Sub-nanometer misalignment aberrations calibration of the Fizeau interferometer for high-numerical-aperture spherical surface ultra-precision measurement

Misalignment aberrations in Fizeau interferometric testing system can significantly influence the measurement results in the case of high-numerical-aperture test spherical surfaces, and it is hard to separate the high-order misalignment aberrations from the measured data. The traditional calibration method, which is based on linear-approximation, is applicable in calibrating only the linear misalignment aberration in measurement of high-numerical-aperture spherical surfaces. Based on modified power term for interferometry and 4-overlapping averaging 9-frame algorithm, sub-nanometer accuracy high-order calibration method is proposed to calibrate the linear misalignment aberrations as well as high-order misalignment aberrations. Both the computer simulation and experimental results confirm the feasibility and accuracy of the proposed calibration technique, and sub-nanometer misalignment aberrations can be calibrated. The proposed method can also used in spherical surface ultra-precision measurement by other interferometric setups without foreknowledge of numerical aperture of the test surface.