Full-aperture surface reconstruction method for shift-rotation absolute measurement with tilt error suppression

Abstract

We propose a new surface reconstruction method for the absolute measurement of shift rotation that can obtain a full-aperture surface distribution. Our approach reduces the effect of tilt errors on surface reconstruction by increasing the translation ratio of the test mirror. This method requires the test mirror to be measured once in situ, after translation, and after rotation. Because the known measured wavefront is a nonlinear function of the absolute surface distribution, the function of the surface distribution is linearized by performing a Taylor expansion to achieve fast surface reconstruction. Finally, a linear system of equations is constructed to solve the absolute surface distribution. The coefficient matrix is sparse and can quickly and accurately reconstruct the absolute surface distribution. In the simulation, the root mean square error (RMSE) of the reconstructed surface distribution of the method discussed in this study can reach to 0.012nm. Moreover, our method can significantly reduce the effect of tilt errors compared with typical methods, thereby yielding a new, high-precision solution for absolute measurements in interferometry.