Optically phase-locked electronic speckle pattern interferometer system performance for vibration measurement in random displacement fields

The performance of the optically phase-locked electronic speckle pattern interferometer (OPL-ESPI) in the presence of random noise displacements is analyzed. It is shown that a sufficient condition for high visibility of signal speckle contours is that the signal pattern lie within a region of completely spatially coherent noise, i.e., where the random components of the surface vibrations have equal amplitudes and are in phase, and that the region contain the OPL-ESPI system lock point. Under these conditions the effects of the noise vibrations within the region are canceled by the action of the OPL-ESPI optical phase-locked loop, and the complete signal speckle contour pattern is visible. The single-frame speckle contrast and the root-mean-square exposure for sequentially subtracted frames are evaluated for stationary, coherence-separable noise displacements that obey Gauss–Markov temporal statistics. It is shown that these functions decrease as the noise temporal bandwidth and the mean-square displacement difference between the observation point and the lock point increase. Experimental results that illustrate the theoretical development are presented.