A Holistic Self-Calibration Algorithm for $xy$ Precision Metrology Systems

Self-calibration technology is an important approach with the utilization of an artifact plate with mark positions that are not precisely known to calibrate the precision metrology system. In this paper, we study the self-calibration of
$xy$
precision metrology systems and present a holistic self-calibration algorithm based on the least squares method. The proposed strategy utilizes three traditional measurement views of an artifact plate on the
$xy$
metrology stage and provides relevant symmetry, transitivity, and redundancy. The misalignment errors of all measurement views, particularly errors of the translation view, are totally determined by detailed mathematical manipulations. Consequently, a least-squares-based robust estimation law is synthesized to calculate the stage error even under the existence of random measurement noise. Computer simulation validates that the proposed method can accurately realize the stage error when there is no random measurement noise. Furthermore, the calculation accuracy of the proposed scheme under various random measurement noises is studied, and the results verify that the proposed algorithm can effectively attenuate the effects of random measurement noise. The proposed strategy, in fact, provides a well-understood solution to the
$xy$
self-calibration problem for engineers in practical applications.