Diffraction mathematical model of a laser speckle interferometer of transverse displacements of a scattering object

On the basis of diffraction transformations of wave fields, a mathematical model of a speckle interferometer of transverse displacements of a scattering object has been developed and numerical modeling of speckle-modulated interference patterns and signals at the output of the interferometer has been performed. Numerical calculations of the spatial distribution of complex amplitudes of wave fields in an interferometer were used for modeling when the displaced scattering surface was illuminated by two obliquely incident laser Gaussian beams. A statistical numerical experiment was performed to determine the measurement error of the scattering surface displacement caused by the change of realizations of interfering speckle fields. The simulation results are in good agreement with the results of experimental studies of transverse displacements in the range up to 600 micrometers.