Dynamic statistical properties of laser speckle produced in the diffraction field from an out-of-plane vibrating object are studied theoretically and experimentally. The equations expressing the averaged power spectrum and the autocorrelation function of vibrating laser speckle intensity fluctuations are derived for the first time and evaluated numerically. An analysis of those equations shows that the statistical properties of the averaged power spectrum and the autocorrelation function of vibrating speckle are determined by a product of both the derivative value (vibration slope) of vibrating amplitudes of the object and the laser beam width used for illumination of the object. The correlation length and the power spectrum of vibrating speckle are investigated in detail as a function of the vibration slope of the object and the beam width of illumination. It is shown from numerical evaluation of the equations that the power spectral width of vibrating speckles is linearly dependent on the product of the vibration slope and the beam width except for extremely small values. Experiments confirming the theory were performed and show excellent agreement with the theoretical results.
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