Abstract

This paper presents a method for measuring five-degrees-of-freedom errors of a moving stage with a monolithic prism and phase-sensitive detection technique. It consists of a pigtailed laser diode, three position-sensitive detectors (PSDs), a monolithic prism, and additional optical and electronic components. The monolithic prism mounted on the moving stage generates three beams that are detected by three PSDs, respectively, so that the straightness, pitch, yaw, and roll errors can be simultaneously measured. Theoretical analysis of each error measurement process is presented. To reduce the influence of disturbing light, the laser diode is modulated by a sinusoidal wave current, and a phase-sensitive detection technique is developed to demodulate the signals. Compared with a laser interferometer, the deviation errors when measuring the horizontal and vertical straightness errors are better than ±0.25 and ±0.4μm, respectively. The deviation errors for the pitch, yaw, and roll are better than ±0.5, ±0.3, and ±2arcsec, respectively, in comparison with an autocollimator. The system can be assembled to measure five error components of machine tools in an industrial environment.

© 2013 Optical Society of America

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References

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  1. H. Schwenke, W. Knapp, H. Haitjema, A. Weckenmann, R. Schmitt, and F. Delbressine, “Geometric error measurement and compensation of machines—an update,” CIRP Ann. Manuf. Technol. 57, 660–675 (2008).
    [CrossRef]
  2. R. Ramesh, M. A. Mannan, and A. N. Poo, “Error compensation in machine tools—a review: Part I: geometric, cutting-force induced and fixture-dependent errors,” Int. J. Mach. Tools Manuf. 40, 1235–1256 (2000).
    [CrossRef]
  3. J. Ni, “CNC machine accuracy enhancement through real-time error compensation,” Manuf. Sci. Eng. 119, 717–725 (1997).
    [CrossRef]
  4. P. S. Huang and J. Ni, “On-line error compensation of coordinate measuring machines,” Int. J. Mach. Tools Manuf. 35, 725–738 (1995).
    [CrossRef]
  5. J. Ni, P. S. Huang, and S. M. 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, 055110 (2005).
    [CrossRef]
  7. C. Chou, L. Y. Chou, C. K. Peng, Y. C. Huang, and K. C. Fan, “CCD-based CMM geometrical error measurement using Fourier phase shift algorithm,” Int. J. Mach. Tools Manuf. 37, 579–590 (1997).
    [CrossRef]
  8. K. C. Fan, M. J. Chen, and W. M. Huang, “A six-degree-of-freedom measurement system for the motion accuracy of linear stages,” Int. J. Mach. Tools Manuf. 38, 155–164 (1998).
    [CrossRef]
  9. C. Kuang, E. Hong, and J. Ni, “A high-precision five-degree-of-freedom measurement system based on laser collimator and interferometry techniques,” Rev. Sci. Instrum. 78, 095105 (2007).
    [CrossRef]
  10. 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 125, 100–108 (2005).
    [CrossRef]
  11. C. B. 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, 105901 (2011).
    [CrossRef]
  12. C. H. Liu, H. L. Huang, and H. W. Lee, “Five-degrees-of-freedom diffractive laser encoder,” Appl. Opt. 48, 2767–2777 (2009).
    [CrossRef]
  13. Q. Hao, D. Li, and Y. Wang, “High-accuracy long distance alignment using single-mode optical fiber and phase plate,” Opt. Laser Technol. 34, 287–292 (2002).
    [CrossRef]
  14. Q. Hao, Y. Zhao, D. Li, and M. Cao, “Straightness measurement using laser diode and CCD camera,” Chin. J. Lasers 8, 215–220 (1999).
  15. Q. Feng, B. Zhang, and C. Kuang, “A straightness measurement system using a single-mode fiber-coupled laser module,” Opt. Laser Technol. 36, 279–283 (2004).
    [CrossRef]
  16. K. C. Fan and Y. Zhao, “A laser straightness measurement system using optical fiber and modulation techniques,” Int. J. Mach. Tools Manufact. 40, 2073–2081 (2000).
    [CrossRef]
  17. J. Ni and S. M. Wu, “An on-line measurement technique for machine volumetric error compensation,” J. Eng. Ind. 115, 85–92 (1993).
    [CrossRef]

2011 (1)

C. B. 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, 105901 (2011).
[CrossRef]

2009 (1)

2008 (1)

H. Schwenke, W. Knapp, H. Haitjema, A. Weckenmann, R. Schmitt, and F. Delbressine, “Geometric error measurement and compensation of machines—an update,” CIRP Ann. Manuf. Technol. 57, 660–675 (2008).
[CrossRef]

2007 (1)

C. Kuang, E. Hong, and J. Ni, “A high-precision five-degree-of-freedom measurement system based on laser collimator and interferometry techniques,” Rev. Sci. Instrum. 78, 095105 (2007).
[CrossRef]

2005 (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 125, 100–108 (2005).
[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, 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, 279–283 (2004).
[CrossRef]

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, 287–292 (2002).
[CrossRef]

2000 (2)

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

R. Ramesh, M. A. Mannan, and A. N. Poo, “Error compensation in machine tools—a review: Part I: geometric, cutting-force induced and fixture-dependent errors,” Int. J. Mach. Tools Manuf. 40, 1235–1256 (2000).
[CrossRef]

1999 (1)

Q. Hao, Y. Zhao, D. Li, and M. Cao, “Straightness measurement using laser diode and CCD camera,” Chin. J. Lasers 8, 215–220 (1999).

1998 (1)

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

1997 (2)

J. Ni, “CNC machine accuracy enhancement through real-time error compensation,” Manuf. Sci. Eng. 119, 717–725 (1997).
[CrossRef]

C. Chou, L. Y. Chou, C. K. Peng, Y. C. Huang, and K. C. Fan, “CCD-based CMM geometrical error measurement using Fourier phase shift algorithm,” Int. J. Mach. Tools Manuf. 37, 579–590 (1997).
[CrossRef]

1995 (1)

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

1993 (1)

J. Ni and S. M. Wu, “An on-line measurement technique for machine volumetric error compensation,” J. Eng. Ind. 115, 85–92 (1993).
[CrossRef]

1992 (1)

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

Cao, M.

Q. Hao, Y. Zhao, D. Li, and M. Cao, “Straightness measurement using laser diode and CCD camera,” Chin. J. Lasers 8, 215–220 (1999).

Chen, M. J.

K. C. Fan, M. J. Chen, and W. M. Huang, “A six-degree-of-freedom measurement system for the motion accuracy of linear stages,” Int. J. Mach. Tools Manuf. 38, 155–164 (1998).
[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 125, 100–108 (2005).
[CrossRef]

Chou, C.

C. Chou, L. Y. Chou, C. K. Peng, Y. C. Huang, and K. C. Fan, “CCD-based CMM geometrical error measurement using Fourier phase shift algorithm,” Int. J. Mach. Tools Manuf. 37, 579–590 (1997).
[CrossRef]

Chou, L. Y.

C. Chou, L. Y. Chou, C. K. Peng, Y. C. Huang, and K. C. Fan, “CCD-based CMM geometrical error measurement using Fourier phase shift algorithm,” Int. J. Mach. Tools Manuf. 37, 579–590 (1997).
[CrossRef]

Delbressine, F.

H. Schwenke, W. Knapp, H. Haitjema, A. Weckenmann, R. Schmitt, and F. Delbressine, “Geometric error measurement and compensation of machines—an update,” CIRP Ann. Manuf. Technol. 57, 660–675 (2008).
[CrossRef]

Fan, K. C.

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

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

C. Chou, L. Y. Chou, C. K. Peng, Y. C. Huang, and K. C. Fan, “CCD-based CMM geometrical error measurement using Fourier phase shift algorithm,” Int. J. Mach. Tools Manuf. 37, 579–590 (1997).
[CrossRef]

Feng, Q.

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 125, 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, 279–283 (2004).
[CrossRef]

Haitjema, H.

H. Schwenke, W. Knapp, H. Haitjema, A. Weckenmann, R. Schmitt, and F. Delbressine, “Geometric error measurement and compensation of machines—an update,” CIRP Ann. Manuf. Technol. 57, 660–675 (2008).
[CrossRef]

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, 287–292 (2002).
[CrossRef]

Q. Hao, Y. Zhao, D. Li, and M. Cao, “Straightness measurement using laser diode and CCD camera,” Chin. J. Lasers 8, 215–220 (1999).

Hong, E.

C. Kuang, E. Hong, and J. Ni, “A high-precision five-degree-of-freedom measurement system based on laser collimator and interferometry techniques,” Rev. Sci. Instrum. 78, 095105 (2007).
[CrossRef]

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, 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, 055110 (2005).
[CrossRef]

Huang, H. L.

Huang, P. S.

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

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

Huang, W. M.

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

Huang, Y. C.

C. Chou, L. Y. Chou, C. K. Peng, Y. C. Huang, and K. C. Fan, “CCD-based CMM geometrical error measurement using Fourier phase shift algorithm,” Int. J. Mach. Tools Manuf. 37, 579–590 (1997).
[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, 055110 (2005).
[CrossRef]

Kim, G. H.

C. B. 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, 105901 (2011).
[CrossRef]

Knapp, W.

H. Schwenke, W. Knapp, H. Haitjema, A. Weckenmann, R. Schmitt, and F. Delbressine, “Geometric error measurement and compensation of machines—an update,” CIRP Ann. Manuf. Technol. 57, 660–675 (2008).
[CrossRef]

Kuang, C.

C. Kuang, E. Hong, and J. Ni, “A high-precision five-degree-of-freedom measurement system based on laser collimator and interferometry techniques,” Rev. Sci. Instrum. 78, 095105 (2007).
[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 125, 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, 279–283 (2004).
[CrossRef]

Lee, C. B.

C. B. 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, 105901 (2011).
[CrossRef]

Lee, H. W.

Lee, S. K.

C. B. 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, 105901 (2011).
[CrossRef]

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, 287–292 (2002).
[CrossRef]

Q. Hao, Y. Zhao, D. Li, and M. Cao, “Straightness measurement using laser diode and CCD camera,” Chin. J. Lasers 8, 215–220 (1999).

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 125, 100–108 (2005).
[CrossRef]

Liu, C. H.

C. H. Liu, H. L. Huang, and H. W. Lee, “Five-degrees-of-freedom diffractive laser encoder,” Appl. Opt. 48, 2767–2777 (2009).
[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, 055110 (2005).
[CrossRef]

Mannan, M. A.

R. Ramesh, M. A. Mannan, and A. N. Poo, “Error compensation in machine tools—a review: Part I: geometric, cutting-force induced and fixture-dependent errors,” Int. J. Mach. Tools Manuf. 40, 1235–1256 (2000).
[CrossRef]

Ni, J.

C. Kuang, E. Hong, and J. Ni, “A high-precision five-degree-of-freedom measurement system based on laser collimator and interferometry techniques,” Rev. Sci. Instrum. 78, 095105 (2007).
[CrossRef]

J. Ni, “CNC machine accuracy enhancement through real-time error compensation,” Manuf. Sci. Eng. 119, 717–725 (1997).
[CrossRef]

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

J. Ni and S. M. Wu, “An on-line measurement technique for machine volumetric error compensation,” J. Eng. Ind. 115, 85–92 (1993).
[CrossRef]

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

Peng, C. K.

C. Chou, L. Y. Chou, C. K. Peng, Y. C. Huang, and K. C. Fan, “CCD-based CMM geometrical error measurement using Fourier phase shift algorithm,” Int. J. Mach. Tools Manuf. 37, 579–590 (1997).
[CrossRef]

Poo, A. N.

R. Ramesh, M. A. Mannan, and A. N. Poo, “Error compensation in machine tools—a review: Part I: geometric, cutting-force induced and fixture-dependent errors,” Int. J. Mach. Tools Manuf. 40, 1235–1256 (2000).
[CrossRef]

Ramesh, R.

R. Ramesh, M. A. Mannan, and A. N. Poo, “Error compensation in machine tools—a review: Part I: geometric, cutting-force induced and fixture-dependent errors,” Int. J. Mach. Tools Manuf. 40, 1235–1256 (2000).
[CrossRef]

Schmitt, R.

H. Schwenke, W. Knapp, H. Haitjema, A. Weckenmann, R. Schmitt, and F. Delbressine, “Geometric error measurement and compensation of machines—an update,” CIRP Ann. Manuf. Technol. 57, 660–675 (2008).
[CrossRef]

Schwenke, H.

H. Schwenke, W. Knapp, H. Haitjema, A. Weckenmann, R. Schmitt, and F. Delbressine, “Geometric error measurement and compensation of machines—an update,” CIRP Ann. Manuf. Technol. 57, 660–675 (2008).
[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, 287–292 (2002).
[CrossRef]

Weckenmann, A.

H. Schwenke, W. Knapp, H. Haitjema, A. Weckenmann, R. Schmitt, and F. Delbressine, “Geometric error measurement and compensation of machines—an update,” CIRP Ann. Manuf. Technol. 57, 660–675 (2008).
[CrossRef]

Wu, S. M.

J. Ni and S. M. Wu, “An on-line measurement technique for machine volumetric error compensation,” J. Eng. Ind. 115, 85–92 (1993).
[CrossRef]

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

Zhang, 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 125, 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, 279–283 (2004).
[CrossRef]

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 125, 100–108 (2005).
[CrossRef]

Zhao, Y.

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

Q. Hao, Y. Zhao, D. Li, and M. Cao, “Straightness measurement using laser diode and CCD camera,” Chin. J. Lasers 8, 215–220 (1999).

Appl. Opt. (1)

Chin. J. Lasers (1)

Q. Hao, Y. Zhao, D. Li, and M. Cao, “Straightness measurement using laser diode and CCD camera,” Chin. J. Lasers 8, 215–220 (1999).

CIRP Ann. Manuf. Technol. (1)

H. Schwenke, W. Knapp, H. Haitjema, A. Weckenmann, R. Schmitt, and F. Delbressine, “Geometric error measurement and compensation of machines—an update,” CIRP Ann. Manuf. Technol. 57, 660–675 (2008).
[CrossRef]

Int. J. Mach. Tools Manuf. (4)

R. Ramesh, M. A. Mannan, and A. N. Poo, “Error compensation in machine tools—a review: Part I: geometric, cutting-force induced and fixture-dependent errors,” Int. J. Mach. Tools Manuf. 40, 1235–1256 (2000).
[CrossRef]

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

C. Chou, L. Y. Chou, C. K. Peng, Y. C. Huang, and K. C. Fan, “CCD-based CMM geometrical error measurement using Fourier phase shift algorithm,” Int. J. Mach. Tools Manuf. 37, 579–590 (1997).
[CrossRef]

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

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

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

J. Eng. Ind. (2)

J. Ni and S. M. Wu, “An on-line measurement technique for machine volumetric error compensation,” J. Eng. Ind. 115, 85–92 (1993).
[CrossRef]

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

Manuf. Sci. Eng. (1)

J. Ni, “CNC machine accuracy enhancement through real-time error compensation,” Manuf. Sci. Eng. 119, 717–725 (1997).
[CrossRef]

Meas. Sci. Technol. (1)

C. B. 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, 105901 (2011).
[CrossRef]

Opt. Laser Technol. (2)

Q. Feng, B. Zhang, and C. Kuang, “A straightness measurement system using a single-mode fiber-coupled laser module,” Opt. Laser Technol. 36, 279–283 (2004).
[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, 287–292 (2002).
[CrossRef]

Rev. Sci. Instrum. (2)

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, 055110 (2005).
[CrossRef]

C. Kuang, E. Hong, and J. Ni, “A high-precision five-degree-of-freedom measurement system based on laser collimator and interferometry techniques,” Rev. Sci. Instrum. 78, 095105 (2007).
[CrossRef]

Sens. Actuators A (1)

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 125, 100–108 (2005).
[CrossRef]

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Figures (17)

Fig. 1.
Fig. 1.

(A) Schematic of the experimental setup: 1, laser diode; 2, collimator; 3, beam splitter; 4, cemented prism; 4(a), beam-splitting film; 4(b), corner cube; 4(c), semi-reflector surface; 4(d), reflective surface; 5, 6, 7, PSD; 8, lens. (B) Photograph of the monolithic prism.

Fig. 2.
Fig. 2.

(A) A schematic of the phase-sensitive detection. (B) A picture of the PSD signal processing circuit.

Fig. 3.
Fig. 3.

Results of stability test. The standard deviations of the drifts were 0.15 and 0.17 μm in the horizontal and vertical directions, respectively.

Fig. 4.
Fig. 4.

Measuring principle of the straightness error.

Fig. 5.
Fig. 5.

Measuring principle of the pitch and yaw.

Fig. 6.
Fig. 6.

Measuring principle of the roll.

Fig. 7.
Fig. 7.

(A) Setup for the calibration of straightness. (B) Setup for the calibration of pitch and yaw. (C) Setup for the calibration of roll.

Fig. 8.
Fig. 8.

Calibration results for the horizontal straightness. The residual error was within ±0.25μm.

Fig. 9.
Fig. 9.

Calibration results for the vertical straightness. The residual error was within ±0.4μm.

Fig. 10.
Fig. 10.

Calibration results for the pitch. The residual error was within ±0.5arcsec.

Fig. 11.
Fig. 11.

Calibration results for the yaw. The residual error was within ±0.3arcsec.

Fig. 12.
Fig. 12.

Calibration results for the roll. The residual error was within ±2arcsec.

Fig. 13.
Fig. 13.

Influence of the pitch on the roll measurement.

Fig. 14.
Fig. 14.

Horizontal straightness error of the stage.

Fig. 15.
Fig. 15.

Vertical straightness error of the stage.

Fig. 16.
Fig. 16.

Pitch error of the stage.

Fig. 17.
Fig. 17.

Yaw error of the stage.

Equations (21)

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

X=(A+D)(B+C)A+B+C+DY=(A+B)(C+D)A+B+C+D,
Δx=ΔX12;Δy=ΔY12,
α=ΔX2f,β=ΔY2f,
R=RxRyRz=[1000cosαsinα0sinαcosα][cosβ0sinβ010sinβ0cosβ][cosγsinγ0sinγcosγ0001].
R=[1γβγ1αβα1].
N10=12[202]T,N20=12[202]T.
N1=RN10=12[1+βγα1β]T,N2=RN20=12[1+βγα1β]T.
M1=M2=[2βαγ1αγ1αγ1αγ2β].
I2=[(11/n)β(11/n)α1]T,I3=[(11/n)β(11/n)α1]T,I4=[(11/n)β(11/n)α1]T,I5=M1I3=[1(1/n)αγ(1+1/n)β]T,I6=M2I5=[(11/n)β(11/n)α1]T,
12[xx0yy0zz0][1+βγα1β]T=0,
12[xx0+dyy0+dγzz0dβ][1+βγα1β]T=0,
(xx0,yy0,zz0)=k1((11/n)β,(11/n)α,1),
(xx0+d(1+1/n)β,yy0d(α/nγ),zz0d(1+1/n)β)=k2((11/n)β,(11/n)α,1),
[xx1yy1zz1][βα1]T=0,
(x0+Px,y0+Py,z1+Pz),
(x0d(1+1/n)β+Px,y0+d(α/nγ)+Py,z1+d(1+1/n)β+Pz),
γ=ΔY1ΔY2d+αn,
ΔY2ΔY1d=αn,
N1=12[1+βγα1β]T,N2=12[1+βγα+θ1β]T.
ΔY2ΔY1=(αnγ)d+ΔZnθ,
γ=(ΔY1ΔY2)+ΔZnθd+αn.

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