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

Abstract

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 leastsquares-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.Index Terms-Least squares, measurement noise, selfcalibration, stage error, xy metrology system.

A novel on-axis self-calibration approach for precision rotary metrology stages

“…In this paper, we design an artifact plate for rotary self calibration with angular mark lines different from previous researches [18], [19]. One example is shown in Fig.…”

“…Resuitantly, it needs complicated algebraic manipulations to determine the mis alignment errors, which seriously increases the complexity of the self-calibration scheme [18], [19], [21]. For angle self-calibration, an important property, i. e. , the circle closure principle, could directly bridge the gap between GN and Go, i. e. , when n = N -I, Gn+l = GN = Go, which significantly facilitate the self-calibration process.…”

“…• As the proposed scheme is inspired through the X-Y selt·-calibration scheme [18], [19], it has the potential to be integrated with the X -Y self-calibration for synthesis of an XY8z self-calibration strategy. One key issue is that artifact plate should be designed to include both angular and position marks.…”

“…This method is evaluated as a standard process and is followed by many researchers [19], [20], [21], [22], [23]. Inspired by this idea, and noting the problems of existing rotary selt'-calibration schemes, we develop an on-axis selt'-calibration approach for precision rotary metrology stages totally different from previous perspectives.…”

Self-Calibration of Precision XYθz Metrology Stages

“…Fourier transformation was employed in the scheme to meet the challenge of random measurement noise. This method is popularly followed by many engineers and researchers [18][19][20][21]. In [18], a self-calibration algorithm was developed to test the out-of-plane error of two-dimensional profiling stages.…”