Hybrid self-calibration method for reference surface elimination in subaperture stitching interferometry

Subaperture stitching interferometry (SSI) is an essential method for the map testing of large-aperture optical components. The surface map of a reference surface is a typical error source. In this study, we propose a hybrid self-calibration method to eliminate the reference surface error in SSI by combining the modified shift-rotation method and the maximum likelihood method. The traditional shift-rotation method is a general full-aperture absolute interferometric measurement that can retain localized irregularities. The shift-rotation operations are leveraged to generate a couple of subapertures covering the surface under test, whereby a ring of subapertures and a central subaperture are acquired by rotations and a lateral shift, respectively. The modified shift-rotation method is proposed to obtain the rotationally asymmetric components of the test surface in the ring of subapertures. The same components within the central subaperture are retrieved using the maximum likelihood method. Then, the rotationally symmetric components of the test surface are acquired using the least squares method, utilizing the measured data before and after the shift. Reference surface maps are sufficiently eliminated from the measured data. High-frequency components of the test surface are also retained, which engender high-accuracy SSI. Simulations are conducted to verify the proposed method. The positioning errors of the proposed method are analysed and discussed. Subaperture testing experiments of a 100-mm aperture flat are performed and compared with full-aperture absolute measurement results. The stitched errors with 0.018 2 PV and 0.003 2 RMS are obtained.