Abstract

A broad class of partially deterministic fields is considered, which includes the fields permitting prediction over limited distances on the basis of an idealized (model) statement of a problem. It is suggested that a measure of the partial determinism of optical fields should be the degree of determinism D, defined as a normalized coefficient of correlation between the intensities of a measured and a model (calculated) field. The correlation coefficient is calculated using hybrid averaging, namely, space averaging over a finite region combined with ordinary statistical averaging of a quantity in an empirical or theoretical sense. Complicated wave fields in optics, say, those in multimode optical waveguides or inhomogeneous speckle fields, are considered partially deterministic and hence partially predictable. Estimates are given for the distances of deterministic behavior (longitudinal, ζdet, and transverse, ρdet) of the fields in question. It is established that these distances may markedly exceed the corresponding correlation lengths (ζc and ρc). Outside the region of deterministic behavior, optical fields are unpredictable, and in this sense they are random.

© 1987 Optical Society of America

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