Speckle and fringe dynamics in imaging-speckle-pattern interferometry for spatial-filtering velocimetry

This paper analyzes the dynamics of laser speckles and fringes, formed in an imaging-speckle-pattern interferometer with the purpose of sensing linear three-dimensional motion and out-of-plane components of rotation in real time, using optical spatial-filtering-velocimetry techniques. The ensemble-average definition of the cross-correlation function is applied to the intensity distributions, obtained in the observation plane at two positions of the object. The theoretical analysis provides a description for the dynamics of both the speckles and the fringes. The analysis reveals that both the magnitude and direction of all three linear displacement components of the object movement can be determined. Simultaneously, out-of-plane rotation of the object including the corresponding directions can be determined from the spatial gradient of the in-plane fringe motion throughout the observation plane. The theory is confirmed by experimental measurements.