Effects of random vibration in high-speed phase-shifting speckle pattern interferometry

The influence of random vibrations on a dynamic phase shifting speckle pattern interferometer, in which phase difference evaluation is performed using temporal phase shifting and temporal phase unwrapping, is investigated by means of experiments and numerical simulations. A well-defined velocity spectral density function, typical of the spectra found under non-vibration-isolated conditions, is used throughout. Five phase-shifting formulae are studied, with camera framing rates (1,2 and 4 kHz) typical of current dynamic speckle pattern interferometers. Two main aspects were evaluated: firstly the unwrapping reliability, and secondly the noise induced in the phase maps by the vibration. The former was found to be a significant constraint, even for peak velocities well below the Nyquist velocity limit of the interferometer, and is therefore likely to be more important than the latter in many applications. Three analytical criteria for determining the expected unwrapping success rate are proposed and their predictions compared with the measured values. It is demonstrated that shorter sampling windows and higher framing rates are preferred in order to increase the unwrapping success rate, but that longer windows reduce the root mean square error in the phase change maps due to the vibration.