Abstract

A novel laser heterodyne interferometric system with following interference units is proposed for large X-Y-θ planar motion measurement. In this system, two interference units moved by two separate linear stages along x-axis and y-axis are used to follow the large movement of the measured stage so that the simultaneous measurement of three degrees of freedom X-Y-θ parameters of large planar motion is realized. The optical configuration of the proposed system is designed by using the orthogonal linearly polarized beam return method, the measurement principle is described and the mathematic model for simultaneously measuring X-Y-θ planar motion is derived. To verify the feasibility of the proposed system, the experimental setup was constructed and a series of experiments were performed.

© 2017 Optical Society of America

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References

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  1. C. W. Lee and S. W. Kim, “An ultraprecision stage for alignment of wafers in advanced microlithography,” Precis. Eng. 21(2), 113–122 (1997).
    [Crossref]
  2. W. Jywe, T. H. Hsu, and C. H. Liu, “Non–bar, an optical calibration system for five-axis CNC machine tools,” Int. J. Mach. Tools Manuf. 59, 16–23 (2012).
    [Crossref]
  3. Y. M. Liu, M. Q. Yuan, J. R. Cao, J. W. Cui, and J. B. Tan, “Use of two planar gratings to measure 3-DOF displacements of planar moving stage,” In Proceedings of IEEE Trans. Instrum. Meas. (IEEE, 2015), pp.163–169.
    [Crossref]
  4. T. J. Quinn, “Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards,” Metrologia 40(2), 103–133 (2003).
    [Crossref]
  5. H. Bosse and G. Wilkening, “Developments at PTB in nanometrology for support of the semiconductor industry,” Meas. Sci. Technol. 16(11), 2155–2166 (2005).
    [Crossref]
  6. J. Lazar, O. Cip, M. Cizek, J. Hrabina, M. Sery, and P. Klapetek, “Laser interferometric measuring system for positioning in nanometrology,” WSEAS Trans. Cir. and Sys. 9(10), 660–669 (2010).
  7. Y. Lou, L. Yan, B. Chen, and S. Zhang, “Laser homodyne straightness interferometer with simultaneous measurement of six degrees of freedom motion errors for precision linear stage metrology,” Opt. Express 25(6), 6805–6821 (2017).
    [Crossref] [PubMed]
  8. J. H. Zhang and C. H. Menq, “A linear/angular interferometer capable of measuring large angular motion,” Meas. Sci. Technol. 10(12), 1247–1253 (1999).
    [Crossref]
  9. C. H. Menq, J. H. Zhang, and J. Shi, “Design and development of an interferometer with improved angular tolerance and its application to x-y theta measurement,” Rev. Sci. Instrum. 71(12), 4633–4638 (2000).
    [Crossref]
  10. S. Ottonelli, F. D. Lucia, M. Dabbicco, and G. Scamarcio, “All interferometric 6 Degree of freedom sensor based on the laser-self-mixing,” Proc. SPIE 73891L, 1–10 (2009).
  11. 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]
  12. 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]
  13. S. J. Zhao, H. Y. Wei, and Y. Li, “Laser heterodyne interferometer for the simultaneous measurement of displacement and angle using a single reference retroreflector,” Opt. Eng. 54(8), 084112 (2015).
    [Crossref]
  14. B. Chen, E. Zhang, L. Yan, and Y. Liu, “An orthogonal return method for linearly polarized beam based on the Faraday effect and its application in interferometer,” Rev. Sci. Instrum. 85(10), 105103 (2014).
    [Crossref] [PubMed]
  15. Q. B. Feng, Optical Measurement Techniques and Applications (Tsinghua University Press, 2008), Chap. 2.
  16. E. Zhang, B. Chen, L. Yan, T. Yang, Q. Hao, W. Dong, and C. Li, “Laser heterodyne interferometric signal processing method based on rising edge locking with high frequency clock signal,” Opt. Express 21(4), 4638–4652 (2013).
    [Crossref] [PubMed]

2017 (1)

2015 (2)

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]

S. J. Zhao, H. Y. Wei, and Y. Li, “Laser heterodyne interferometer for the simultaneous measurement of displacement and angle using a single reference retroreflector,” Opt. Eng. 54(8), 084112 (2015).
[Crossref]

2014 (1)

B. Chen, E. Zhang, L. Yan, and Y. Liu, “An orthogonal return method for linearly polarized beam based on the Faraday effect and its application in interferometer,” Rev. Sci. Instrum. 85(10), 105103 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (1)

W. Jywe, T. H. Hsu, and C. H. Liu, “Non–bar, an optical calibration system for five-axis CNC machine tools,” Int. J. Mach. Tools Manuf. 59, 16–23 (2012).
[Crossref]

2010 (1)

J. Lazar, O. Cip, M. Cizek, J. Hrabina, M. Sery, and P. Klapetek, “Laser interferometric measuring system for positioning in nanometrology,” WSEAS Trans. Cir. and Sys. 9(10), 660–669 (2010).

2009 (2)

S. Ottonelli, F. D. Lucia, M. Dabbicco, and G. Scamarcio, “All interferometric 6 Degree of freedom sensor based on the laser-self-mixing,” Proc. SPIE 73891L, 1–10 (2009).

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]

2005 (1)

H. Bosse and G. Wilkening, “Developments at PTB in nanometrology for support of the semiconductor industry,” Meas. Sci. Technol. 16(11), 2155–2166 (2005).
[Crossref]

2003 (1)

T. J. Quinn, “Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards,” Metrologia 40(2), 103–133 (2003).
[Crossref]

2000 (1)

C. H. Menq, J. H. Zhang, and J. Shi, “Design and development of an interferometer with improved angular tolerance and its application to x-y theta measurement,” Rev. Sci. Instrum. 71(12), 4633–4638 (2000).
[Crossref]

1999 (1)

J. H. Zhang and C. H. Menq, “A linear/angular interferometer capable of measuring large angular motion,” Meas. Sci. Technol. 10(12), 1247–1253 (1999).
[Crossref]

1997 (1)

C. W. Lee and S. W. Kim, “An ultraprecision stage for alignment of wafers in advanced microlithography,” Precis. Eng. 21(2), 113–122 (1997).
[Crossref]

Bosse, H.

H. Bosse and G. Wilkening, “Developments at PTB in nanometrology for support of the semiconductor industry,” Meas. Sci. Technol. 16(11), 2155–2166 (2005).
[Crossref]

Cao, J. R.

Y. M. Liu, M. Q. Yuan, J. R. Cao, J. W. Cui, and J. B. Tan, “Use of two planar gratings to measure 3-DOF displacements of planar moving stage,” In Proceedings of IEEE Trans. Instrum. Meas. (IEEE, 2015), pp.163–169.
[Crossref]

Chen, B.

Cip, O.

J. Lazar, O. Cip, M. Cizek, J. Hrabina, M. Sery, and P. Klapetek, “Laser interferometric measuring system for positioning in nanometrology,” WSEAS Trans. Cir. and Sys. 9(10), 660–669 (2010).

Cizek, M.

J. Lazar, O. Cip, M. Cizek, J. Hrabina, M. Sery, and P. Klapetek, “Laser interferometric measuring system for positioning in nanometrology,” WSEAS Trans. Cir. and Sys. 9(10), 660–669 (2010).

Cui, J. W.

Y. M. Liu, M. Q. Yuan, J. R. Cao, J. W. Cui, and J. B. Tan, “Use of two planar gratings to measure 3-DOF displacements of planar moving stage,” In Proceedings of IEEE Trans. Instrum. Meas. (IEEE, 2015), pp.163–169.
[Crossref]

Dabbicco, M.

S. Ottonelli, F. D. Lucia, M. Dabbicco, and G. Scamarcio, “All interferometric 6 Degree of freedom sensor based on the laser-self-mixing,” Proc. SPIE 73891L, 1–10 (2009).

Dong, W.

Feng, Q.

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]

Hao, Q.

Hrabina, J.

J. Lazar, O. Cip, M. Cizek, J. Hrabina, M. Sery, and P. Klapetek, “Laser interferometric measuring system for positioning in nanometrology,” WSEAS Trans. Cir. and Sys. 9(10), 660–669 (2010).

Hsu, T. H.

W. Jywe, T. H. Hsu, and C. H. Liu, “Non–bar, an optical calibration system for five-axis CNC machine tools,” Int. J. Mach. Tools Manuf. 59, 16–23 (2012).
[Crossref]

Jywe, W.

W. Jywe, T. H. Hsu, and C. H. Liu, “Non–bar, an optical calibration system for five-axis CNC machine tools,” Int. J. Mach. Tools Manuf. 59, 16–23 (2012).
[Crossref]

Kim, S. W.

C. W. Lee and S. W. Kim, “An ultraprecision stage for alignment of wafers in advanced microlithography,” Precis. Eng. 21(2), 113–122 (1997).
[Crossref]

Klapetek, P.

J. Lazar, O. Cip, M. Cizek, J. Hrabina, M. Sery, and P. Klapetek, “Laser interferometric measuring system for positioning in nanometrology,” WSEAS Trans. Cir. and Sys. 9(10), 660–669 (2010).

Lazar, J.

J. Lazar, O. Cip, M. Cizek, J. Hrabina, M. Sery, and P. Klapetek, “Laser interferometric measuring system for positioning in nanometrology,” WSEAS Trans. Cir. and Sys. 9(10), 660–669 (2010).

Lee, C. W.

C. W. Lee and S. W. Kim, “An ultraprecision stage for alignment of wafers in advanced microlithography,” Precis. Eng. 21(2), 113–122 (1997).
[Crossref]

Li, C.

E. Zhang, B. Chen, L. Yan, T. Yang, Q. Hao, W. Dong, and C. Li, “Laser heterodyne interferometric signal processing method based on rising edge locking with high frequency clock signal,” Opt. Express 21(4), 4638–4652 (2013).
[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]

Li, Y.

S. J. Zhao, H. Y. Wei, and Y. Li, “Laser heterodyne interferometer for the simultaneous measurement of displacement and angle using a single reference retroreflector,” Opt. Eng. 54(8), 084112 (2015).
[Crossref]

Liu, C. H.

W. Jywe, T. H. Hsu, and C. H. Liu, “Non–bar, an optical calibration system for five-axis CNC machine tools,” Int. J. Mach. Tools Manuf. 59, 16–23 (2012).
[Crossref]

Liu, Y.

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, and Y. Liu, “An orthogonal return method for linearly polarized beam based on the Faraday effect and its application in interferometer,” Rev. Sci. Instrum. 85(10), 105103 (2014).
[Crossref] [PubMed]

Liu, Y. M.

Y. M. Liu, M. Q. Yuan, J. R. Cao, J. W. Cui, and J. B. Tan, “Use of two planar gratings to measure 3-DOF displacements of planar moving stage,” In Proceedings of IEEE Trans. Instrum. Meas. (IEEE, 2015), pp.163–169.
[Crossref]

Lou, Y.

Lucia, F. D.

S. Ottonelli, F. D. Lucia, M. Dabbicco, and G. Scamarcio, “All interferometric 6 Degree of freedom sensor based on the laser-self-mixing,” Proc. SPIE 73891L, 1–10 (2009).

Menq, C. H.

C. H. Menq, J. H. Zhang, and J. Shi, “Design and development of an interferometer with improved angular tolerance and its application to x-y theta measurement,” Rev. Sci. Instrum. 71(12), 4633–4638 (2000).
[Crossref]

J. H. Zhang and C. H. Menq, “A linear/angular interferometer capable of measuring large angular motion,” Meas. Sci. Technol. 10(12), 1247–1253 (1999).
[Crossref]

Ottonelli, S.

S. Ottonelli, F. D. Lucia, M. Dabbicco, and G. Scamarcio, “All interferometric 6 Degree of freedom sensor based on the laser-self-mixing,” Proc. SPIE 73891L, 1–10 (2009).

Quinn, T. J.

T. J. Quinn, “Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards,” Metrologia 40(2), 103–133 (2003).
[Crossref]

Scamarcio, G.

S. Ottonelli, F. D. Lucia, M. Dabbicco, and G. Scamarcio, “All interferometric 6 Degree of freedom sensor based on the laser-self-mixing,” Proc. SPIE 73891L, 1–10 (2009).

Sery, M.

J. Lazar, O. Cip, M. Cizek, J. Hrabina, M. Sery, and P. Klapetek, “Laser interferometric measuring system for positioning in nanometrology,” WSEAS Trans. Cir. and Sys. 9(10), 660–669 (2010).

Shi, J.

C. H. Menq, J. H. Zhang, and J. Shi, “Design and development of an interferometer with improved angular tolerance and its application to x-y theta measurement,” Rev. Sci. Instrum. 71(12), 4633–4638 (2000).
[Crossref]

Tan, J. B.

Y. M. Liu, M. Q. Yuan, J. R. Cao, J. W. Cui, and J. B. Tan, “Use of two planar gratings to measure 3-DOF displacements of planar moving stage,” In Proceedings of IEEE Trans. Instrum. Meas. (IEEE, 2015), pp.163–169.
[Crossref]

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]

Wei, H. Y.

S. J. Zhao, H. Y. Wei, and Y. Li, “Laser heterodyne interferometer for the simultaneous measurement of displacement and angle using a single reference retroreflector,” Opt. Eng. 54(8), 084112 (2015).
[Crossref]

Wilkening, G.

H. Bosse and G. Wilkening, “Developments at PTB in nanometrology for support of the semiconductor industry,” Meas. Sci. Technol. 16(11), 2155–2166 (2005).
[Crossref]

Xu, B.

Yan, L.

Yang, T.

Yuan, M. Q.

Y. M. Liu, M. Q. Yuan, J. R. Cao, J. W. Cui, and J. B. Tan, “Use of two planar gratings to measure 3-DOF displacements of planar moving stage,” In Proceedings of IEEE Trans. Instrum. Meas. (IEEE, 2015), pp.163–169.
[Crossref]

Zhang, E.

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, and Y. Liu, “An orthogonal return method for linearly polarized beam based on the Faraday effect and its application in interferometer,” Rev. Sci. Instrum. 85(10), 105103 (2014).
[Crossref] [PubMed]

E. Zhang, B. Chen, L. Yan, T. Yang, Q. Hao, W. Dong, and C. Li, “Laser heterodyne interferometric signal processing method based on rising edge locking with high frequency clock signal,” Opt. Express 21(4), 4638–4652 (2013).
[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, J. H.

C. H. Menq, J. H. Zhang, and J. Shi, “Design and development of an interferometer with improved angular tolerance and its application to x-y theta measurement,” Rev. Sci. Instrum. 71(12), 4633–4638 (2000).
[Crossref]

J. H. Zhang and C. H. Menq, “A linear/angular interferometer capable of measuring large angular motion,” Meas. Sci. Technol. 10(12), 1247–1253 (1999).
[Crossref]

Zhang, S.

Zhao, S. J.

S. J. Zhao, H. Y. Wei, and Y. Li, “Laser heterodyne interferometer for the simultaneous measurement of displacement and angle using a single reference retroreflector,” Opt. Eng. 54(8), 084112 (2015).
[Crossref]

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

W. Jywe, T. H. Hsu, and C. H. Liu, “Non–bar, an optical calibration system for five-axis CNC machine tools,” Int. J. Mach. Tools Manuf. 59, 16–23 (2012).
[Crossref]

Meas. Sci. Technol. (2)

H. Bosse and G. Wilkening, “Developments at PTB in nanometrology for support of the semiconductor industry,” Meas. Sci. Technol. 16(11), 2155–2166 (2005).
[Crossref]

J. H. Zhang and C. H. Menq, “A linear/angular interferometer capable of measuring large angular motion,” Meas. Sci. Technol. 10(12), 1247–1253 (1999).
[Crossref]

Metrologia (1)

T. J. Quinn, “Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards,” Metrologia 40(2), 103–133 (2003).
[Crossref]

Opt. Eng. (1)

S. J. Zhao, H. Y. Wei, and Y. Li, “Laser heterodyne interferometer for the simultaneous measurement of displacement and angle using a single reference retroreflector,” Opt. Eng. 54(8), 084112 (2015).
[Crossref]

Opt. Express (3)

Precis. Eng. (1)

C. W. Lee and S. W. Kim, “An ultraprecision stage for alignment of wafers in advanced microlithography,” Precis. Eng. 21(2), 113–122 (1997).
[Crossref]

Proc. SPIE (1)

S. Ottonelli, F. D. Lucia, M. Dabbicco, and G. Scamarcio, “All interferometric 6 Degree of freedom sensor based on the laser-self-mixing,” Proc. SPIE 73891L, 1–10 (2009).

Rev. Sci. Instrum. (3)

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]

B. Chen, E. Zhang, L. Yan, and Y. Liu, “An orthogonal return method for linearly polarized beam based on the Faraday effect and its application in interferometer,” Rev. Sci. Instrum. 85(10), 105103 (2014).
[Crossref] [PubMed]

C. H. Menq, J. H. Zhang, and J. Shi, “Design and development of an interferometer with improved angular tolerance and its application to x-y theta measurement,” Rev. Sci. Instrum. 71(12), 4633–4638 (2000).
[Crossref]

WSEAS Trans. Cir. and Sys. (1)

J. Lazar, O. Cip, M. Cizek, J. Hrabina, M. Sery, and P. Klapetek, “Laser interferometric measuring system for positioning in nanometrology,” WSEAS Trans. Cir. and Sys. 9(10), 660–669 (2010).

Other (2)

Y. M. Liu, M. Q. Yuan, J. R. Cao, J. W. Cui, and J. B. Tan, “Use of two planar gratings to measure 3-DOF displacements of planar moving stage,” In Proceedings of IEEE Trans. Instrum. Meas. (IEEE, 2015), pp.163–169.
[Crossref]

Q. B. Feng, Optical Measurement Techniques and Applications (Tsinghua University Press, 2008), Chap. 2.

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Figures (5)

Fig. 1
Fig. 1 Schematic of the laser heterodyne interferometric system with following interference units for measuring X-Y-θ planar motion. FR: faraday rotator, M: mirror, PBS: polarizing beam splitter, QP: quarter-wave plate, P: polarizer, PD: photodetector, CC: corner cube.
Fig. 2
Fig. 2 Schematic for simultaneously measuring X-Y-θ parameters.
Fig. 3
Fig. 3 Experimental setup for X-Y-θ planar motion measurement
Fig. 4
Fig. 4 Experimental results of X-Y-θ simultaneous measurement experiment. (a) x-axis displacement measurement. To make the plots visible, the red dot line is shifted by 10 mm from the actual values. (b) y-axis displacement measurement. (c) angle measurement. The red dot line is shifted by 0.001° from the actual values.
Fig. 5
Fig. 5 Experimental results of angle measurement comparison in range of ± 10°. (a) positive rotation angle measurement and (b) negative rotation angle measurement. The red dot line is shifted by 1° from the actual values.

Equations (4)

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

L x = l 11 + l 12 + 8 n H sin θ tan [ arc sin ( n sin θ n ) ] 4 Δ l ( θ ) 8 n s ( 1 cos θ )
Δ l ( θ ) = 2 n H 1 ( n sin θ n ) 2 2 n H
L y = l 21 + l 22 + 8 n Hsin θ tan [ arcsin ( n sin θ n ) ] 4 Δ l ( θ ) 8 n s ( 1 cos θ )
θ = arc sin ( l 12 l 11 4 n L 0 ) = arc sin ( l 22 l 21 4 n L 0 )

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