A transitive algorithm for self-calibration of two-dimensional ultra-precision stages

Self-calibration is one of the important approaches to obtain greater measurement accuracy in precision engineering applications. This paper presents a simple method for self-calibration of two-dimensional ultra-precision stages while previous attempts to solve this problem are often quite complicated or under some impractical assumptions. Specifically, by measuring a rigid artifact at three locations on the stage, a transitive algorithm based on direct point-to-point comparison is constructed to separate the stage error from the artifact error under some conditions. The proposed method also provides a framework for researchers to solve the self-calibration problem from another perspective. The algorithm has been tested by computer simulation and the simulation results show that the proposed method can achieve accurate self-calibration.