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

Abstract

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.

Phase Shifting Approaches and Multi-Channel Interferograms Position Registration for Simultaneous Phase-Shifting Interferometry: A Review

“…Qian et al [39] applied simultaneous phase shifting to Mach-Zender interferometry for dynamic measurement of liquid refractive index, in which the first-order diffraction energy from the used 2D Ronchi phase grating reaches about 60% of the total incident light energy. Chen et al [40][41][42] have established a SPSI based on 2D diffraction grating splitting and polarization phase-shifting technique, which is shown in Figure 7. In the polarized Twyman-Green structure, the measured information is introduced and two orthogonal linearly polarized beams emit through the PBS.…”

“…The polarizer mask including four linear polarizers is placed at angles of 0, π/4, π/2 and 3π/4 in a rectangular arrangement in a clockwise direction. Chen et al [40][41][42] have established a SPSI based on 2D diffraction grating splitting and polarization phase-shifting technique, which is shown in Figure 7. In the polarized Twyman-Green structure, the measured information is introduced and two orthogonal linearly polarized beams emit through the PBS.…”