Absolute surface metrology using gradient descent-optimized multi-surface phase-shifting interferometry for interferometer systematic error calibration.

Conventional surface measurement belongs to relative measurement, which offers a fast detection speed. However, the inherent wavefront error of the interferometer can affect the accuracy of surface detection. Therefore, it is necessary to use an absolute measurement method to calibrate the system error of the interferometer. Traditional rotation-based measurement methods are simple to operate but cannot separate the rotationally symmetric component of the test lens's surface. Moreover, they often require repeated rotations at the same angle, which may introduce rotational errors. The rotation-translation method can solve for rotationally symmetric errors but requires high-precision translation of the reference surface, making system calibration inconvenient. This paper combines multi-surface phase-shifting interferometry with the gradient descent algorithm with redistribution of rotationally symmetric terms to propose what we believe to be a novel rotation-based measurement method. It can automatically identify the rotation angle without requiring a constant rotation angle, while also eliminating the rotationally symmetric error that traditional rotation methods cannot separate. The measurement is completed with only one auxiliary test lens undergoing two rotational measurements. Simulation analysis shows that the surface root mean square (RMS) error of the proposed scheme is on the order of 10-4λ. Using this method, the system error of a self-built 4-inch aperture interferometer was conveniently detected and corrected. The results were compared with those from a reliable commercial interferometer, verifying the accuracy of the proposed scheme.