Abstract

Simultaneous phase-shifting interferometry based on a $2\times 2$ retarder array with random fast-axes (RARF-SPSI) is proposed for real-time wavefront measurements. The retarder array is used as the phase-shift component, where the phase retardances are $\pi /2$, $\pi$, $3\pi /2$, and $2\pi$ and the four fast-axes of the four retarders can be somewhat random. In this paper, the mathematical model of RARF-SPSI is built by using a Stokes vector and a Mueller matrix, the phase demodulation method through solving equations is derived, and the coefficient matrix of the equations that is associated with the azimuth of the fast-axes is calculated by Fourier analysis. Then the corresponding simulation analysis is executed. In the experiment, four simultaneous phase-shifting interferograms are captured and the phase distribution under test is demodulated through the proposed method. Compared with the four-bucket phase-shifting algorithm adopted in traditional simultaneous phase-shifting interferometry, the ripple error is suppressed well. The advantage of the proposed RARF-SPSI is that there is no need to calibrate the fast-axes of the phase-shift component before measuring; in other words, the phase demodulation error caused by the azimuth error of fast-axes is eliminated.

© 2015 Optical Society of America

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