Connection of electromagnetic degrees of coherence in space-time and space-frequency domains

We study the relationship between the electromagnetic degrees of coherence of stationary random fields in the space-time and space-frequency domains. In contrast to a known result on scalar fields, it appears that, due to the structure of the electromagnetic degree of coherence, no general closed-form relationship exists for the electromagnetic degrees in the two domains. However, relations that illustrate the similarities and differences between the two quantities can be established by specific considerations covering quasi-monochromatic and broadband situations of electromagnetic Gaussian Schell-model beams and blackbody radiation.