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We generalize the concept of degree of polarization of single-mode fields to multi-mode fields by introducing a new parameter that we define degree of mutual coherence. The new definition enables characterizing by a single parameter the quality of the signal corrupted by various linear and nonlinear impairments at the output of an optical transmission system employing spatial division multiplexing. We propose two workable schemes based on standard optics to measure the degree of coherence, one valid for generic fields, another applying only to CW fields affected by ASE noise. We apply the notion of degree of mutual coherence to the characterization of the nonlinear mode coupling caused by two-pulse collisions in spatially multiplexed WDM systems. We show that a collision between pulses transmitted in different WDM channels produces nonlinear power transfer between degenerate spatial modes belonging to the same channel. Finally, we quantify the effect of multiple collisions in terms of reduction of the degree of mutual coherence under the assumption that uncorrelated messages are transmitted over different WDM channels.