Correction of Eccentricity Error in Absolute Flat Surface Testing by Shift-Rotation Method

Aiming at the problem of eccentricity error in shift-rotationn absolute measurement method in the detection process, a three-dimensional surface-based image registration eccentricity error correction method is proposed. First, the shift-rotation absolute measurement method is used to obtain the surface shape of the mirror under rotation 0 degrees and rotation 180 degrees. Then, the similarity function is constructed by using the 3D surface shape data to realize the registration of the tested mirror shape at 0 degrees and 180 degrees, so as to obtain the eccentricity error. The numerical simulation results show that the peak and valley value of the residual profile is 7. 783 nm and the square mean root value is 0.578 nm before the correction of the eccentricity error. After correcting the eccentricity error, the peak and valley value of the residual profile is 0. 034 nm, and the square mean root value is 0. 004 nm. The results show that the correction method is feasible and can effectively improve the measurement accuracy of the shift-rotation method, which provides an important reference for the absolute measurement of high-precision optical element surface.