The problem of the dynamics of speckles in the image plane of the object, caused by random movements of scattering centers is solved. We consider three cases: 1) during the observation the points move at random, but constant speeds, and 2) the relative displacement of any pair of points is a continuous random process, and 3) the motion of the centers is the sum of a deterministic movement and random displacement. For the cases 1) and 2) the characteristics of temporal and spectral autocorrelation function of the radiation intensity can be used for determining of individually and the average relative displacement of the centers, their dispersion and the relaxation time. For the case 3) is showed that under certain conditions, the optical signal contains a periodic component, the number of periods is proportional to the derivations of the deterministic displacements. The results of experiments conducted to test and application of theory are given.

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