Modified three-step iterative algorithm for phase-shifting interferometry in the presence of vibration

To suppress the sensitivity of phase-shifting interferometry to mechanical vibration, a modified three-step iteration algorithm (MTIA) is proposed. The wavefront phase, x-and y-directional phase shifts are calculated in three individual steps in an iteration cycle. MTIA solves the tilt factors of phase shift through orthogonal decomposition and linear regression, avoiding the nonlinear optimization. The advantage of MTIA lies in its ability of calculating and compensating tilt-shifting error and fringe contrast variation caused by vibration. The simulations show that MTIA could provide more accurate results than an algorithm without contrast compensation. The superiority of MTIA is demonstrated experimentally. The experiment results show that MTIA could suppress the effect of vibration on surface measurement, which is of amplitude larger than the wavelength and of frequency over a large range. MTIA manifests good insensitivity to exposure time increase as well. (C) 2015 Optical Society of America