Vibration errors in phase-shifting interferometer

Abstract

Unexpected mechanical vibrations can significantly degrade the otherwise high accuracy of phase-shifting interferometer (PSI). Because the data acquisition takes place over time, sensitivity to vibration is as a function of the frequency, the phase, the amplitude of vibrations, the smoothness of test surface and the slope coefficient of reference plane. A complete, nonlinear, continuing mathematical model of PSI with well defined longitudinal and transverse vibrations is presented. The approach to quantifying vibration is using the discrete sum formula instead of the continuing integral model. Computer simulations are performed over a range of vibration frequencies and amplitudes for 4,7,11 and 15 frames phase-shift algorithms. Numerical simulation results demonstrate the methods to increase the accuracy of PSI is to choose more phase steps and higher speed CCD camera and PSI with small slope coefficient of reference surface and good smooth test surface has low sensitivity to transverse vibration. Finally programs basing on the phase-shifting interference theory are given to imitate the process of obtaining interferogram with vibrations. After intensity signal is processed through PSI algorithm and phase unwrapping algorithm, the sensitivity of PSI to vibration is achieved and described by the difference of the computer phase and test phase. The results of numerical simulation are supported by several examples on dummy experimental platform.