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Three-dimensional coherence matrix and degree of polarization

Inspecting three-dimensional partially polarized light fields we show that there is no unambiguous correspondence between the three-dimensional field and coherence matrix (or light beam tensor). Therefore, it is needed to clarify the definition of unpolarized light. We believe that unpolarized field should be treated as light of equiprobable polarizations similar to the case of two-dimensional light. Then degree of polarization bridges two definitions of the three-dimensional degrees of polarization known in literature. We reveal that only 6 Stokes parameters are sufficient to describe the coherence matrix. All these parameters can be retrieved from the in-plane measurements of two-dimensional coherence matrices.