Least-square based self-calibration of two-dimensional ultra-precision stages

This paper develops a comparative simple method for self-calibration of two-dimensional ultra-precision stages to effectively attenuate the effects of random measurement noise while previous attempts are often complex or under some impractical assumptions. In detail, by measuring a rigid artifact at several locations on the stage, a transitive calibration algorithm based on direct point-to-point comparison is synthesized to separate the systematic measurement error from the measurement error. Through the transitivity obtained from the offset operation and the redundance obtained as a result of repeated offset operations, a robust estimation of the systematic measurement errors can be obtained by a least-square solution of equations. The algorithm has been tested by computer with and without random measurement noise and the simulation results show that the proposed method can realize rather accurate self-calibration even under the existence of random measurement noise. The proposed strategy also provides new perspective as another alternative to solve the multi-dimensional self-calibration problems.