Absolute flat test by a coherent shift-rotation method with yaw-angle monitoring

A coherent shift-rotation method with yaw-angle monitoring (CSR-YAM) is proposed for the absolute measurement of flat surfaces. The method features a simple testing configuration and a convenient procedure, which requires only a single auxiliary mirror for yaw-angle monitoring and avoids redundant homing operation of the test surface. A corresponding surface reconstruction system is established based on the shift-rotation difference maps and the measured relative yaw angles, which is complete and can recover pixel-level absolute surface without theoretical error. Also, considering the high dimensionality of the reconstruction system, an efficient and low-cost iterative solver is provided for surface recovery. Simulations demonstrate the high accuracy, efficiency, and robustness of the proposed method, and experimental results show good agreement with direct measurements using a sub-nanometer root-mean-square (RMS) transmission flat.