We present an optical method for detection of in-plane movement of a diffusing object. The technique is based on spatial filtering of the laser speckle pattern, which is produced by illumination of the object with coherent light. Two interlaced differential comb photodetector arrays act as a periodic filter to the spatial-frequency spectrum of the speckle pattern intensity. The detector produces a zero-offset, periodic output signal versus displacement that permits measurement of the movement at arbitrarily low speed. The direction of the movement can be detected with the help of the quadrature signal, which is produced by a second pair of interlaced comb photodetector arrays. When speckle size and period of the comb photodetector arrays are matched, the output signal versus displacement is quasi-sinusoidal with statistical amplitude and phase. First- and second-order statistics of the signal are investigated. First the probability density function and the autocorrelation function of the complex Fourier transform of the speckle pattern intensity are determined. Then the statistical properties of the spectrum of the filtered signal and of the signal itself are calculated. It turns out that the amplitude of the signal is Rayleigh distributed. Both the autocorrelation function of the signal and the probability density function of the measured phase difference for a given displacement are calculated. The potential accuracy of displacement measurements is analyzed. In addition, the signal quality is investigated with respect to the geometry of the detector. The theoretical results are experimentally verified.
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