Self-calibration algorithm for testing out-of-plane errors of two-dimensional profiling stages

Yoo, Seungwoo; Kim, Seung-Woo

doi:10.1016/j.ijmachtools.2004.01.017

Cited by 25 publications

(18 citation statements)

References 6 publications

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“…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.…”

Section: A Viewmentioning

confidence: 99%

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

Zhu

et al. 2013

2013 IEEE/ASME International Conference on Advanced Intelligent Mechatronics

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Ahstract-Precision rotary metrology stages need calibration technology to determine the stage error for improvement of angle measurement accuracy. In this paper, we study the calibration of precision rotary metrology stages, and present an on-axis angle self-calibration approach different from previous perspectives. Without resorting to specially designed angle com parators or added read-heads, the proposed scheme fully utilizes different measurement views of a newly designed artifact plate on the uncalibrated rotary stage. The measurement deviation of each mark line from its nominal angle position, is rigidly modeled as the combination of stage error, artifact error, misalignment error and random measurement noise. Based on the circle closure principle and mathematical definition of the axis orientation, the misalignment error of each measurement view can be directly determined by rigid algebraic processing. A least-square based calculation law is finally synthesized to determine the stage error. Computer simulation validates that the proposed method can realize the stage error accurately even there exist various random measurement noises. Finally, a practical description on how to measure the angular marks of different measurement views is provided. The proposed strat egy essentially provides a novel on-axis angle self-calibration principle with accuracy, simplicity and robustness orientation to meet industrial requirements.978-1-4673-5320-5/13/$31.00 ©2013 IEEE

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Section: A Viewmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Zhu

et al. 2013

2013 IEEE/ASME International Conference on Advanced Intelligent Mechatronics

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“…After calculating O and R, (15) and (18) (20) where P m,n = U 0,x,m,n − U 1,y,m,n − 2Oy n − 2Rx m , and Q m,n = U 0,y,m,n + U 1,x,m,n − 2Ox m + 2Ry n .…”

Section: B Viewmentioning

confidence: 99%

“…As an effective and economical calibration technique, selfcalibration has attracted much attention and has been applied to precision applications [12], [13] such as nanopositioners [14], profiling stages [15], scanning probe microscope [16], and coordinate measuring machines [17]. For example, Takac studied 1-D self-calibration and developed a calibration that made a set of tool graduation marks appear to have identical spacing with relative scale [18].…”

Section: Introductionmentioning

confidence: 99%

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

Zhu

et al. 2012

IEEE Trans. Instrum. Meas.

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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.

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“…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.…”

Section: Introductionmentioning

confidence: 99%

Self-Calibration of Precision XYθ_z Metrology Stages

Hu¹,

Zhu²,

Liu³

2019

Standards, Methods and Solutions of Metrology

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This chapter studies the on-axis calibration for precision XYθ z metrology stages and presents a holistic XYθ z 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 XYθ z metrology stages. In detail, the artifact plate is placed on the uncalibrated XYθ z metrology stages in four measurement postures or views. Then, the measurement error can be modeled as the construction of XYθ z systematic measurement error (i.e. stage error), artifact error, misalignment error, and random measurement noise. With a new property proposed, redundance of the XYθ z stage error is obtained, while the misalignment errors of all measurement views are determined by rigid mathematical processing. Resultantly, a least squarebased XYθ z 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 XYθ z self-calibration procedure to meet practical industrial requirements.

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Self-calibration algorithm for testing out-of-plane errors of two-dimensional profiling stages

Cited by 25 publications

References 6 publications

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

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

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

Self-Calibration of Precision XYθ_z Metrology Stages

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Self-calibration algorithm for testing out-of-plane errors of two-dimensional profiling stages

Cited by 25 publications

References 6 publications

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

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

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

Self-Calibration of Precision XYθz Metrology Stages

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Self-Calibration of Precision XYθ_z Metrology Stages