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The review describes the principles and examples of practical realization of diagnostic approaches based on the coherence theory, optical singularities and interference techniques. The presentation is based on the unified correlation-optics and coherence-theory concepts. The applications of general principles are demonstrated by several examples including the study of inhomogeneities and fluctuations in water solutions and methods for sensitive diagnostics of random phase objects (e.g., rough surfaces). The specific manifestations of the correlation-optics paradigms are illustrated in applications to non-monochromatic fields structured both in space and time. For such fields, the transient patterns of the internal energy flows (Poynting vector distribution) and transient states of polarization are described. The single-shot spectral interference is analyzed as a version of the correlation-optics approach adapted to ultra-short light pulses. As a characteristic example of such pulses, uniting the spatio-temporal and singular properties, the spatio-temporal optical vortices are considered in detail; their properties, methods of generation, diagnostics, and possible applications are exposed and characterized. Prospects of further research and applications are discussed.
Angelsky et al. (Mon,) studied this question.