Abstract

A novel method for simultaneously measuring six degree-of-freedom (6DOF) geometric motion errors is proposed in this paper, and the corresponding measurement instrument is developed. Simultaneous measurement of 6DOF geometric motion errors using a polarization maintaining fiber-coupled dual-frequency laser is accomplished for the first time to the best of the authors’ knowledge. Dual-frequency laser beams that are orthogonally linear polarized were adopted as the measuring datum. Positioning error measurement was achieved by heterodyne interferometry, and other 5DOF geometric motion errors were obtained by fiber collimation measurement. A series of experiments was performed to verify the effectiveness of the developed instrument. The experimental results showed that the stability and accuracy of the positioning error measurement are 31.1 nm and 0.5 μm, respectively. For the straightness error measurements, the stability and resolution are 60 and 40 nm, respectively, and the maximum deviation of repeatability is ± 0.15 μm in the x direction and ± 0.1 μm in the y direction. For pitch and yaw measurements, the stabilities are 0.03″ and 0.04″, the maximum deviations of repeatability are ± 0.18″ and ± 0.24″, and the accuracies are 0.4″ and 0.35″, respectively. The stability and resolution of roll measurement are 0.29″ and 0.2″, respectively, and the accuracy is 0.6″.

© 2016 Optical Society of America

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References

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  1. A. C. Okafor and Y. M. Ertekin, “Vertical machining center accuracy characterization using laser interferometer: part 1. Linear positional errors,” J. Mater. Process. Technol. 105(3), 394–406 (2000).
    [Crossref]
  2. A. C. Okafor and Y. M. Ertekin, “Vertical machining center accuracy characterization using laser interferometer: part 2. Angular errors,” J. Mater. Process. Technol. 105(3), 407–420 (2000).
    [Crossref]
  3. S. Shimizu, H.-s. Lee, and N. Imai, “Simultaneous measuring method of table motion errors in 6 degrees of freedom,” Int. J. Jpn Soc. Precis. Eng. 28, 273–274 (1994).
  4. P. Huang and J. Ni, “On-line error compensation of coordinate measuring machines,” Int. J. Mach. Tools Manuf. 35(5), 725–738 (1995).
    [Crossref]
  5. J. Ni, P. Huang, and S. Wu, “A multi-degree-of-freedom measuring system for CMM geometric errors,” J. Eng. Ind. 114, 362–369 (1992).
  6. C.-H. Liu, W.-Y. Jywe, C.-C. Hsu, and T.-H. Hsu, “Development of a laser-based high-precision six-degrees-of-freedom motion errors measuring system for linear stage,” Rev. Sci. Instrum. 76(5), 055110 (2005).
    [Crossref]
  7. 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]
  8. K.-C. Fan and M.-J. Chen, “A 6-degree-of-freedom measurement system for the accuracy of XY stages,” Precis. Eng. 24(1), 15–23 (2000).
    [Crossref]
  9. K.-C. Fan, M.-J. Chen, and W. Huang, “A six-degree-of-freedom measurement system for the motion accuracy of linear stages,” Int. J. Mach. Tools Manuf. 38(3), 155–164 (1998).
    [Crossref]
  10. 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]
  11. H.-L. Hsieh and S.-W. Pan, “Development of a grating-based interferometer for six-degree-of-freedom displacement and angle measurements,” Opt. Express 23(3), 2451–2465 (2015).
    [Crossref] [PubMed]
  12. J.-A. Kim, K.-C. Kim, E. W. Bae, S. Kim, and Y. K. Kwak, “Six-degree-of-freedom displacement measurement system using a diffraction grating,” Rev. Sci. Instrum. 71(8), 3214–3219 (2000).
    [Crossref]
  13. 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]
  14. K. C. Lau and Y.-Q. Liu, “Five-axis/six-axis laser measuring system,” US Patent. 6049377 (2000).
  15. N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4(9), 907–926 (1993).
    [Crossref]
  16. 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]
  17. C. Cui, Q. Feng, and B. Zhang, “Compensation for straightness measurement systematic errors in six degree-of-freedom motion error simultaneous measurement system,” Appl. Opt. 54(11), 3122–3131 (2015).
    [Crossref] [PubMed]
  18. C. Kuang, E. Hong, and Q. Feng, “High-accuracy method for measuring two-dimensional angles of a linear guideway,” Opt. Eng. 46(5), 051016 (2007).
    [Crossref]
  19. T. Zhang, Q. Feng, C. Cui, and B. Zhang, “Research on error compensation method for dual-beam measurement of roll angle based on rhombic prism,” Chin. Opt. Lett. 12(7), 071201 (2014).
    [Crossref]
  20. W. Gao, P. S. Huang, T. Yamada, and S. Kiyono, “A compact and sensitive two-dimensional angle probe for flatness measurement of large silicon wafers,” Precis. Eng. 26(4), 396–404 (2002).
    [Crossref]

2015 (2)

2014 (1)

2013 (2)

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]

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]

2011 (1)

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]

2007 (1)

C. Kuang, E. Hong, and Q. Feng, “High-accuracy method for measuring two-dimensional angles of a linear guideway,” Opt. Eng. 46(5), 051016 (2007).
[Crossref]

2005 (1)

C.-H. Liu, W.-Y. Jywe, C.-C. Hsu, and T.-H. Hsu, “Development of a laser-based high-precision six-degrees-of-freedom motion errors measuring system for linear stage,” Rev. Sci. Instrum. 76(5), 055110 (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]

2002 (1)

W. Gao, P. S. Huang, T. Yamada, and S. Kiyono, “A compact and sensitive two-dimensional angle probe for flatness measurement of large silicon wafers,” Precis. Eng. 26(4), 396–404 (2002).
[Crossref]

2000 (4)

K.-C. Fan and M.-J. Chen, “A 6-degree-of-freedom measurement system for the accuracy of XY stages,” Precis. Eng. 24(1), 15–23 (2000).
[Crossref]

J.-A. Kim, K.-C. Kim, E. W. Bae, S. Kim, and Y. K. Kwak, “Six-degree-of-freedom displacement measurement system using a diffraction grating,” Rev. Sci. Instrum. 71(8), 3214–3219 (2000).
[Crossref]

A. C. Okafor and Y. M. Ertekin, “Vertical machining center accuracy characterization using laser interferometer: part 1. Linear positional errors,” J. Mater. Process. Technol. 105(3), 394–406 (2000).
[Crossref]

A. C. Okafor and Y. M. Ertekin, “Vertical machining center accuracy characterization using laser interferometer: part 2. Angular errors,” J. Mater. Process. Technol. 105(3), 407–420 (2000).
[Crossref]

1998 (1)

K.-C. Fan, M.-J. Chen, and W. Huang, “A six-degree-of-freedom measurement system for the motion accuracy of linear stages,” Int. J. Mach. Tools Manuf. 38(3), 155–164 (1998).
[Crossref]

1995 (1)

P. Huang and J. Ni, “On-line error compensation of coordinate measuring machines,” Int. J. Mach. Tools Manuf. 35(5), 725–738 (1995).
[Crossref]

1994 (1)

S. Shimizu, H.-s. Lee, and N. Imai, “Simultaneous measuring method of table motion errors in 6 degrees of freedom,” Int. J. Jpn Soc. Precis. Eng. 28, 273–274 (1994).

1993 (1)

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4(9), 907–926 (1993).
[Crossref]

1992 (1)

J. Ni, P. Huang, and S. Wu, “A multi-degree-of-freedom measuring system for CMM geometric errors,” J. Eng. Ind. 114, 362–369 (1992).

Bae, E. W.

J.-A. Kim, K.-C. Kim, E. W. Bae, S. Kim, and Y. K. Kwak, “Six-degree-of-freedom displacement measurement system using a diffraction grating,” Rev. Sci. Instrum. 71(8), 3214–3219 (2000).
[Crossref]

Bin, Z.

Bobroff, N.

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4(9), 907–926 (1993).
[Crossref]

Chen, M.-J.

K.-C. Fan and M.-J. Chen, “A 6-degree-of-freedom measurement system for the accuracy of XY stages,” Precis. Eng. 24(1), 15–23 (2000).
[Crossref]

K.-C. Fan, M.-J. Chen, and W. Huang, “A six-degree-of-freedom measurement system for the motion accuracy of linear stages,” Int. J. Mach. Tools Manuf. 38(3), 155–164 (1998).
[Crossref]

Cui, C.

Cuifang, K.

Cunxing, C.

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]

Ertekin, Y. M.

A. C. Okafor and Y. M. Ertekin, “Vertical machining center accuracy characterization using laser interferometer: part 2. Angular errors,” J. Mater. Process. Technol. 105(3), 407–420 (2000).
[Crossref]

A. C. Okafor and Y. M. Ertekin, “Vertical machining center accuracy characterization using laser interferometer: part 1. Linear positional errors,” J. Mater. Process. Technol. 105(3), 394–406 (2000).
[Crossref]

Fan, K.-C.

K.-C. Fan and M.-J. Chen, “A 6-degree-of-freedom measurement system for the accuracy of XY stages,” Precis. Eng. 24(1), 15–23 (2000).
[Crossref]

K.-C. Fan, M.-J. Chen, and W. Huang, “A six-degree-of-freedom measurement system for the motion accuracy of linear stages,” Int. J. Mach. Tools Manuf. 38(3), 155–164 (1998).
[Crossref]

Feng, Q.

C. Cui, Q. Feng, and B. Zhang, “Compensation for straightness measurement systematic errors in six degree-of-freedom motion error simultaneous measurement system,” Appl. Opt. 54(11), 3122–3131 (2015).
[Crossref] [PubMed]

T. Zhang, Q. Feng, C. Cui, and B. Zhang, “Research on error compensation method for dual-beam measurement of roll angle based on rhombic prism,” Chin. Opt. Lett. 12(7), 071201 (2014).
[Crossref]

C. Kuang, E. Hong, and Q. Feng, “High-accuracy method for measuring two-dimensional angles of a linear guideway,” Opt. Eng. 46(5), 051016 (2007).
[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.

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]

W. Gao, P. S. Huang, T. Yamada, and S. Kiyono, “A compact and sensitive two-dimensional angle probe for flatness measurement of large silicon wafers,” Precis. Eng. 26(4), 396–404 (2002).
[Crossref]

Hong, E.

C. Kuang, E. Hong, and Q. Feng, “High-accuracy method for measuring two-dimensional angles of a linear guideway,” Opt. Eng. 46(5), 051016 (2007).
[Crossref]

Hsieh, H.-L.

Hsu, C.-C.

C.-H. Liu, W.-Y. Jywe, C.-C. Hsu, and T.-H. Hsu, “Development of a laser-based high-precision six-degrees-of-freedom motion errors measuring system for linear stage,” Rev. Sci. Instrum. 76(5), 055110 (2005).
[Crossref]

Hsu, T.-H.

C.-H. Liu, W.-Y. Jywe, C.-C. Hsu, and T.-H. Hsu, “Development of a laser-based high-precision six-degrees-of-freedom motion errors measuring system for linear stage,” Rev. Sci. Instrum. 76(5), 055110 (2005).
[Crossref]

Huang, P.

P. Huang and J. Ni, “On-line error compensation of coordinate measuring machines,” Int. J. Mach. Tools Manuf. 35(5), 725–738 (1995).
[Crossref]

J. Ni, P. Huang, and S. Wu, “A multi-degree-of-freedom measuring system for CMM geometric errors,” J. Eng. Ind. 114, 362–369 (1992).

Huang, P. S.

W. Gao, P. S. Huang, T. Yamada, and S. Kiyono, “A compact and sensitive two-dimensional angle probe for flatness measurement of large silicon wafers,” Precis. Eng. 26(4), 396–404 (2002).
[Crossref]

Huang, W.

K.-C. Fan, M.-J. Chen, and W. Huang, “A six-degree-of-freedom measurement system for the motion accuracy of linear stages,” Int. J. Mach. Tools Manuf. 38(3), 155–164 (1998).
[Crossref]

Imai, N.

S. Shimizu, H.-s. Lee, and N. Imai, “Simultaneous measuring method of table motion errors in 6 degrees of freedom,” Int. J. Jpn Soc. Precis. Eng. 28, 273–274 (1994).

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]

Jywe, W.-Y.

C.-H. Liu, W.-Y. Jywe, C.-C. Hsu, and T.-H. Hsu, “Development of a laser-based high-precision six-degrees-of-freedom motion errors measuring system for linear stage,” Rev. Sci. Instrum. 76(5), 055110 (2005).
[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]

Kim, J.-A.

J.-A. Kim, K.-C. Kim, E. W. Bae, S. Kim, and Y. K. Kwak, “Six-degree-of-freedom displacement measurement system using a diffraction grating,” Rev. Sci. Instrum. 71(8), 3214–3219 (2000).
[Crossref]

Kim, K.-C.

J.-A. Kim, K.-C. Kim, E. W. Bae, S. Kim, and Y. K. Kwak, “Six-degree-of-freedom displacement measurement system using a diffraction grating,” Rev. Sci. Instrum. 71(8), 3214–3219 (2000).
[Crossref]

Kim, S.

J.-A. Kim, K.-C. Kim, E. W. Bae, S. Kim, and Y. K. Kwak, “Six-degree-of-freedom displacement measurement system using a diffraction grating,” Rev. Sci. Instrum. 71(8), 3214–3219 (2000).
[Crossref]

Kiyono, S.

W. Gao, P. S. Huang, T. Yamada, and S. Kiyono, “A compact and sensitive two-dimensional angle probe for flatness measurement of large silicon wafers,” Precis. Eng. 26(4), 396–404 (2002).
[Crossref]

Kuang, C.

C. Kuang, E. Hong, and Q. Feng, “High-accuracy method for measuring two-dimensional angles of a linear guideway,” Opt. Eng. 46(5), 051016 (2007).
[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]

Kwak, Y. K.

J.-A. Kim, K.-C. Kim, E. W. Bae, S. Kim, and Y. K. Kwak, “Six-degree-of-freedom displacement measurement system using a diffraction grating,” Rev. Sci. Instrum. 71(8), 3214–3219 (2000).
[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, H.-s.

S. Shimizu, H.-s. Lee, and N. Imai, “Simultaneous measuring method of table motion errors in 6 degrees of freedom,” Int. J. Jpn Soc. Precis. Eng. 28, 273–274 (1994).

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]

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]

Liu, C.-H.

C.-H. Liu, W.-Y. Jywe, C.-C. Hsu, and T.-H. Hsu, “Development of a laser-based high-precision six-degrees-of-freedom motion errors measuring system for linear stage,” Rev. Sci. Instrum. 76(5), 055110 (2005).
[Crossref]

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]

Ni, J.

P. Huang and J. Ni, “On-line error compensation of coordinate measuring machines,” Int. J. Mach. Tools Manuf. 35(5), 725–738 (1995).
[Crossref]

J. Ni, P. Huang, and S. Wu, “A multi-degree-of-freedom measuring system for CMM geometric errors,” J. Eng. Ind. 114, 362–369 (1992).

Okafor, A. C.

A. C. Okafor and Y. M. Ertekin, “Vertical machining center accuracy characterization using laser interferometer: part 2. Angular errors,” J. Mater. Process. Technol. 105(3), 407–420 (2000).
[Crossref]

A. C. Okafor and Y. M. Ertekin, “Vertical machining center accuracy characterization using laser interferometer: part 1. Linear positional errors,” J. Mater. Process. Technol. 105(3), 394–406 (2000).
[Crossref]

Pan, S.-W.

Qibo, F.

Shimizu, S.

S. Shimizu, H.-s. Lee, and N. Imai, “Simultaneous measuring method of table motion errors in 6 degrees of freedom,” Int. J. Jpn Soc. Precis. Eng. 28, 273–274 (1994).

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]

Wu, S.

J. Ni, P. Huang, and S. Wu, “A multi-degree-of-freedom measuring system for CMM geometric errors,” J. Eng. Ind. 114, 362–369 (1992).

Yamada, T.

W. Gao, P. S. Huang, T. Yamada, and S. Kiyono, “A compact and sensitive two-dimensional angle probe for flatness measurement of large silicon wafers,” Precis. Eng. 26(4), 396–404 (2002).
[Crossref]

Yusheng, Z.

Zhang, B.

Zhang, T.

Appl. Opt. (1)

Chin. Opt. Lett. (1)

Int. J. Jpn Soc. Precis. Eng. (1)

S. Shimizu, H.-s. Lee, and N. Imai, “Simultaneous measuring method of table motion errors in 6 degrees of freedom,” Int. J. Jpn Soc. Precis. Eng. 28, 273–274 (1994).

Int. J. Mach. Tools Manuf. (2)

P. Huang and J. Ni, “On-line error compensation of coordinate measuring machines,” Int. J. Mach. Tools Manuf. 35(5), 725–738 (1995).
[Crossref]

K.-C. Fan, M.-J. Chen, and W. Huang, “A six-degree-of-freedom measurement system for the motion accuracy of linear stages,” Int. J. Mach. Tools Manuf. 38(3), 155–164 (1998).
[Crossref]

J. Eng. Ind. (1)

J. Ni, P. Huang, and S. Wu, “A multi-degree-of-freedom measuring system for CMM geometric errors,” J. Eng. Ind. 114, 362–369 (1992).

J. Mater. Process. Technol. (2)

A. C. Okafor and Y. M. Ertekin, “Vertical machining center accuracy characterization using laser interferometer: part 1. Linear positional errors,” J. Mater. Process. Technol. 105(3), 394–406 (2000).
[Crossref]

A. C. Okafor and Y. M. Ertekin, “Vertical machining center accuracy characterization using laser interferometer: part 2. Angular errors,” J. Mater. Process. Technol. 105(3), 407–420 (2000).
[Crossref]

Meas. Sci. Technol. (2)

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]

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4(9), 907–926 (1993).
[Crossref]

Opt. Eng. (1)

C. Kuang, E. Hong, and Q. Feng, “High-accuracy method for measuring two-dimensional angles of a linear guideway,” Opt. Eng. 46(5), 051016 (2007).
[Crossref]

Opt. Express (2)

Opt. Laser Technol. (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]

Precis. Eng. (3)

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]

K.-C. Fan and M.-J. Chen, “A 6-degree-of-freedom measurement system for the accuracy of XY stages,” Precis. Eng. 24(1), 15–23 (2000).
[Crossref]

W. Gao, P. S. Huang, T. Yamada, and S. Kiyono, “A compact and sensitive two-dimensional angle probe for flatness measurement of large silicon wafers,” Precis. Eng. 26(4), 396–404 (2002).
[Crossref]

Rev. Sci. Instrum. (2)

J.-A. Kim, K.-C. Kim, E. W. Bae, S. Kim, and Y. K. Kwak, “Six-degree-of-freedom displacement measurement system using a diffraction grating,” Rev. Sci. Instrum. 71(8), 3214–3219 (2000).
[Crossref]

C.-H. Liu, W.-Y. Jywe, C.-C. Hsu, and T.-H. Hsu, “Development of a laser-based high-precision six-degrees-of-freedom motion errors measuring system for linear stage,” Rev. Sci. Instrum. 76(5), 055110 (2005).
[Crossref]

Other (1)

K. C. Lau and Y.-Q. Liu, “Five-axis/six-axis laser measuring system,” US Patent. 6049377 (2000).

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Figures (10)

Fig. 1
Fig. 1

Schematic of the system for simultaneously measuring 6DOF geometric motion errors.

Fig. 2
Fig. 2

Schematic of positioning error measurement.

Fig. 3
Fig. 3

Schematic of straightness error measurement.

Fig. 4
Fig. 4

Schematic of pitch and yaw measurements.

Fig. 5
Fig. 5

Schematic of roll measurement.

Fig. 6
Fig. 6

Schematic of straightness error measurement with common-path compensation.

Fig. 7
Fig. 7

Results of stability experiments.

Fig. 8
Fig. 8

Test for resolution of straightness error measurement.

Fig. 9
Fig. 9

Practical application of the developed instrument.

Fig. 10
Fig. 10

Results of repeatability and comparison experiments.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

E 1 = E 0 sin( 2π f 1 t+ ϕ 1 ) e i E 2 = E 0 sin( 2π f 2 t+ ϕ 2 ) e j
I D1 = [ cos( π 4 ) E 1 +sin( π 4 ) E 2 ] 2 = E 0 2 2 { sin 2 ( 2π f 1 t+ ϕ 1 )+ sin 2 ( 2π f 2 t+ ϕ 2 ) +cos[ 2π( f 1 f 2 )t+( ϕ 1 ϕ 2 ) ]cos[ 2π( f 1 + f 2 )t+( ϕ 1 + ϕ 2 ) ] }
I r = E 0 2 2 cos[ 2π( f 1 f 2 )t+( ϕ 1 ϕ 2 ) ]
I D2 = [ cos( π 4 ) E 1 '+sin( π 4 ) E 2 ' ] 2 = E 0 2 2 { sin 2 ( 2π f 1 t+ ϕ 1 + ϕ ref )+ sin 2 ( 2π f 2 t+ ϕ 2 + ϕ meas ) +cos[ 2π( f 1 f 2 )t+( ϕ 1 ϕ 2 )+( ϕ ref ϕ meas ) ] cos[ 2π( f 1 + f 2 )t+( ϕ 1 + ϕ 2 )+( ϕ ref + ϕ meas ) ] }
I m = E 0 2 2 cos[ 2π( f 1 f 2 )t+( ϕ 1 ϕ 2 )+Δϕ ]
Δϕ= 4nπL λ
ΔZ=LL'= λΔϕ 4nπ L'
ΔX= Δ X QD1 2 = Δ X QD2 2 ΔY= Δ Y QD1 2 = Δ Y QD2 2
ΔX= Δ X QD1 +Δ X QD2 4 ΔY= Δ Y QD1 +Δ Y QD2 4
α= Δ Y QD3 2 f 1 β= Δ X QD3 2 f 1
γ= Δ Y 2 Δ Y 1 h = Δ Y QD2 Δ Y QD1 2h
Δα= Δ Y QD4 f 2 Δβ= Δ X QD4 f 2
ΔX= X QD1 2 ±lΔβ ΔY= Y QD1 2 ±lΔα
α= Δ Y QD3 2f ±Δα β= Δ X QD3 2f ±Δβ

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