Abstract

Collinear calibration is a typical and common method for a laser (heterodyne) interferometer, but it usually suffers from the influence of the tilt of the target retroreflectors and the dissymmetry of the optical paths during the calibration. This paper mainly analyzes and models the calibration error caused by the tilt error of the target retroreflectors and reveals the error source that is the disturbance from the rotary error of the guideway slider pair. Experimental results prove the validity of the analysis and model of the calibration error. The calibration error is up to 0.5 μm when the tilt error is 0.36°, which is large enough to equal the maximum tolerance of laser interferometer (0.5 μm) in use.

© 2013 Optical Society of America

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  29. L. Cai, J. Lu, and Y. Wei, “Calibration method for wavelength of laser interferometer,” Proceedings of 1st National Measurement Conference of China (1998), pp. 463–468.
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2012

S. Tang, Z. Wang, L. Zhong, J. Gao, and J. Guo, “Error analysis of a plane mirror interferometer based on geometric optical paths,” Opt. Express 20, 5108–5118 (2012).
[CrossRef]

2011

A. Takahashi, Y. Takigawa, and N. Miwa, “Error contributor of defocus and quadratic caustic in line scale measurement,” Meas. Sci. Technol. 22, 015302 (2011).

2010

I. Hahn, M. Weilert, X. Wang, and R. Goullioud, “A heterodyne interferometer for angle metrology,” Rev. Sci. Instrum. 81, 1–6 (2010).
[CrossRef]

2009

J. Park, M. Y. Lee, and D. Y. Lee, “A nano-metrology system with a two-dimensional combined optical and X-ray interferometer and an atomic force microscope,” Microsyst. Technol. 15, 1879–1884 (2009).
[CrossRef]

2008

P. F. Luo, S. P. Pan, and C. L. Lee, “Application of computer vision and laser interferometer to two-dimensional inspection,” Opt. Eng. 47, 123601 (2008).
[CrossRef]

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

K. J. Yan, J. Liu, F. Gao, and H. Wang, “Study of geometric errors detection method for NC machine tools based on non-contact circular track,” Proc. SPIE 7130, 71305K (2008).
[CrossRef]

M. Pisani, “Multiple reflection Michelson interferometer with picometer resolution,” Opt. Express 16, 21558–21563 (2008).
[CrossRef]

2007

Z. Zhang, and C. H. Menq, “Laser interferometric system for six-axis motion measurement,” Rev. Sci. Instrum. 78, 1–8 (2007).
[CrossRef]

H. Hussein, M. A. Sobee, and M. Amer, “Calibration of a Michelson-type laser wavemeter and evaluation of its accuracy,” Opt. Laser Eng. 48, 393–397 (2007).
[CrossRef]

2006

J. Li, Y. Zhao, X. Tao, and G. Zhu, “A way to calibrate laser interferometer by common path,” Acta Metrologica Sin. 27, 58–61 (2006).

M. Pisani and M. Astrua, “Angle amplification for nanoradian measurements,” Appl. Opt. 45, 1725–1729 (2006).
[CrossRef]

H. J. Büchner and G. Jäger, “A novel plane mirror interferometer without using corner cube reflectors,” Meas. Sci. Technol. 17, 746–752 (2006).
[CrossRef]

Z. Cheng, H. Gao, Z. Zhang, H. Huang, and J. Zhu, “Study of a dual-frequency laser interferometer with unique optical subdivision techniques,” Appl. Opt. 45, 2246–2250 (2006).
[CrossRef]

W. Gao, Y. Arai, A. Shibuya, S. Kiyono, and C. H. Park, “Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage,” Precis. Eng. 30, 96–103 (2006).
[CrossRef]

2005

H. Bosse and G. Wilkening, “Developments at PTB in nanometrology for support of the semiconductor industry,” Meas. Sci. Technol. 16, 2155–2166 (2005).
[CrossRef]

2004

K. Iwasawa, A. Iwama, and K. Mistsui, “Development of a measuring method for several types of programmed tool paths for NC machine tools using a laser displacement interferometer and a rotary encoder,” Precis. Eng. 28, 399–408 (2004).
[CrossRef]

2003

H. Haitjema, S. J. A. G. Cosijins, N. J. J. Roset, M. J. Jansen, and P.H.J. Schellekens, “Improving a commercially available heterodyne laser interferometer to sub-nm uncertainty,” Proc. SPIE 5190, 347–354 (2003).
[CrossRef]

2002

P. G. Halverson and R. E. Spero, “Signal processing and testing of displacement metrology gauges with picometre-scale cyclic nonlinearity,” J. Opt. A 4, S304–S310 (2002).
[CrossRef]

2001

F. Meil, N. Jeanmonod, C. Thiess, and R. Thalmann, “Calibration of a 2D reference mirror system of a photomask measuring instrument,” Proc. SPIE 4401, 227–233 (2001).
[CrossRef]

C. Wang and B. Griffin, “A noncontact laser technique for circular contouring accuracy measurement,” Rev. Sci. Instrum. 72, 1594–1596 (2001).
[CrossRef]

D. A. Swyt, S. D. Philips, and J. Palmateer, “Developments at NIST on Traceability in dimensional measurements,” Proc. SPIE 4401, 245–252 (2001).
[CrossRef]

1999

S. Sandwith, “Thermal stability of laser tracking interferometer calibration,” Proc. SPIE 3835, 93–103 (1999).
[CrossRef]

1998

M. Frennberg, M. Johansson, S. Källberg, U. Kärn, and L. R. Pendrill, “Long gauge block interferometer using two frequency-stabilised lasers,” Proc. SPIE 3477, 35–44 (1998).
[CrossRef]

1997

D. L. Cohen, “Performance degradation of a Michelson interferometer when its misalignment angle is a rapidly varying, random time series,” Appl. Opt. 36, 4034–4042 (1997).
[CrossRef]

1996

F. G. P. Peeters, “Interferometer with added flexibility in its use,” Opt. Eng. 35, 1953–1956 (1996).
[CrossRef]

1993

M. M. Colavita, M. Shao, and M. D. Rayman, “Orbiting stellar interferometer for astrometry and imaging,” Appl. Opt. 32, 1789–1797 (1993).
[CrossRef]

Amer, M.

H. Hussein, M. A. Sobee, and M. Amer, “Calibration of a Michelson-type laser wavemeter and evaluation of its accuracy,” Opt. Laser Eng. 48, 393–397 (2007).
[CrossRef]

Arai, Y.

W. Gao, Y. Arai, A. Shibuya, S. Kiyono, and C. H. Park, “Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage,” Precis. Eng. 30, 96–103 (2006).
[CrossRef]

Astrua, M.

M. Pisani and M. Astrua, “Angle amplification for nanoradian measurements,” Appl. Opt. 45, 1725–1729 (2006).
[CrossRef]

Bosse, H.

H. Bosse and G. Wilkening, “Developments at PTB in nanometrology for support of the semiconductor industry,” Meas. Sci. Technol. 16, 2155–2166 (2005).
[CrossRef]

Büchner, H. J.

H. J. Büchner and G. Jäger, “A novel plane mirror interferometer without using corner cube reflectors,” Meas. Sci. Technol. 17, 746–752 (2006).
[CrossRef]

Cai, L.

L. Cai, J. Lu, and Y. Wei, “Calibration method for wavelength of laser interferometer,” Proceedings of 1st National Measurement Conference of China (1998), pp. 463–468.

Cheng, Z.

Z. Cheng, H. Gao, Z. Zhang, H. Huang, and J. Zhu, “Study of a dual-frequency laser interferometer with unique optical subdivision techniques,” Appl. Opt. 45, 2246–2250 (2006).
[CrossRef]

Cohen, D. L.

D. L. Cohen, “Performance degradation of a Michelson interferometer when its misalignment angle is a rapidly varying, random time series,” Appl. Opt. 36, 4034–4042 (1997).
[CrossRef]

Colavita, M. M.

M. M. Colavita, M. Shao, and M. D. Rayman, “Orbiting stellar interferometer for astrometry and imaging,” Appl. Opt. 32, 1789–1797 (1993).
[CrossRef]

Cosijins, S. J. A. G.

H. Haitjema, S. J. A. G. Cosijins, N. J. J. Roset, M. J. Jansen, and P.H.J. Schellekens, “Improving a commercially available heterodyne laser interferometer to sub-nm uncertainty,” Proc. SPIE 5190, 347–354 (2003).
[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. 57, 660–675 (2008).
[CrossRef]

Frennberg, M.

M. Frennberg, M. Johansson, S. Källberg, U. Kärn, and L. R. Pendrill, “Long gauge block interferometer using two frequency-stabilised lasers,” Proc. SPIE 3477, 35–44 (1998).
[CrossRef]

Gao, F.

K. J. Yan, J. Liu, F. Gao, and H. Wang, “Study of geometric errors detection method for NC machine tools based on non-contact circular track,” Proc. SPIE 7130, 71305K (2008).
[CrossRef]

Gao, H.

Z. Cheng, H. Gao, Z. Zhang, H. Huang, and J. Zhu, “Study of a dual-frequency laser interferometer with unique optical subdivision techniques,” Appl. Opt. 45, 2246–2250 (2006).
[CrossRef]

Gao, J.

S. Tang, Z. Wang, L. Zhong, J. Gao, and J. Guo, “Error analysis of a plane mirror interferometer based on geometric optical paths,” Opt. Express 20, 5108–5118 (2012).
[CrossRef]

S. Tang, Z. Wang, Z. Jiang, J. Gao, and J. Guo, “A new measuring method for circular motion accuracy of NC machine tools based on dual-frequency laser interferometer,” in Proceedings of IEEE International Symposium on Assembly and Manufacturing ISAM2011 (IEEE, 2011), pp. 1–6.

Gao, W.

W. Gao, Y. Arai, A. Shibuya, S. Kiyono, and C. H. Park, “Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage,” Precis. Eng. 30, 96–103 (2006).
[CrossRef]

Goullioud, R.

I. Hahn, M. Weilert, X. Wang, and R. Goullioud, “A heterodyne interferometer for angle metrology,” Rev. Sci. Instrum. 81, 1–6 (2010).
[CrossRef]

Griffin, B.

C. Wang and B. Griffin, “A noncontact laser technique for circular contouring accuracy measurement,” Rev. Sci. Instrum. 72, 1594–1596 (2001).
[CrossRef]

Guo, J.

S. Tang, Z. Wang, L. Zhong, J. Gao, and J. Guo, “Error analysis of a plane mirror interferometer based on geometric optical paths,” Opt. Express 20, 5108–5118 (2012).
[CrossRef]

S. Tang, Z. Wang, Z. Jiang, J. Gao, and J. Guo, “A new measuring method for circular motion accuracy of NC machine tools based on dual-frequency laser interferometer,” in Proceedings of IEEE International Symposium on Assembly and Manufacturing ISAM2011 (IEEE, 2011), pp. 1–6.

Hahn, I.

I. Hahn, M. Weilert, X. Wang, and R. Goullioud, “A heterodyne interferometer for angle metrology,” Rev. Sci. Instrum. 81, 1–6 (2010).
[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. 57, 660–675 (2008).
[CrossRef]

H. Haitjema, S. J. A. G. Cosijins, N. J. J. Roset, M. J. Jansen, and P.H.J. Schellekens, “Improving a commercially available heterodyne laser interferometer to sub-nm uncertainty,” Proc. SPIE 5190, 347–354 (2003).
[CrossRef]

Halverson, P. G.

P. G. Halverson and R. E. Spero, “Signal processing and testing of displacement metrology gauges with picometre-scale cyclic nonlinearity,” J. Opt. A 4, S304–S310 (2002).
[CrossRef]

Huang, H.

Z. Cheng, H. Gao, Z. Zhang, H. Huang, and J. Zhu, “Study of a dual-frequency laser interferometer with unique optical subdivision techniques,” Appl. Opt. 45, 2246–2250 (2006).
[CrossRef]

Hussein, H.

H. Hussein, M. A. Sobee, and M. Amer, “Calibration of a Michelson-type laser wavemeter and evaluation of its accuracy,” Opt. Laser Eng. 48, 393–397 (2007).
[CrossRef]

Iwama, A.

K. Iwasawa, A. Iwama, and K. Mistsui, “Development of a measuring method for several types of programmed tool paths for NC machine tools using a laser displacement interferometer and a rotary encoder,” Precis. Eng. 28, 399–408 (2004).
[CrossRef]

Iwasawa, K.

K. Iwasawa, A. Iwama, and K. Mistsui, “Development of a measuring method for several types of programmed tool paths for NC machine tools using a laser displacement interferometer and a rotary encoder,” Precis. Eng. 28, 399–408 (2004).
[CrossRef]

Jäger, G.

H. J. Büchner and G. Jäger, “A novel plane mirror interferometer without using corner cube reflectors,” Meas. Sci. Technol. 17, 746–752 (2006).
[CrossRef]

Jansen, M. J.

H. Haitjema, S. J. A. G. Cosijins, N. J. J. Roset, M. J. Jansen, and P.H.J. Schellekens, “Improving a commercially available heterodyne laser interferometer to sub-nm uncertainty,” Proc. SPIE 5190, 347–354 (2003).
[CrossRef]

Jeanmonod, N.

F. Meil, N. Jeanmonod, C. Thiess, and R. Thalmann, “Calibration of a 2D reference mirror system of a photomask measuring instrument,” Proc. SPIE 4401, 227–233 (2001).
[CrossRef]

Jiang, Z.

S. Tang, Z. Wang, Z. Jiang, J. Gao, and J. Guo, “A new measuring method for circular motion accuracy of NC machine tools based on dual-frequency laser interferometer,” in Proceedings of IEEE International Symposium on Assembly and Manufacturing ISAM2011 (IEEE, 2011), pp. 1–6.

Johansson, M.

M. Frennberg, M. Johansson, S. Källberg, U. Kärn, and L. R. Pendrill, “Long gauge block interferometer using two frequency-stabilised lasers,” Proc. SPIE 3477, 35–44 (1998).
[CrossRef]

Källberg, S.

M. Frennberg, M. Johansson, S. Källberg, U. Kärn, and L. R. Pendrill, “Long gauge block interferometer using two frequency-stabilised lasers,” Proc. SPIE 3477, 35–44 (1998).
[CrossRef]

Kärn, U.

M. Frennberg, M. Johansson, S. Källberg, U. Kärn, and L. R. Pendrill, “Long gauge block interferometer using two frequency-stabilised lasers,” Proc. SPIE 3477, 35–44 (1998).
[CrossRef]

Kiyono, S.

W. Gao, Y. Arai, A. Shibuya, S. Kiyono, and C. H. Park, “Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage,” Precis. Eng. 30, 96–103 (2006).
[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. 57, 660–675 (2008).
[CrossRef]

Lee, C. L.

P. F. Luo, S. P. Pan, and C. L. Lee, “Application of computer vision and laser interferometer to two-dimensional inspection,” Opt. Eng. 47, 123601 (2008).
[CrossRef]

Lee, D. Y.

J. Park, M. Y. Lee, and D. Y. Lee, “A nano-metrology system with a two-dimensional combined optical and X-ray interferometer and an atomic force microscope,” Microsyst. Technol. 15, 1879–1884 (2009).
[CrossRef]

Lee, M. Y.

J. Park, M. Y. Lee, and D. Y. Lee, “A nano-metrology system with a two-dimensional combined optical and X-ray interferometer and an atomic force microscope,” Microsyst. Technol. 15, 1879–1884 (2009).
[CrossRef]

Li, J.

J. Li, Y. Zhao, X. Tao, and G. Zhu, “A way to calibrate laser interferometer by common path,” Acta Metrologica Sin. 27, 58–61 (2006).

Liu, J.

K. J. Yan, J. Liu, F. Gao, and H. Wang, “Study of geometric errors detection method for NC machine tools based on non-contact circular track,” Proc. SPIE 7130, 71305K (2008).
[CrossRef]

Lu, J.

L. Cai, J. Lu, and Y. Wei, “Calibration method for wavelength of laser interferometer,” Proceedings of 1st National Measurement Conference of China (1998), pp. 463–468.

Luo, P. F.

P. F. Luo, S. P. Pan, and C. L. Lee, “Application of computer vision and laser interferometer to two-dimensional inspection,” Opt. Eng. 47, 123601 (2008).
[CrossRef]

Meil, F.

F. Meil, N. Jeanmonod, C. Thiess, and R. Thalmann, “Calibration of a 2D reference mirror system of a photomask measuring instrument,” Proc. SPIE 4401, 227–233 (2001).
[CrossRef]

Menq, C. H.

Z. Zhang, and C. H. Menq, “Laser interferometric system for six-axis motion measurement,” Rev. Sci. Instrum. 78, 1–8 (2007).
[CrossRef]

Mistsui, K.

K. Iwasawa, A. Iwama, and K. Mistsui, “Development of a measuring method for several types of programmed tool paths for NC machine tools using a laser displacement interferometer and a rotary encoder,” Precis. Eng. 28, 399–408 (2004).
[CrossRef]

Miwa, N.

A. Takahashi, Y. Takigawa, and N. Miwa, “Error contributor of defocus and quadratic caustic in line scale measurement,” Meas. Sci. Technol. 22, 015302 (2011).

Palmateer, J.

D. A. Swyt, S. D. Philips, and J. Palmateer, “Developments at NIST on Traceability in dimensional measurements,” Proc. SPIE 4401, 245–252 (2001).
[CrossRef]

Pan, S. P.

P. F. Luo, S. P. Pan, and C. L. Lee, “Application of computer vision and laser interferometer to two-dimensional inspection,” Opt. Eng. 47, 123601 (2008).
[CrossRef]

Park, C. H.

W. Gao, Y. Arai, A. Shibuya, S. Kiyono, and C. H. Park, “Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage,” Precis. Eng. 30, 96–103 (2006).
[CrossRef]

Park, J.

J. Park, M. Y. Lee, and D. Y. Lee, “A nano-metrology system with a two-dimensional combined optical and X-ray interferometer and an atomic force microscope,” Microsyst. Technol. 15, 1879–1884 (2009).
[CrossRef]

Peeters, F. G. P.

F. G. P. Peeters, “Interferometer with added flexibility in its use,” Opt. Eng. 35, 1953–1956 (1996).
[CrossRef]

Pendrill, L. R.

M. Frennberg, M. Johansson, S. Källberg, U. Kärn, and L. R. Pendrill, “Long gauge block interferometer using two frequency-stabilised lasers,” Proc. SPIE 3477, 35–44 (1998).
[CrossRef]

Philips, S. D.

D. A. Swyt, S. D. Philips, and J. Palmateer, “Developments at NIST on Traceability in dimensional measurements,” Proc. SPIE 4401, 245–252 (2001).
[CrossRef]

Pisani, M.

M. Pisani, “Multiple reflection Michelson interferometer with picometer resolution,” Opt. Express 16, 21558–21563 (2008).
[CrossRef]

M. Pisani and M. Astrua, “Angle amplification for nanoradian measurements,” Appl. Opt. 45, 1725–1729 (2006).
[CrossRef]

Rayman, M. D.

M. M. Colavita, M. Shao, and M. D. Rayman, “Orbiting stellar interferometer for astrometry and imaging,” Appl. Opt. 32, 1789–1797 (1993).
[CrossRef]

Roset, N. J. J.

H. Haitjema, S. J. A. G. Cosijins, N. J. J. Roset, M. J. Jansen, and P.H.J. Schellekens, “Improving a commercially available heterodyne laser interferometer to sub-nm uncertainty,” Proc. SPIE 5190, 347–354 (2003).
[CrossRef]

Sandwith, S.

S. Sandwith, “Thermal stability of laser tracking interferometer calibration,” Proc. SPIE 3835, 93–103 (1999).
[CrossRef]

Schellekens, P.H.J.

H. Haitjema, S. J. A. G. Cosijins, N. J. J. Roset, M. J. Jansen, and P.H.J. Schellekens, “Improving a commercially available heterodyne laser interferometer to sub-nm uncertainty,” Proc. SPIE 5190, 347–354 (2003).
[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. 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. 57, 660–675 (2008).
[CrossRef]

Shao, M.

M. M. Colavita, M. Shao, and M. D. Rayman, “Orbiting stellar interferometer for astrometry and imaging,” Appl. Opt. 32, 1789–1797 (1993).
[CrossRef]

Shibuya, A.

W. Gao, Y. Arai, A. Shibuya, S. Kiyono, and C. H. Park, “Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage,” Precis. Eng. 30, 96–103 (2006).
[CrossRef]

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H. Hussein, M. A. Sobee, and M. Amer, “Calibration of a Michelson-type laser wavemeter and evaluation of its accuracy,” Opt. Laser Eng. 48, 393–397 (2007).
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A. Takahashi, Y. Takigawa, and N. Miwa, “Error contributor of defocus and quadratic caustic in line scale measurement,” Meas. Sci. Technol. 22, 015302 (2011).

Tang, S.

S. Tang, Z. Wang, L. Zhong, J. Gao, and J. Guo, “Error analysis of a plane mirror interferometer based on geometric optical paths,” Opt. Express 20, 5108–5118 (2012).
[CrossRef]

S. Tang, Z. Wang, Z. Jiang, J. Gao, and J. Guo, “A new measuring method for circular motion accuracy of NC machine tools based on dual-frequency laser interferometer,” in Proceedings of IEEE International Symposium on Assembly and Manufacturing ISAM2011 (IEEE, 2011), pp. 1–6.

Tao, X.

J. Li, Y. Zhao, X. Tao, and G. Zhu, “A way to calibrate laser interferometer by common path,” Acta Metrologica Sin. 27, 58–61 (2006).

Thalmann, R.

F. Meil, N. Jeanmonod, C. Thiess, and R. Thalmann, “Calibration of a 2D reference mirror system of a photomask measuring instrument,” Proc. SPIE 4401, 227–233 (2001).
[CrossRef]

Thiess, C.

F. Meil, N. Jeanmonod, C. Thiess, and R. Thalmann, “Calibration of a 2D reference mirror system of a photomask measuring instrument,” Proc. SPIE 4401, 227–233 (2001).
[CrossRef]

Wang, C.

C. Wang and B. Griffin, “A noncontact laser technique for circular contouring accuracy measurement,” Rev. Sci. Instrum. 72, 1594–1596 (2001).
[CrossRef]

Wang, H.

K. J. Yan, J. Liu, F. Gao, and H. Wang, “Study of geometric errors detection method for NC machine tools based on non-contact circular track,” Proc. SPIE 7130, 71305K (2008).
[CrossRef]

Wang, X.

I. Hahn, M. Weilert, X. Wang, and R. Goullioud, “A heterodyne interferometer for angle metrology,” Rev. Sci. Instrum. 81, 1–6 (2010).
[CrossRef]

Wang, Z.

S. Tang, Z. Wang, L. Zhong, J. Gao, and J. Guo, “Error analysis of a plane mirror interferometer based on geometric optical paths,” Opt. Express 20, 5108–5118 (2012).
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S. Tang, Z. Wang, Z. Jiang, J. Gao, and J. Guo, “A new measuring method for circular motion accuracy of NC machine tools based on dual-frequency laser interferometer,” in Proceedings of IEEE International Symposium on Assembly and Manufacturing ISAM2011 (IEEE, 2011), pp. 1–6.

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

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L. Cai, J. Lu, and Y. Wei, “Calibration method for wavelength of laser interferometer,” Proceedings of 1st National Measurement Conference of China (1998), pp. 463–468.

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I. Hahn, M. Weilert, X. Wang, and R. Goullioud, “A heterodyne interferometer for angle metrology,” Rev. Sci. Instrum. 81, 1–6 (2010).
[CrossRef]

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H. Bosse and G. Wilkening, “Developments at PTB in nanometrology for support of the semiconductor industry,” Meas. Sci. Technol. 16, 2155–2166 (2005).
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K. J. Yan, J. Liu, F. Gao, and H. Wang, “Study of geometric errors detection method for NC machine tools based on non-contact circular track,” Proc. SPIE 7130, 71305K (2008).
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Zhang, Z.

Z. Zhang, and C. H. Menq, “Laser interferometric system for six-axis motion measurement,” Rev. Sci. Instrum. 78, 1–8 (2007).
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Z. Cheng, H. Gao, Z. Zhang, H. Huang, and J. Zhu, “Study of a dual-frequency laser interferometer with unique optical subdivision techniques,” Appl. Opt. 45, 2246–2250 (2006).
[CrossRef]

Zhao, Y.

J. Li, Y. Zhao, X. Tao, and G. Zhu, “A way to calibrate laser interferometer by common path,” Acta Metrologica Sin. 27, 58–61 (2006).

Zhong, L.

S. Tang, Z. Wang, L. Zhong, J. Gao, and J. Guo, “Error analysis of a plane mirror interferometer based on geometric optical paths,” Opt. Express 20, 5108–5118 (2012).
[CrossRef]

Zhu, G.

J. Li, Y. Zhao, X. Tao, and G. Zhu, “A way to calibrate laser interferometer by common path,” Acta Metrologica Sin. 27, 58–61 (2006).

Zhu, J.

Z. Cheng, H. Gao, Z. Zhang, H. Huang, and J. Zhu, “Study of a dual-frequency laser interferometer with unique optical subdivision techniques,” Appl. Opt. 45, 2246–2250 (2006).
[CrossRef]

Acta Metrologica Sin.

J. Li, Y. Zhao, X. Tao, and G. Zhu, “A way to calibrate laser interferometer by common path,” Acta Metrologica Sin. 27, 58–61 (2006).

Appl. Opt.

Z. Cheng, H. Gao, Z. Zhang, H. Huang, and J. Zhu, “Study of a dual-frequency laser interferometer with unique optical subdivision techniques,” Appl. Opt. 45, 2246–2250 (2006).
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[CrossRef]

CIRP Ann.

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

J. Opt. A

P. G. Halverson and R. E. Spero, “Signal processing and testing of displacement metrology gauges with picometre-scale cyclic nonlinearity,” J. Opt. A 4, S304–S310 (2002).
[CrossRef]

Meas. Sci. Technol.

H. Bosse and G. Wilkening, “Developments at PTB in nanometrology for support of the semiconductor industry,” Meas. Sci. Technol. 16, 2155–2166 (2005).
[CrossRef]

H. J. Büchner and G. Jäger, “A novel plane mirror interferometer without using corner cube reflectors,” Meas. Sci. Technol. 17, 746–752 (2006).
[CrossRef]

A. Takahashi, Y. Takigawa, and N. Miwa, “Error contributor of defocus and quadratic caustic in line scale measurement,” Meas. Sci. Technol. 22, 015302 (2011).

Microsyst. Technol.

J. Park, M. Y. Lee, and D. Y. Lee, “A nano-metrology system with a two-dimensional combined optical and X-ray interferometer and an atomic force microscope,” Microsyst. Technol. 15, 1879–1884 (2009).
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M. Pisani, “Multiple reflection Michelson interferometer with picometer resolution,” Opt. Express 16, 21558–21563 (2008).
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S. Tang, Z. Wang, L. Zhong, J. Gao, and J. Guo, “Error analysis of a plane mirror interferometer based on geometric optical paths,” Opt. Express 20, 5108–5118 (2012).
[CrossRef]

Opt. Laser Eng.

H. Hussein, M. A. Sobee, and M. Amer, “Calibration of a Michelson-type laser wavemeter and evaluation of its accuracy,” Opt. Laser Eng. 48, 393–397 (2007).
[CrossRef]

Precis. Eng.

W. Gao, Y. Arai, A. Shibuya, S. Kiyono, and C. H. Park, “Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage,” Precis. Eng. 30, 96–103 (2006).
[CrossRef]

K. Iwasawa, A. Iwama, and K. Mistsui, “Development of a measuring method for several types of programmed tool paths for NC machine tools using a laser displacement interferometer and a rotary encoder,” Precis. Eng. 28, 399–408 (2004).
[CrossRef]

Proc. SPIE

K. J. Yan, J. Liu, F. Gao, and H. Wang, “Study of geometric errors detection method for NC machine tools based on non-contact circular track,” Proc. SPIE 7130, 71305K (2008).
[CrossRef]

F. Meil, N. Jeanmonod, C. Thiess, and R. Thalmann, “Calibration of a 2D reference mirror system of a photomask measuring instrument,” Proc. SPIE 4401, 227–233 (2001).
[CrossRef]

H. Haitjema, S. J. A. G. Cosijins, N. J. J. Roset, M. J. Jansen, and P.H.J. Schellekens, “Improving a commercially available heterodyne laser interferometer to sub-nm uncertainty,” Proc. SPIE 5190, 347–354 (2003).
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D. A. Swyt, S. D. Philips, and J. Palmateer, “Developments at NIST on Traceability in dimensional measurements,” Proc. SPIE 4401, 245–252 (2001).
[CrossRef]

Rev. Sci. Instrum.

Z. Zhang, and C. H. Menq, “Laser interferometric system for six-axis motion measurement,” Rev. Sci. Instrum. 78, 1–8 (2007).
[CrossRef]

C. Wang and B. Griffin, “A noncontact laser technique for circular contouring accuracy measurement,” Rev. Sci. Instrum. 72, 1594–1596 (2001).
[CrossRef]

I. Hahn, M. Weilert, X. Wang, and R. Goullioud, “A heterodyne interferometer for angle metrology,” Rev. Sci. Instrum. 81, 1–6 (2010).
[CrossRef]

Other

S. Tang, Z. Wang, Z. Jiang, J. Gao, and J. Guo, “A new measuring method for circular motion accuracy of NC machine tools based on dual-frequency laser interferometer,” in Proceedings of IEEE International Symposium on Assembly and Manufacturing ISAM2011 (IEEE, 2011), pp. 1–6.

XL-80 laser interferometer product manual of Renishaw Corporation (Renishaw, 2007).

L. Cai, J. Lu, and Y. Wei, “Calibration method for wavelength of laser interferometer,” Proceedings of 1st National Measurement Conference of China (1998), pp. 463–468.

ISO 10012-1, “Quality assurance requirements for measuring equipment-Part 1: metrological confirmation system for measuring equipment first edition,” Corrected and reprinted (1993).

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Figures (8)

Fig. 1.
Fig. 1.

Scheme of the collinear calibration of laser interferometer.

Fig. 2.
Fig. 2.

Optical path of the light beam in the corner reflector.

Fig. 3.
Fig. 3.

Change of the optical path under the impact of tilt error.

Fig. 4.
Fig. 4.

Curve of the calibration error with the change of tilt error.

Fig. 5.
Fig. 5.

Principle scheme for experimental optical paths.

Fig. 6.
Fig. 6.

Diagram of the experimental field.

Fig. 7.
Fig. 7.

Results of calibration errors for CCW rotation.

Fig. 8.
Fig. 8.

Results of calibration errors for CW rotation.

Equations (14)

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

ΔlA=ΔlB,
ΔxA=ΔxB,
ΔxA(ΔxB)=0,
l=2ηhcosβ,
ηsinβ=nsinβ,
Δlθ=lθl0=2ηh(ηη2n2sin2θ1),
ΔLA=ΔlAx+Δlθ,
ΔlAx=2nΔx,
ΔLA=2nΔx+2ηh(ηη2n2sin2θ1).
ΔLB=ΔlBx+Δlθ,
ΔlBx=ΔlAx=2nΔx.
ΔLB=2nΔx+2ηh(ηη2n2sin2θ1).
EΔx=ΔxA(ΔxB)=ΔLA2n(ΔLB2n).
EΔx=2hηn(ηη2n2sin2θ1).

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