Linear relations of partially polarized and coherent electromagnetic fields

We show that having a Wolf degree of coherence of unit modulus or having intrinsic degrees of coherence of unit modulus imply different relations between the electric fields of the light. The mean square meaning of such relations is discussed. On the one hand, we demonstrate that if the intrinsic degrees of coherence are equal to 1, then there is a linear relation between the electrical fields. On the other hand, we show that a Wolf degree of coherence of unit modulus corresponds to a stronger property that implies that the fields have to be proportional.