Phase extraction using multi-directional moiré fringes for multi-lateral shearing interferometry

The multi-lateral shearing interferometers (multi-LSIs) are featured in the improved accuracy and noise resistance of wavefront reconstruction using phase differences in multiple directions. Nowadays the multidirectional phase differences are usually extracted from multi-LSIs' interferogram using the fast Fourier transform (FFT) method, whose accuracy is limited by spectral leakage effect. To improve the measurement accuracy of multi-LSIs, a phase extraction method developed from moiré technique is proposed in this paper. Using virtual gratings with properly large carrier frequencies, the desired phase information in each of the multiple directions can be modulated into low-frequency domain of the corresponding moiré pattern with larger separations between unnecessary side lobes. In this way, low-pass filters with higher cut-off frequencies can be applied in moiré technique to reduce the inaccuracy induced by spectral leakage effect. Meanwhile, phase shifting method can be applied to extract phase information from a single fringe pattern with better noise resistance by easily introducing phase shifts in computer generated virtual gratings. Simulation results show that the proposed method has higher accuracy and better anti-noise performance than the FFT method when spectral leakage effect exists. To demonstrate accuracy of the proposed method, a null test experiment of the quadriwave LSI has been conducted and experimental results show that measurement accuracy of the quadriwave LSI can be significantly improved by substituting the FFT method with the proposed method in phase extraction process.