Algorithm for Autonomously Calibrating Reference Flat of Interferometer and Residual Influence of Linear Shift with Two-Flat Method

摘要

A two-flat method for autonomously calibrating the reference flat of an interferometer is proposed with mathematical analysis. The calibration method is comprised of two steps. The first step is multiple rotations of a specimen, and the second is multiple linear shifts of it. hi this study, the usual assumptions regarding the rotation are unnecessary, but the pitching error caused by a linear shift is assumed to be continuous with respect to the linear shift and approximated by zero for any sufficiently small linear shift. The flatness of a reference flat is determined based on the fact that the flatness derived mainly by rotation equals that derived mainly by linear shifts. Based on the above assumptions, the proposed algorithm, which is realized by mainly utilizing basic knowledge of linear algebra in functional space, can be used to determine the rotating tilt errors and linear shift errors, allowing the reference flat to be calibrated accurately, hi this paper, the mathematical algorithm for autonomously calibrating the reference flat is explained in detail.