The van Cittert-Zernike theorem is formulated for the normalized cross-spectral density matrix of fields emitted by spatially incoherent sources. This formulation shows that sources with homogeneous polarization characteristics at second-order lead in the far field to normalized cross-spectral density matrices that possess high-symmetry properties. These symmetry properties are lost with polarization inhomogeneities of the source. These results are illustrated with ring-shaped sources.
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