Can two planar sources with the same sets of Stokes parameters generate beams with different degrees of polarization?

It is shown that two stochastic electromagnetic beams that propagate from the source plane z = 0 into the half-space z > 0 may have different degrees of polarization throughout the half-space, even though they have the same sets of Stokes parameters in the source plane. This fact is due to a possible difference in the coherence properties of the field in that plane, but other reasons are also possible. The result is illustrated by an example.