Unified measures for optical fields: degree of polarization and effective degree of coherence

The connection between the degree of polarization and the effective degree of coherence is established. It is shown that from the formal point of view, the degree of polarization is a quantity analogous to the degree of coherence for scalar fields, provided that the coherence properties are examined as an average in some given domain. It is also demonstrated that the effective degree of coherence has a geometrical interpretation as the distance between the given mixed state and the incoherent state, normalized by the maximum distance in the geometry examined. The meaning of an analogous quantity in quantum optics is briefly discussed.