We revisit the spectral coherence properties of far-field radiation emanating from an aperture in a blackbody cavity on the basis of Kirchhoff's boundary conditions. We point out that the far zone cross-spectral density matrix derived earlier in the literature by separately propagating all three aperture-field components does not show transversality of the field at nonparaxial directions. This is not the case when Luneburg's diffraction integrals are applied on the transverse source field components to determine the entire far field. We compare the electromagnetic degrees of coherence for the two methods and show that over important angular separations their values coincide with high accuracy. The results of this work and of others concerning the far-field intensity, polarization, and paraxial angular coherence are in full agreement.
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