Simultaneous phase-shifting interferometry: immune to azimuth error of fast-axes in retarder array

Simultaneous phase-shifting interferometry based on a 2×2 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 π/2, π, 3π/2, and 2π 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.