Self-Calibration of Precision XYθz Metrology Stages

This chapter studies the on-axis calibration for precision XYθz metrology stages and presents a holistic XYθz self-calibration approach. The proposed approach uses an artifact plate, specially designed with XY grid mark lines and angular mark lines, as a tool to be measured by the XYθz metrology stages. In detail, the artifact plate is placed on the uncalibrated XYθz metrology stages in four measurement postures or views. Then, the measurement error can be modeled as the construction of XYθz systematic measurement error (i.e. stage error), artifact error, misalignment error, and random measurement noise. With a new property proposed, redundance of the XYθz stage error is obtained, while the misalignment errors of all measurement views are determined by rigid mathematical processing. Resultantly, a least squarebased XYθz self-calibration law is synthesized for final determination of the stage error. Computer simulation is conducted, and the calculation results validate that the proposed scheme can accurately realize the stage error even under the existence of various random measurement noise. Finally, the designed artifact plate is developed and illustrated for explanation of a standard XYθz self-calibration procedure to meet practical industrial requirements.