Absolute test for flat surfaces by shifted and rotated maps with yaw angle monitored

An absolute testing method for flat surfaces, termed the shifted and rotated maps with yaw angle monitored (SR-YAM) technique, has been developed. This approach requires only four measurement configurations: the initial position, a position translated along the x axis, a 90° rotated position, and a subsequent x -translation applied after the rotation. The relative yaw angles among these four configurations are precisely monitored using an autocollimator. The reconstruction model shows that this method can recover the absolute surface form at pixel-level resolution with no theoretical error including all the two-order terms. The proposed method exhibits both simplicity and completeness, necessitating only four test maps, two degrees of motion, and two flat surfaces. Theoretical simulations and experiments on flats were conducted and compared with the existing absolute data to show it can realize sub-nanometer accuracy.