Three-dimensional stage self-calibration: A general theory framework

In this paper, a general self-calibration theory framework is presented for three-dimensional precision stages to determine the stage error. Four measurement views of a cubic artifact on the three-dimensional precision stage are utilized to provide the symmetry, transitivity and redundance. The firstorder components of the stage error, i.e., the nonorthogonality and the scale difference, are determined through the first three measurement views. And the residual components of the stage error are then figured out by a least-square based calculation law, which completes the stage error determination. Additionally, the parasitic errors related to the artifact and the misalignment errors of all measurement views can all be identified through algebraic manipulations. Computer simulation is finally carried out and the results validate that the proposed algorithm can accurately realize the stage error. The proposed scheme actually provides a framework as a principle to solve the three-dimensional self-calibration problem for practical engineers.