Vibration error-compensation technique in phase shifting moire interferometry

Undesirable vibrations can greatly degrade the accuracy of phase shifting moire interferometry. Although moire interferometry is always equipped with a somehow elaborate system to dampen or to eliminate vibration, such as granite slab and air table, it is common to see the phase fluctuation of moire diagram attributable to the various vibration during the measurement process. The sensitivity of moire interferometry to vibration is rooted in the fundamental principles of the instrument. Typically, an imaging system collects interference patterns for a sequence of reference phases, and then a computer unwraps the original wave-front phase by analyzing the variations of intensity. Compared with classical interferometry, an experiment by grating rosette moire interferometry with different principle of image formation is carried out and a corresponding efficient phase calculation method is developed to eliminate or compensate the effects of mechanical vibrations. In the decomposition and reconstitution of phase-shifting fringe patterns using discrete Fourier series, the phase-shifting fundamental coefficients (a(0), a(1) and b(1)) are extracted from 10 samples in one phase shift cycle, with which three images with 120 degree intervals are obtained. Besides, a mathematical model for the phase error is derived by vibration frequency content or spectrum. Combined with traditional phase shifting algorithm, the proposed data post-processing technique can effectively reduce the phase ripple caused by vibrations. The result is supported by numerical simulations in MATLAB software and experiments with grating rosette moire interferometry.