of an imaging spectrometer. Evolution from the tight near-field spatial position cross-correlations to the far-field momentum cross-correlations, accompanied by changeless spectral cross-correlations, is observed. Intensity autocorrelation functions and beam profiles are also monitored as they provide the number of degrees of freedom constituting the down-converted beams. The strength of intensity cross-correlations as an alternative quantity for the determination of the number of degrees of freedom is also measured. The relation between the beam coherence and the number of degrees of freedom is discussed.