Calibration of the astigmatism errors induced by misalignment of quadri-wave lateral shearing interferometer

Error calibration is one of the most important factors to realize the quadri-wave lateral shearing interferometer (QWLSI) with high accuracy. The misalignment errors of QWLSI, such as the tilt of grating and the tilt of charge coupled device (CCD), will affect the measurement accuracy. The astigmatism errors induced by the tilt of grating and CCD during the alignment process of QWLSI, which are neglected in previous studies, are analyzed and presented in analytical expressions in this paper. Firstly, the additional phase difference in X and Y directions induced by the tilt of grating and CCD are analyzed using the optical wave interference theory. Representing the phase difference in the two directions and the test wavefront with the combinations of Zernike polynomials respectively, we further obtain the analytical expressions between the Zernike coefficients of the phase difference and the Zernike coefficients of the test wavefront, according to the wavefront reconstruction theory. Then the analytical expressions for the measurement errors induced by the tilt of grating and CCD, which are mainly astigmatism, can be obtained. The analytical results show that the misalignment induced astigmatism errors are inversely proportional to the shearing ratio and proportional to the tilt angle of grating and CCD. The alignment experiment of a home-made QWLSI under null test condition is conducted to verify the correctness of the theoretical analysis. With different shearing ratios for the QWLSI, the astigmatism errors, which are induced by the tilt of grating in experimental results, are consistent with the theoretical analysis results. This paper can provide technical support for the alignment of QWLSI with small shearing ratio and high precision.