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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. [ABSTRACT FROM AUTHOR]

In ptychography, the precise axial distance between the sample and the detector is of vital importance to retrieve the tested object with high quality, but the axial distance error cannot be entirely eliminated in the practical experiments. An autofocusing strategy based on dichotomy is proposed to rapidly correct the axial distance error. In this strategy, the total variation function that is valid for both amplitude- and phase-modulating specimens is applied to determine whether the current distance is smaller or larger than the true distance. Further, the dichotomy is used to exponentially shrink the step-size of the correction by iterative computations, which means that for the early iterations large modified step-size is used and for later iterations only small step-size is considered. Therefore, the dichotomy is beneficial to quickly confirm the accurate axial distance with few computations. Simulations and experiments are conducted to demonstrate that our proposed strategy, based on the extended ptychographic iterative engine (ePIE), is capable of calibrating the sample–detector distance with high accuracy and efficiency. [ABSTRACT FROM AUTHOR]