Generalized Two-Point Method Using Inverse Filtering for Surface Profile Measurement – Theoretical Analysis and Experimental Results for Error Propagation –

Eiki Okuyama; Hiromi Ishikawa

doi:10.20965/ijat.2014.p0043

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IJAT Vol.8 No.1 pp. 43-48

doi: 10.20965/ijat.2014.p0043

(2014)

Paper:

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Generalized Two-Point Method Using Inverse Filtering for Surface Profile Measurement – Theoretical Analysis and Experimental Results for Error Propagation –

Eiki Okuyama and Hiromi Ishikawa

Akita University, Akita 010-8502, Japan

Received:

August 1, 2013

Accepted:

November 1, 2013

Published:

January 5, 2014

Keywords:

surface profile measurement, straightness, generalized two-point method, error propagation, software datum

Abstract

Error separation techniques of the surface profile from parasitic motions have been developed for the straightness profile measurement of a mechanical workpiece. These are known as software datums, which separate the surface profile from the parasitic motions by using multiple sensors and/or multiple orientations. The authors proposed a generalized twopoint method that used the difference with either integration or inverse filtering. This method can take any sampling interval. In this article, the relationship between the ratio of the sensor distance to the sampling interval and the error propagation at the lowest spatial frequency is clarified. Furthermore, experimental results are described to support the theoretical analysis of the error propagation.

Cite this article as:

E. Okuyama and H. Ishikawa, “Generalized Two-Point Method Using Inverse Filtering for Surface Profile Measurement – Theoretical Analysis and Experimental Results for Error Propagation –,” Int. J. Automation Technol., Vol.8 No.1, pp. 43-48, 2014.

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References

[1] D. J. Whitehouse, “Some theoretical aspects of error separation techniques in surface metrology,” J. of Physics E, Scientific Instruments, 9, 531-536, 1976.
[2] H. Tanaka and H. Sato, “Basic characteristics of straightness measurement method by two sequential points,” Transactions of the JSME(C), 48, 436, 1930-1937, 1982.
[3] S. Kiyono, E. Okuyama, and M. Sumita, “Study on measurement of surface undulation (2nd report),” J. of JSPE, 54, 3, 513-518, 1988. (in Japanese)
[4] C. J. Evans et. al., “Self-Calibration: Reversal, Redundancy, Error Separation, and ‘Absolute testing’,” Annuals of CIRP, 45, 617-634, 1996.
[5] I. Weingartner and C. Elster, “System of four distance sensors for high-accuracy measurement of topography,” Precision Engineering, 28, 164-170, 2004.
[6] P. Yang, et. al., “Multi-probe scanning system comprising three laser interferometers and one autocollimator for measuring flat bar mirror profile with nanometer accuracy,” Precision Engineering, 35, 686-692, 2011.
[7] A. Dubra, C. Paterson, and C. Dainty, “Wave-front reconstruction from shear phase maps by use of the discrete Fourier transform,” Applied optics, 43, 5, 1108-1113, 2004.
[8] C. Elster, “Exact wave-front reconstruction from two lateral shearing interferograms,” Optical society of America, 16, 9, 2281-2285, 1999.
[9] X. Shen, K. Kotani, and K. Takamasu, “Study on spatial frequency domain 2-point method,” J. of JSPE, 73, 6, 653-658, 2007. (in Japanese)
[10] E. Okuyama and Y. Ishizuka, “Generalized two-point method for straightness error motion measurement in low spatial frequency domain,” Proc. of the 12th EUSPEN int. conf., 2012.
[11] E. Okuyama, Y. Ishizuka, and H. Ishikawa, “Generalized twopoint method using inverse filtering for straightness profile measurement,” Proc. of the ICPT, 2012.
[12] E. Okuyama, H. Takahashi, and H. Ishikawa, “Software Datum Design for Cross-Axis Motion Measurement of X-Stage Based on Least Uncertainty Criterion,” Int. J. of Automation Technology, Vol.5, No.2, 2011.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] D. J. Whitehouse, “Some theoretical aspects of error separation techniques in surface metrology,” J. of Physics E, Scientific Instruments, 9, 531-536, 1976.

[2] [2] H. Tanaka and H. Sato, “Basic characteristics of straightness measurement method by two sequential points,” Transactions of the JSME(C), 48, 436, 1930-1937, 1982.

[3] [3] S. Kiyono, E. Okuyama, and M. Sumita, “Study on measurement of surface undulation (2nd report),” J. of JSPE, 54, 3, 513-518, 1988. (in Japanese)

[4] [4] C. J. Evans et. al., “Self-Calibration: Reversal, Redundancy, Error Separation, and ‘Absolute testing’,” Annuals of CIRP, 45, 617-634, 1996.

[5] [5] I. Weingartner and C. Elster, “System of four distance sensors for high-accuracy measurement of topography,” Precision Engineering, 28, 164-170, 2004.

[6] [6] P. Yang, et. al., “Multi-probe scanning system comprising three laser interferometers and one autocollimator for measuring flat bar mirror profile with nanometer accuracy,” Precision Engineering, 35, 686-692, 2011.

[7] [7] A. Dubra, C. Paterson, and C. Dainty, “Wave-front reconstruction from shear phase maps by use of the discrete Fourier transform,” Applied optics, 43, 5, 1108-1113, 2004.

[8] [8] C. Elster, “Exact wave-front reconstruction from two lateral shearing interferograms,” Optical society of America, 16, 9, 2281-2285, 1999.

[9] [9] X. Shen, K. Kotani, and K. Takamasu, “Study on spatial frequency domain 2-point method,” J. of JSPE, 73, 6, 653-658, 2007. (in Japanese)

[10] [10] E. Okuyama and Y. Ishizuka, “Generalized two-point method for straightness error motion measurement in low spatial frequency domain,” Proc. of the 12th EUSPEN int. conf., 2012.

[11] [11] E. Okuyama, Y. Ishizuka, and H. Ishikawa, “Generalized twopoint method using inverse filtering for straightness profile measurement,” Proc. of the ICPT, 2012.

[12] [12] E. Okuyama, H. Takahashi, and H. Ishikawa, “Software Datum Design for Cross-Axis Motion Measurement of X-Stage Based on Least Uncertainty Criterion,” Int. J. of Automation Technology, Vol.5, No.2, 2011.