Order parameters and the irreversible behavior of spatial coherence in the time and frequency domains

We analyze the relation between the space-frequency and space-time coherence properties of scalar optical fields when deterministic and/or random linear transformations are performed in the frequency domain. Particular attention is paid to the irreversibility of the coherence properties under random operations. We introduce two time-domain order parameters, neither of which can increase under random transformations that preserve the power spectrum. We also identify different classes of spectrally completely coherent stochastic fields that the descriptors of coherence introduce. The results can be useful in the research of light propagation through random media.