DETECTION OF MOVEMENT WITH LASER SPECKLE PATTERNS - STATISTICAL PROPERTIES

We present an optical method for detection of in-plane movement of a d iffusing object. The technique is based on spatial filtering of the la ser speckle pattern, which is produced by illumination of the object w ith coherent light. Two interlaced differential comb photodetector arr ays act as a periodic filter to the spatial-frequency spectrum of the speckle pattern intensity. The detector produces a zero-offset, period ic output signal versus displacement that permits measurement of the m ovement 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 s ize and period of the comb photodetector arrays are matched, the outpu t signal versus displacement is quasi-sinusoidal with statistical ampl itude and phase. First-and second-order statistics of the signal are i nvestigated. First the probability density function and the autocorrel ation function of the complex Fourier transform of the speckle pattern intensity are determined. Then the statistical properties of the spec trum of the filtered signal and of the signal itself are calculated. I t turns out that the amplitude of the signal is Rayleigh distributed. Both the autocorrelation function of the signal and the probability de nsity function of the measured phase difference for a given displaceme nt are calculated. The potential accuracy of displacement measurements is analyzed. In addition, the signal quality is investigated with res pect to the geometry of the detector. The theoretical results are expe rimentally verified. (C) 1998 Optical Society of America.