Abstract

A laser homodyne straightness interferometer with simultaneous measurement of six degrees of freedom motion errors is proposed for precision linear stage metrology. In this interferometer, the vertical straightness error and its position are measured by interference fringe counting, the yaw and pitch errors are obtained by measuring the spacing changes of interference fringe and the horizontal straightness and roll errors are determined by laser collimation. The merit of this interferometer is that four degrees of freedom motion errors are obtained by using laser interferometry with high accuracy. The optical configuration of the proposed interferometer is designed. The principle of the simultaneous measurement of six degrees of freedom errors including yaw, pitch, roll, two straightness errors and straightness error’s position of measured linear stage is depicted in detail, and the compensation of crosstalk effects on straightness error and its position measurements is presented. At last, an experimental setup is constructed and several experiments are performed to demonstrate the feasibility of the proposed interferometer and the compensation method.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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  4. C. Kuang, Q. Feng, B. Zhang, B. Liu, S. Chen, and Z. Zhang, “A four-degree-of-freedom laser measurement system (FDMS) using a single-mode fiber-coupled laser module,” Sens. Actuators A Phys. 125(1), 100–108 (2005).
    [Crossref]
  5. F. Qibo, Z. Bin, C. Cunxing, K. Cuifang, Z. Yusheng, and Y. Fenglin, “Development of a simple system for simultaneously measuring 6DOF geometric motion errors of a linear guide,” Opt. Express 21(22), 25805–25819 (2013).
    [Crossref] [PubMed]
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    [Crossref]
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  23. L. Yan, B. Chen, C. Zhang, E. Zhang, and Y. Yang, “Analysis and verification of the nonlinear error resulting from the misalignment of a polarizing beam splitter in a heterodyne interferometer,” Meas. Sci. Technol. 26(8), 085006 (2015).
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    [Crossref] [PubMed]

2016 (2)

X. Yu, S. R. Gillmer, S. C. Woody, and J. D. Ellis, “Development of a compact, fiber-coupled, six degree-of-freedom measurement system for precision linear stage metrology,” Rev. Sci. Instrum. 87(6), 065109 (2016).
[Crossref] [PubMed]

C. Cui, Q. Feng, B. Zhang, and Y. Zhao, “System for simultaneously measuring 6DOF geometric motion errors using a polarization maintaining fiber-coupled dual-frequency laser,” Opt. Express 24(6), 6735–6748 (2016).
[Crossref] [PubMed]

2015 (3)

2013 (3)

R. Smith and F. K. Fuss, “Theoretical analysis of interferometer wave front tilt and fringe radiant flux on a rectangular photodetector,” Sensors (Basel) 13(9), 11861–11898 (2013).
[Crossref] [PubMed]

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

F. Qibo, Z. Bin, C. Cunxing, K. Cuifang, Z. Yusheng, and Y. Fenglin, “Development of a simple system for simultaneously measuring 6DOF geometric motion errors of a linear guide,” Opt. Express 21(22), 25805–25819 (2013).
[Crossref] [PubMed]

2012 (1)

C.-H. Liu and C.-H. Cheng, “Development of a grating based multi-degree-of-freedom laser linear encoder using diffracted light,” Sens. Actuators A Phys. 181(7), 87–93 (2012).
[Crossref]

2011 (3)

2010 (2)

D. Wang, Y. Yang, D. Liu, and Y. Zhuo, “High-precision technique for in-situ testing of the PZT scanner based on fringe analysis,” Opt. Commun. 283(16), 3115–3121 (2010).
[Crossref]

A. Kimura, W. Gao, and L. J. Zeng, “Position and out-of-straightness measurement of a precision linear air-bearing stage by using a two-degree-of-freedom linear encoder,” Meas. Sci. Technol. 21(5), 054005 (2010).
[Crossref]

2009 (1)

B. Chen, E. Zhang, L. Yan, C. Li, W. Tang, and Q. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80(11), 115113 (2009).
[Crossref] [PubMed]

2008 (1)

C.-M. Wu, “A generalized, periodic nonlinearity-reduced interferometer for straightness measurements,” Rev. Sci. Instrum. 79(6), 065101 (2008).
[Crossref] [PubMed]

2005 (2)

Q. Chen, D. Lin, J. Wu, J. Yan, and C. Yin, “Straightness/coaxiality measurement system with transverse Zeeman dual-frequency laser,” Meas. Sci. Technol. 16(10), 2030–2037 (2005).
[Crossref]

C. Kuang, Q. Feng, B. Zhang, B. Liu, S. Chen, and Z. Zhang, “A four-degree-of-freedom laser measurement system (FDMS) using a single-mode fiber-coupled laser module,” Sens. Actuators A Phys. 125(1), 100–108 (2005).
[Crossref]

2004 (1)

Q. Feng, B. Zhang, and C. Kuang, “A straightness measurement system using a single-mode fiber-coupled laser module,” Opt. Laser Technol. 36(4), 279–283 (2004).
[Crossref]

2003 (1)

2002 (1)

Q. Hao, D. Li, and Y. Wang, “High-accuracy long distance alignment using single-mode optical fiber and phase plate,” Opt. Laser Technol. 34(4), 287–292 (2002).
[Crossref]

2001 (1)

S.-T. Lin, “A laser interferometer for measuring straightness,” Opt. Laser Technol. 33(3), 195–199 (2001).
[Crossref]

2000 (1)

K. C. Fan and Y. Zhao, “A laser straightness measurement system using optical fiber and modulation techniques,” Int. J. Mach. Tools Manuf. 40(14), 2073–2081 (2000).
[Crossref]

1996 (1)

C.-M. Wu and C.-S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7(1), 62–68 (1996).
[Crossref]

Bin, Z.

Chen, B.

L. Yan, B. Chen, C. Zhang, E. Zhang, and Y. Yang, “Analysis and verification of the nonlinear error resulting from the misalignment of a polarizing beam splitter in a heterodyne interferometer,” Meas. Sci. Technol. 26(8), 085006 (2015).
[Crossref]

B. Chen, B. Xu, L. Yan, E. Zhang, and Y. Liu, “Laser straightness interferometer system with rotational error compensation and simultaneous measurement of six degrees of freedom error parameters,” Opt. Express 23(7), 9052–9073 (2015).
[Crossref] [PubMed]

B. Chen, E. Zhang, L. Yan, C. Li, W. Tang, and Q. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80(11), 115113 (2009).
[Crossref] [PubMed]

Chen, J. C.

Chen, Q.

Q. Chen, D. Lin, J. Wu, J. Yan, and C. Yin, “Straightness/coaxiality measurement system with transverse Zeeman dual-frequency laser,” Meas. Sci. Technol. 16(10), 2030–2037 (2005).
[Crossref]

Chen, S.

C. Kuang, Q. Feng, B. Zhang, B. Liu, S. Chen, and Z. Zhang, “A four-degree-of-freedom laser measurement system (FDMS) using a single-mode fiber-coupled laser module,” Sens. Actuators A Phys. 125(1), 100–108 (2005).
[Crossref]

Cheng, C.-H.

C.-H. Liu and C.-H. Cheng, “Development of a grating based multi-degree-of-freedom laser linear encoder using diffracted light,” Sens. Actuators A Phys. 181(7), 87–93 (2012).
[Crossref]

Chiu, C.-S.

Cui, C.

Cuifang, K.

Cunxing, C.

Deturche, R.

Dian, S.

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

Ellis, J. D.

X. Yu, S. R. Gillmer, S. C. Woody, and J. D. Ellis, “Development of a compact, fiber-coupled, six degree-of-freedom measurement system for precision linear stage metrology,” Rev. Sci. Instrum. 87(6), 065109 (2016).
[Crossref] [PubMed]

Fan, K. C.

K. C. Fan and Y. Zhao, “A laser straightness measurement system using optical fiber and modulation techniques,” Int. J. Mach. Tools Manuf. 40(14), 2073–2081 (2000).
[Crossref]

Feng, Q.

C. Cui, Q. Feng, B. Zhang, and Y. Zhao, “System for simultaneously measuring 6DOF geometric motion errors using a polarization maintaining fiber-coupled dual-frequency laser,” Opt. Express 24(6), 6735–6748 (2016).
[Crossref] [PubMed]

B. Chen, E. Zhang, L. Yan, C. Li, W. Tang, and Q. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80(11), 115113 (2009).
[Crossref] [PubMed]

C. Kuang, Q. Feng, B. Zhang, B. Liu, S. Chen, and Z. Zhang, “A four-degree-of-freedom laser measurement system (FDMS) using a single-mode fiber-coupled laser module,” Sens. Actuators A Phys. 125(1), 100–108 (2005).
[Crossref]

Q. Feng, B. Zhang, and C. Kuang, “A straightness measurement system using a single-mode fiber-coupled laser module,” Opt. Laser Technol. 36(4), 279–283 (2004).
[Crossref]

Fenglin, Y.

Fuss, F. K.

R. Smith and F. K. Fuss, “Theoretical analysis of interferometer wave front tilt and fringe radiant flux on a rectangular photodetector,” Sensors (Basel) 13(9), 11861–11898 (2013).
[Crossref] [PubMed]

Gao, W.

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

A. Kimura, W. Gao, and L. J. Zeng, “Position and out-of-straightness measurement of a precision linear air-bearing stage by using a two-degree-of-freedom linear encoder,” Meas. Sci. Technol. 21(5), 054005 (2010).
[Crossref]

Ge, Z.

Gillmer, S. R.

X. Yu, S. R. Gillmer, S. C. Woody, and J. D. Ellis, “Development of a compact, fiber-coupled, six degree-of-freedom measurement system for precision linear stage metrology,” Rev. Sci. Instrum. 87(6), 065109 (2016).
[Crossref] [PubMed]

Hao, Q.

Q. Hao, D. Li, and Y. Wang, “High-accuracy long distance alignment using single-mode optical fiber and phase plate,” Opt. Laser Technol. 34(4), 287–292 (2002).
[Crossref]

Hsieh, H. L.

Hsieh, H.-L.

Huang, M.-S.

Ito, S.

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

Kim, G. H.

C. Lee, G. H. Kim, and S. K. Lee, “Design and construction of a single unit multi-function optical encoder for a six-degree-of-freedom motion error measurement in an ultraprecision linear stage,” Meas. Sci. Technol. 22(10), 105901 (2011).
[Crossref]

Kimura, A.

A. Kimura, W. Gao, and L. J. Zeng, “Position and out-of-straightness measurement of a precision linear air-bearing stage by using a two-degree-of-freedom linear encoder,” Meas. Sci. Technol. 21(5), 054005 (2010).
[Crossref]

Kuang, C.

C. Kuang, Q. Feng, B. Zhang, B. Liu, S. Chen, and Z. Zhang, “A four-degree-of-freedom laser measurement system (FDMS) using a single-mode fiber-coupled laser module,” Sens. Actuators A Phys. 125(1), 100–108 (2005).
[Crossref]

Q. Feng, B. Zhang, and C. Kuang, “A straightness measurement system using a single-mode fiber-coupled laser module,” Opt. Laser Technol. 36(4), 279–283 (2004).
[Crossref]

Lee, C.

C. Lee, G. H. Kim, and S. K. Lee, “Design and construction of a single unit multi-function optical encoder for a six-degree-of-freedom motion error measurement in an ultraprecision linear stage,” Meas. Sci. Technol. 22(10), 105901 (2011).
[Crossref]

Lee, J. Y.

Lee, S. K.

C. Lee, G. H. Kim, and S. K. Lee, “Design and construction of a single unit multi-function optical encoder for a six-degree-of-freedom motion error measurement in an ultraprecision linear stage,” Meas. Sci. Technol. 22(10), 105901 (2011).
[Crossref]

Lerondel, G.

Li, C.

B. Chen, E. Zhang, L. Yan, C. Li, W. Tang, and Q. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80(11), 115113 (2009).
[Crossref] [PubMed]

Li, D.

Q. Hao, D. Li, and Y. Wang, “High-accuracy long distance alignment using single-mode optical fiber and phase plate,” Opt. Laser Technol. 34(4), 287–292 (2002).
[Crossref]

Li, X.

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

Lin, D.

Q. Chen, D. Lin, J. Wu, J. Yan, and C. Yin, “Straightness/coaxiality measurement system with transverse Zeeman dual-frequency laser,” Meas. Sci. Technol. 16(10), 2030–2037 (2005).
[Crossref]

Lin, S.-T.

Liu, B.

C. Kuang, Q. Feng, B. Zhang, B. Liu, S. Chen, and Z. Zhang, “A four-degree-of-freedom laser measurement system (FDMS) using a single-mode fiber-coupled laser module,” Sens. Actuators A Phys. 125(1), 100–108 (2005).
[Crossref]

Liu, C.-H.

C.-H. Liu and C.-H. Cheng, “Development of a grating based multi-degree-of-freedom laser linear encoder using diffracted light,” Sens. Actuators A Phys. 181(7), 87–93 (2012).
[Crossref]

Liu, D.

D. Wang, Y. Yang, D. Liu, and Y. Zhuo, “High-precision technique for in-situ testing of the PZT scanner based on fringe analysis,” Opt. Commun. 283(16), 3115–3121 (2010).
[Crossref]

Liu, Y.

Lu, M. P.

Muto, H.

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

Pan, S.-W.

Qibo, F.

Shimizu, Y.

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

Smith, R.

R. Smith and F. K. Fuss, “Theoretical analysis of interferometer wave front tilt and fringe radiant flux on a rectangular photodetector,” Sensors (Basel) 13(9), 11861–11898 (2013).
[Crossref] [PubMed]

Su, C.-S.

C.-M. Wu and C.-S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7(1), 62–68 (1996).
[Crossref]

Takeda, M.

Tang, W.

B. Chen, E. Zhang, L. Yan, C. Li, W. Tang, and Q. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80(11), 115113 (2009).
[Crossref] [PubMed]

Wang, D.

D. Wang, Y. Yang, D. Liu, and Y. Zhuo, “High-precision technique for in-situ testing of the PZT scanner based on fringe analysis,” Opt. Commun. 283(16), 3115–3121 (2010).
[Crossref]

Wang, Y.

Q. Hao, D. Li, and Y. Wang, “High-accuracy long distance alignment using single-mode optical fiber and phase plate,” Opt. Laser Technol. 34(4), 287–292 (2002).
[Crossref]

Woody, S. C.

X. Yu, S. R. Gillmer, S. C. Woody, and J. D. Ellis, “Development of a compact, fiber-coupled, six degree-of-freedom measurement system for precision linear stage metrology,” Rev. Sci. Instrum. 87(6), 065109 (2016).
[Crossref] [PubMed]

Wu, C.-M.

C.-M. Wu, “A generalized, periodic nonlinearity-reduced interferometer for straightness measurements,” Rev. Sci. Instrum. 79(6), 065101 (2008).
[Crossref] [PubMed]

C.-M. Wu and C.-S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7(1), 62–68 (1996).
[Crossref]

Wu, J.

Q. Chen, D. Lin, J. Wu, J. Yan, and C. Yin, “Straightness/coaxiality measurement system with transverse Zeeman dual-frequency laser,” Meas. Sci. Technol. 16(10), 2030–2037 (2005).
[Crossref]

Xu, B.

Yan, J.

Q. Chen, D. Lin, J. Wu, J. Yan, and C. Yin, “Straightness/coaxiality measurement system with transverse Zeeman dual-frequency laser,” Meas. Sci. Technol. 16(10), 2030–2037 (2005).
[Crossref]

Yan, L.

L. Yan, B. Chen, C. Zhang, E. Zhang, and Y. Yang, “Analysis and verification of the nonlinear error resulting from the misalignment of a polarizing beam splitter in a heterodyne interferometer,” Meas. Sci. Technol. 26(8), 085006 (2015).
[Crossref]

B. Chen, B. Xu, L. Yan, E. Zhang, and Y. Liu, “Laser straightness interferometer system with rotational error compensation and simultaneous measurement of six degrees of freedom error parameters,” Opt. Express 23(7), 9052–9073 (2015).
[Crossref] [PubMed]

B. Chen, E. Zhang, L. Yan, C. Li, W. Tang, and Q. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80(11), 115113 (2009).
[Crossref] [PubMed]

Yang, Y.

L. Yan, B. Chen, C. Zhang, E. Zhang, and Y. Yang, “Analysis and verification of the nonlinear error resulting from the misalignment of a polarizing beam splitter in a heterodyne interferometer,” Meas. Sci. Technol. 26(8), 085006 (2015).
[Crossref]

D. Wang, Y. Yang, D. Liu, and Y. Zhuo, “High-precision technique for in-situ testing of the PZT scanner based on fringe analysis,” Opt. Commun. 283(16), 3115–3121 (2010).
[Crossref]

Yeh, S.-L.

Yin, C.

Q. Chen, D. Lin, J. Wu, J. Yan, and C. Yin, “Straightness/coaxiality measurement system with transverse Zeeman dual-frequency laser,” Meas. Sci. Technol. 16(10), 2030–2037 (2005).
[Crossref]

Yu, X.

X. Yu, S. R. Gillmer, S. C. Woody, and J. D. Ellis, “Development of a compact, fiber-coupled, six degree-of-freedom measurement system for precision linear stage metrology,” Rev. Sci. Instrum. 87(6), 065109 (2016).
[Crossref] [PubMed]

Yusheng, Z.

Zeng, L. J.

A. Kimura, W. Gao, and L. J. Zeng, “Position and out-of-straightness measurement of a precision linear air-bearing stage by using a two-degree-of-freedom linear encoder,” Meas. Sci. Technol. 21(5), 054005 (2010).
[Crossref]

Zhang, B.

C. Cui, Q. Feng, B. Zhang, and Y. Zhao, “System for simultaneously measuring 6DOF geometric motion errors using a polarization maintaining fiber-coupled dual-frequency laser,” Opt. Express 24(6), 6735–6748 (2016).
[Crossref] [PubMed]

C. Kuang, Q. Feng, B. Zhang, B. Liu, S. Chen, and Z. Zhang, “A four-degree-of-freedom laser measurement system (FDMS) using a single-mode fiber-coupled laser module,” Sens. Actuators A Phys. 125(1), 100–108 (2005).
[Crossref]

Q. Feng, B. Zhang, and C. Kuang, “A straightness measurement system using a single-mode fiber-coupled laser module,” Opt. Laser Technol. 36(4), 279–283 (2004).
[Crossref]

Zhang, C.

L. Yan, B. Chen, C. Zhang, E. Zhang, and Y. Yang, “Analysis and verification of the nonlinear error resulting from the misalignment of a polarizing beam splitter in a heterodyne interferometer,” Meas. Sci. Technol. 26(8), 085006 (2015).
[Crossref]

Zhang, E.

L. Yan, B. Chen, C. Zhang, E. Zhang, and Y. Yang, “Analysis and verification of the nonlinear error resulting from the misalignment of a polarizing beam splitter in a heterodyne interferometer,” Meas. Sci. Technol. 26(8), 085006 (2015).
[Crossref]

B. Chen, B. Xu, L. Yan, E. Zhang, and Y. Liu, “Laser straightness interferometer system with rotational error compensation and simultaneous measurement of six degrees of freedom error parameters,” Opt. Express 23(7), 9052–9073 (2015).
[Crossref] [PubMed]

B. Chen, E. Zhang, L. Yan, C. Li, W. Tang, and Q. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80(11), 115113 (2009).
[Crossref] [PubMed]

Zhang, Z.

C. Kuang, Q. Feng, B. Zhang, B. Liu, S. Chen, and Z. Zhang, “A four-degree-of-freedom laser measurement system (FDMS) using a single-mode fiber-coupled laser module,” Sens. Actuators A Phys. 125(1), 100–108 (2005).
[Crossref]

Zhao, Y.

C. Cui, Q. Feng, B. Zhang, and Y. Zhao, “System for simultaneously measuring 6DOF geometric motion errors using a polarization maintaining fiber-coupled dual-frequency laser,” Opt. Express 24(6), 6735–6748 (2016).
[Crossref] [PubMed]

K. C. Fan and Y. Zhao, “A laser straightness measurement system using optical fiber and modulation techniques,” Int. J. Mach. Tools Manuf. 40(14), 2073–2081 (2000).
[Crossref]

Zhuo, Y.

D. Wang, Y. Yang, D. Liu, and Y. Zhuo, “High-precision technique for in-situ testing of the PZT scanner based on fringe analysis,” Opt. Commun. 283(16), 3115–3121 (2010).
[Crossref]

Appl. Opt. (2)

Int. J. Mach. Tools Manuf. (1)

K. C. Fan and Y. Zhao, “A laser straightness measurement system using optical fiber and modulation techniques,” Int. J. Mach. Tools Manuf. 40(14), 2073–2081 (2000).
[Crossref]

Meas. Sci. Technol. (5)

A. Kimura, W. Gao, and L. J. Zeng, “Position and out-of-straightness measurement of a precision linear air-bearing stage by using a two-degree-of-freedom linear encoder,” Meas. Sci. Technol. 21(5), 054005 (2010).
[Crossref]

C. Lee, G. H. Kim, and S. K. Lee, “Design and construction of a single unit multi-function optical encoder for a six-degree-of-freedom motion error measurement in an ultraprecision linear stage,” Meas. Sci. Technol. 22(10), 105901 (2011).
[Crossref]

Q. Chen, D. Lin, J. Wu, J. Yan, and C. Yin, “Straightness/coaxiality measurement system with transverse Zeeman dual-frequency laser,” Meas. Sci. Technol. 16(10), 2030–2037 (2005).
[Crossref]

C.-M. Wu and C.-S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7(1), 62–68 (1996).
[Crossref]

L. Yan, B. Chen, C. Zhang, E. Zhang, and Y. Yang, “Analysis and verification of the nonlinear error resulting from the misalignment of a polarizing beam splitter in a heterodyne interferometer,” Meas. Sci. Technol. 26(8), 085006 (2015).
[Crossref]

Opt. Commun. (1)

D. Wang, Y. Yang, D. Liu, and Y. Zhuo, “High-precision technique for in-situ testing of the PZT scanner based on fringe analysis,” Opt. Commun. 283(16), 3115–3121 (2010).
[Crossref]

Opt. Express (5)

Opt. Laser Technol. (3)

S.-T. Lin, “A laser interferometer for measuring straightness,” Opt. Laser Technol. 33(3), 195–199 (2001).
[Crossref]

Q. Hao, D. Li, and Y. Wang, “High-accuracy long distance alignment using single-mode optical fiber and phase plate,” Opt. Laser Technol. 34(4), 287–292 (2002).
[Crossref]

Q. Feng, B. Zhang, and C. Kuang, “A straightness measurement system using a single-mode fiber-coupled laser module,” Opt. Laser Technol. 36(4), 279–283 (2004).
[Crossref]

Precis. Eng. (1)

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

Rev. Sci. Instrum. (3)

C.-M. Wu, “A generalized, periodic nonlinearity-reduced interferometer for straightness measurements,” Rev. Sci. Instrum. 79(6), 065101 (2008).
[Crossref] [PubMed]

X. Yu, S. R. Gillmer, S. C. Woody, and J. D. Ellis, “Development of a compact, fiber-coupled, six degree-of-freedom measurement system for precision linear stage metrology,” Rev. Sci. Instrum. 87(6), 065109 (2016).
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B. Chen, E. Zhang, L. Yan, C. Li, W. Tang, and Q. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80(11), 115113 (2009).
[Crossref] [PubMed]

Sens. Actuators A Phys. (2)

C. Kuang, Q. Feng, B. Zhang, B. Liu, S. Chen, and Z. Zhang, “A four-degree-of-freedom laser measurement system (FDMS) using a single-mode fiber-coupled laser module,” Sens. Actuators A Phys. 125(1), 100–108 (2005).
[Crossref]

C.-H. Liu and C.-H. Cheng, “Development of a grating based multi-degree-of-freedom laser linear encoder using diffracted light,” Sens. Actuators A Phys. 181(7), 87–93 (2012).
[Crossref]

Sensors (Basel) (1)

R. Smith and F. K. Fuss, “Theoretical analysis of interferometer wave front tilt and fringe radiant flux on a rectangular photodetector,” Sensors (Basel) 13(9), 11861–11898 (2013).
[Crossref] [PubMed]

Other (2)

R. R. Baldwin, “Interferometer system for measuring straightness and roll,” U.S. Patent, 3790284 (1974).

D. R. McMurtry and R. J. Chaney, “Straightness interferometer system,” U.S. Patent, 5026163 (1991).

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Figures (13)

Fig. 1
Fig. 1

Schematic of the laser homodyne straightness interferometer with simultaneous measurement of six degrees of freedom motion errors. WP: Wollaston prism; RR: retro-reflector.

Fig. 2
Fig. 2

Schematic of the yaw and pitch errors measurement. (a) The variation of propagating direction of the measuring beam according to the yaw and pitch errors; (b) The spacing of interference fringe at the initial position; (c) The spacing of interference fringe with the yaw and pitch errors.

Fig. 3
Fig. 3

Schematic of the vertical straightness error and its position measurement. (a) The optical configuration; (b) The geometric relationship between WP and RR.

Fig. 4
Fig. 4

Schematic of the horizontal straightness and roll errors measurement. (a) The shift of RR in the y direction; (b) The rotation of RR around the z direction; (c) The analytical model of emergent points corresponding to upper and down right-angle prisms of RR.

Fig. 5
Fig. 5

Schematic of the influence of the pitch error on the OPDs corresponding to the two measuring beams.

Fig. 6
Fig. 6

The experimental setup.

Fig. 7
Fig. 7

The experimental results of yaw and pitch measurements.

Fig. 8
Fig. 8

The experimental result of roll measurement.

Fig. 9
Fig. 9

The experimental result of horizontal straightness error measurement.

Fig. 10
Fig. 10

The experimental results of vertical straightness error measurement.

Fig. 11
Fig. 11

The experimental results of straightness error’s position measurement.

Fig. 12
Fig. 12

Simultaneous measurement and repeatability experimental results.

Fig. 13
Fig. 13

Schematic of interference fringe image processing.

Tables (1)

Tables Icon

Table 1 Repeatability results of simultaneously measuring six degrees of freedom motion errors of the stage.

Equations (26)

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{ Δ x CCD = λ Y M Y R Δ y CCD = λ X M X R ,
{ Δ x CCD = λ ( Y M 2β ) Y R Δ y CCD = λ ( X M +2α ) X R ,
{ α= λ 2 ( 1 Δ y CCD 1 Δ y CCD ) β= λ 2 ( 1 Δ x CCD 1 Δ x CCD ) ,
{ J ^ 1 = E 0 cos( 2πft+ φ 1 ) e ^ x = E 0 exp( i φ 1 ) e ^ x J ^ 2 = E 0 cos( 2πft+ φ 2 ) e ^ y = E 0 exp( i φ 2 ) e ^ y ,
J ^ 3 = 1 2 E 0 ( 1 i )exp( i φ 1 )+ 1 2 E 0 ( 1 i )exp( i φ 2 ) = 1 2 E 0 ( exp( i φ 1 φ 2 2 )+exp( i φ 1 φ 2 2 ) iexp( i φ 1 φ 2 2 )+iexp( i φ 1 φ 2 2 ) )exp( i φ 1 + φ 2 2 ) = E 0 ( cos Δφ 2 sin Δφ 2 )exp( i φ 1 + φ 2 2 ),
I D1 = [ 2 4 E 0 ( cos Δφ 2 +sin Δφ 2 )exp( i φ 1 + φ 2 2 ) ] 2 = 1 4 E 0 2 cos 2 ( Δφ 2 π 4 ) exp 2 ( i φ 1 + φ 2 2 ) =A cos 2 ( Δφ 2 π 4 ),
I D2 = [ 1 2 E 0 ( cos Δφ 2 )exp( i φ 1 + φ 2 2 ) ] 2 =A cos 2 Δφ 2 ,
I D3 = [ 1 2 E 0 ( sin Δφ 2 )exp( i φ 1 + φ 2 2 ) ] 2 =A sin 2 Δφ 2 .
I D2D1 =A[ cos 2 Δφ 2 cos 2 ( Δφ 2 π 4 ) ]= 2 2 Asin( Δφ+ π 4 ),
I D3D1 =A[ sin 2 Δφ 2 cos 2 ( Δφ 2 π 4 ) ]= 2 2 Acos( Δφ+ π 4 ),
ΔL= λ 4π Δφ,
{ I D4 = A 1 + B 1 sinϕ I D5 = A 2 + B 2 cosϕ ,
L 1 = λ 4π ϕ=( N+ε ) λ 2 ,
Δh= ΔL 2sinθ ,
s= 2 L 1 ΔL 2cosθ ,
Δ x QD1 =( y uo y uo ),
Δ x QD2 = y do y do ,
γ 1 2 y uo y uo ( y do y do ) x uo x do = Δ x QD1 +Δ x QD2 2( s 0 +sB W 2cosθ )sin2θ ,
w= Δ x QPD2 Δ x QPD1 4 Hγ,
L 1 = L 1 + 1 2 ( 1 cosθ + 1 cosθcos2β )( H+ H 1 cosθ )β 1 2 ( 1 cosθcos2β 1 cosθ )( s 0 +s ),
ΔL=Δ L + 1 2 ( 1 cosθ + 1 cosθcos2β )( H 1 + H 2 )cosθβ,
s s + 1 2cosθ ( 1 cosθ + 1 cosθcos2β )Hβ 1 2cosθ ( 1 cosθcos2β 1 cosθ )( s 0 + s ),
Δh=Δ h + 1 2 ( 1+ 1 cos2β )( s 0 +sB W 2cosθ )β,
Δ x QD1 =Δ x QD1 ( 2B+ W cosθ W ncosθ )α,
Δ x QD2 =Δ x QD2 +( 2B+ W cosθ W ncosθ )α,
w= Δ x QD2 Δ x QD1 4 Hγ( B+ W 2cosθ W 2ncosθ )α,

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