Abstract

A profile of an X-axis stage mirror results in a phase error of gratings in Scanning Beam Interference Lithography. Traditional methods of measuring the profile require extra probes and another large stage mirror on Y-axis, or requires other operations such as rotating measured object to adjust the zero-adjustment errors. This paper introduces a three-probe system removing the need for Y-axis optical path structure and proposes a bidirectional integration model to solve the problem of zero-adjustment error, simplifying the optical path structure and the measurement process. This method is confirmed by theoretical analysis and experimental results, which is better than traditional methods and can also be used in other application fields of three-point method.

© 2017 Optical Society of America

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References

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  1. H. Yu, X. Li, J. Zhu, H. Yu, X. Qi, and S. Feng, “Reducing the line curvature error of mechanically ruled gratings by interferometric control,” Appl. Phys. B 117(1), 279–286 (2014).
    [Crossref]
  2. Q. Zhou, X. Li, K. Ni, R. Tian, and J. Pang, “Holographic fabrication of large-constant concave gratings for wide-range flat-field spectrometers with the addition of a concave lens,” Opt. Express 24(2), 732–738 (2016).
    [Crossref] [PubMed]
  3. M. Schumann, T. Bückmann, N. Gruhler, M. Wegener, and W. Pernice, “Hybrid 2D-3D optical devices for integrated optics by direct laser writing,” Light Sci. Appl. 3(6), 175 (2014).
    [Crossref]
  4. R. K. Heilmann, C. G. Chen, P. T. Konkola, and M. L. Schattenburg, “Dimensional metrology for nanometre-scale science and engineering: towards sub-nanometre accurate encoders,” Nat. Nanotechnol. 15(10), 504 (2004).
    [Crossref]
  5. J. C. Montoya, C. H. Chang, R. K. Heilmann, and M. L. Schattenburg, “Doppler writing and linewidth control for scanning beam interference lithography,” J. Vac. Sci. Technol. B 23(6), 2640–2645 (2005).
    [Crossref]
  6. W. Cheng, J. Zhu, Y. Zhang, A. Zeng, and H. Huang, “Status and Development of Scanning Beam Interference Lithography System,” Laser Optoelectronics Prog. 52, 1–12 (2015).
  7. S. Jiang, M. Bayanheshig, W. Pan, Li, and Y. Song, “An Accurate Method for Measuring Interference Fringe Period in Scanning Beam Interference Lithography System,” Acta Opt. Sin. 35, 55–64 (2015).
  8. L. He, X. Wang, and M. Ma, “Non- Flatness Measurement of Wafer Stage Mirrors in a Step-and-Scan Lithographic Tool,” Chin. J. Lasers 34, 519–525 (2007).
  9. J. Montoya, R. Heilmann, and M. Schattenburg, “Measuring two-axis stage mirror non-flatness using linear/angular interferometers,” in ASPE(2004), pp. 382–385.
  10. S. Kiyono and W. Gao, “Profile measurement of machined surface with a new differential method,” Precis. Eng. 16(3), 212–218 (1994).
    [Crossref]
  11. Z. Liu, W. Li, J. Wang, S. Jiang, Y. Song, M. Pan, and Bayanheshig, “Online detection of profile deviation for nano precision 2-D stage mirror,” Opt. Precision Eng. 24, 40–47 (2016).
  12. Q. Lv, W. Li, Y. Bayanheshig, Z. Bai, Liu, and W. Wang, “Interferometric precision displacement measurement system based on diffraction grating,” Chin. Opt. 10(1), 39-50 (2016).
  13. P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Multi-probe scanning system comprising three laser interferometers and one autocollimator for measuring flat bar mirror profile with nanometer accuracy,” Precis. Eng. 35(4), 686–692 (2011).
    [Crossref]
  14. Z. Q. Yin and S. Y. Li, “High accuracy error separation technique for on-machine measuring straightness,” Precis. Eng. 30(2), 192–200 (2006).
    [Crossref]
  15. J. Hwang, C. H. Park, W. Gao, and S. W. Kim, “A three-probe system for measuring the parallelism and straightness of a pair of rails for ultra-precision guideways,” Int. J. Mach. Tools Manuf. 47(7-8), 1053–1058 (2007).
    [Crossref]
  16. P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Development of high-precision micro-coordinate measuring machine: Multi-probe measurement system for measuring yaw and straightness motion error of linear stage,” Precis. Eng. 35(3), 424–430 (2011).
    [Crossref]
  17. W. Gao, J. C. Lee, Y. Arai, C. H. Park, W. Gao, J. C. Lee, Y. Arai, and C. H. Park, “An Improved Three-Probe Method for Precision Measurement of Straightness Verbesserung der Drei-Sensoren-Methode für die Präzisions-Geradheitsmessung,” Plattform Für Methoden Systeme Und Anwendungen Der Messtechnik 76, 259–265 (2009).
  18. P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Calibration for multiple motion errors of X-Y table on micro-coordinate measuring machine (M-CMM) by utilizing multi-probe scanning method,” Isupen 8, 1–6 (2013).
  19. W. Gao, J. Yokoyama, H. Kojima, and S. Kiyono, “Precision measurement of cylinder straightness using a scanning multi-probe system,” Precis. Eng. 26(3), 279–288 (2002).
    [Crossref]
  20. H. Ma, C. Zhuang, and Z. Xiong, “Multipoint Recursive Sequential Three-point Method for On-machine Roundness Measurement,” Procedia Cirp 31, 459–464 (2015).
    [Crossref]
  21. W. Gao, J. Yokoyama, S. Kiyono, and N. Hitomi, “A scanning multiprobe straightness measurement system for alignment of linear collider accelerator,” Key Eng. Mater. 295, 253–258 (2005).
    [Crossref]

2016 (3)

Q. Zhou, X. Li, K. Ni, R. Tian, and J. Pang, “Holographic fabrication of large-constant concave gratings for wide-range flat-field spectrometers with the addition of a concave lens,” Opt. Express 24(2), 732–738 (2016).
[Crossref] [PubMed]

Z. Liu, W. Li, J. Wang, S. Jiang, Y. Song, M. Pan, and Bayanheshig, “Online detection of profile deviation for nano precision 2-D stage mirror,” Opt. Precision Eng. 24, 40–47 (2016).

Q. Lv, W. Li, Y. Bayanheshig, Z. Bai, Liu, and W. Wang, “Interferometric precision displacement measurement system based on diffraction grating,” Chin. Opt. 10(1), 39-50 (2016).

2015 (3)

W. Cheng, J. Zhu, Y. Zhang, A. Zeng, and H. Huang, “Status and Development of Scanning Beam Interference Lithography System,” Laser Optoelectronics Prog. 52, 1–12 (2015).

S. Jiang, M. Bayanheshig, W. Pan, Li, and Y. Song, “An Accurate Method for Measuring Interference Fringe Period in Scanning Beam Interference Lithography System,” Acta Opt. Sin. 35, 55–64 (2015).

H. Ma, C. Zhuang, and Z. Xiong, “Multipoint Recursive Sequential Three-point Method for On-machine Roundness Measurement,” Procedia Cirp 31, 459–464 (2015).
[Crossref]

2014 (2)

M. Schumann, T. Bückmann, N. Gruhler, M. Wegener, and W. Pernice, “Hybrid 2D-3D optical devices for integrated optics by direct laser writing,” Light Sci. Appl. 3(6), 175 (2014).
[Crossref]

H. Yu, X. Li, J. Zhu, H. Yu, X. Qi, and S. Feng, “Reducing the line curvature error of mechanically ruled gratings by interferometric control,” Appl. Phys. B 117(1), 279–286 (2014).
[Crossref]

2013 (1)

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Calibration for multiple motion errors of X-Y table on micro-coordinate measuring machine (M-CMM) by utilizing multi-probe scanning method,” Isupen 8, 1–6 (2013).

2011 (2)

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Development of high-precision micro-coordinate measuring machine: Multi-probe measurement system for measuring yaw and straightness motion error of linear stage,” Precis. Eng. 35(3), 424–430 (2011).
[Crossref]

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Multi-probe scanning system comprising three laser interferometers and one autocollimator for measuring flat bar mirror profile with nanometer accuracy,” Precis. Eng. 35(4), 686–692 (2011).
[Crossref]

2009 (1)

W. Gao, J. C. Lee, Y. Arai, C. H. Park, W. Gao, J. C. Lee, Y. Arai, and C. H. Park, “An Improved Three-Probe Method for Precision Measurement of Straightness Verbesserung der Drei-Sensoren-Methode für die Präzisions-Geradheitsmessung,” Plattform Für Methoden Systeme Und Anwendungen Der Messtechnik 76, 259–265 (2009).

2007 (2)

L. He, X. Wang, and M. Ma, “Non- Flatness Measurement of Wafer Stage Mirrors in a Step-and-Scan Lithographic Tool,” Chin. J. Lasers 34, 519–525 (2007).

J. Hwang, C. H. Park, W. Gao, and S. W. Kim, “A three-probe system for measuring the parallelism and straightness of a pair of rails for ultra-precision guideways,” Int. J. Mach. Tools Manuf. 47(7-8), 1053–1058 (2007).
[Crossref]

2006 (1)

Z. Q. Yin and S. Y. Li, “High accuracy error separation technique for on-machine measuring straightness,” Precis. Eng. 30(2), 192–200 (2006).
[Crossref]

2005 (2)

J. C. Montoya, C. H. Chang, R. K. Heilmann, and M. L. Schattenburg, “Doppler writing and linewidth control for scanning beam interference lithography,” J. Vac. Sci. Technol. B 23(6), 2640–2645 (2005).
[Crossref]

W. Gao, J. Yokoyama, S. Kiyono, and N. Hitomi, “A scanning multiprobe straightness measurement system for alignment of linear collider accelerator,” Key Eng. Mater. 295, 253–258 (2005).
[Crossref]

2004 (1)

R. K. Heilmann, C. G. Chen, P. T. Konkola, and M. L. Schattenburg, “Dimensional metrology for nanometre-scale science and engineering: towards sub-nanometre accurate encoders,” Nat. Nanotechnol. 15(10), 504 (2004).
[Crossref]

2002 (1)

W. Gao, J. Yokoyama, H. Kojima, and S. Kiyono, “Precision measurement of cylinder straightness using a scanning multi-probe system,” Precis. Eng. 26(3), 279–288 (2002).
[Crossref]

1994 (1)

S. Kiyono and W. Gao, “Profile measurement of machined surface with a new differential method,” Precis. Eng. 16(3), 212–218 (1994).
[Crossref]

Arai, Y.

W. Gao, J. C. Lee, Y. Arai, C. H. Park, W. Gao, J. C. Lee, Y. Arai, and C. H. Park, “An Improved Three-Probe Method for Precision Measurement of Straightness Verbesserung der Drei-Sensoren-Methode für die Präzisions-Geradheitsmessung,” Plattform Für Methoden Systeme Und Anwendungen Der Messtechnik 76, 259–265 (2009).

W. Gao, J. C. Lee, Y. Arai, C. H. Park, W. Gao, J. C. Lee, Y. Arai, and C. H. Park, “An Improved Three-Probe Method for Precision Measurement of Straightness Verbesserung der Drei-Sensoren-Methode für die Präzisions-Geradheitsmessung,” Plattform Für Methoden Systeme Und Anwendungen Der Messtechnik 76, 259–265 (2009).

Bai, Z.

Q. Lv, W. Li, Y. Bayanheshig, Z. Bai, Liu, and W. Wang, “Interferometric precision displacement measurement system based on diffraction grating,” Chin. Opt. 10(1), 39-50 (2016).

Bayanheshig,

Z. Liu, W. Li, J. Wang, S. Jiang, Y. Song, M. Pan, and Bayanheshig, “Online detection of profile deviation for nano precision 2-D stage mirror,” Opt. Precision Eng. 24, 40–47 (2016).

Bayanheshig, M.

S. Jiang, M. Bayanheshig, W. Pan, Li, and Y. Song, “An Accurate Method for Measuring Interference Fringe Period in Scanning Beam Interference Lithography System,” Acta Opt. Sin. 35, 55–64 (2015).

Bayanheshig, Y.

Q. Lv, W. Li, Y. Bayanheshig, Z. Bai, Liu, and W. Wang, “Interferometric precision displacement measurement system based on diffraction grating,” Chin. Opt. 10(1), 39-50 (2016).

Bückmann, T.

M. Schumann, T. Bückmann, N. Gruhler, M. Wegener, and W. Pernice, “Hybrid 2D-3D optical devices for integrated optics by direct laser writing,” Light Sci. Appl. 3(6), 175 (2014).
[Crossref]

Chang, C. H.

J. C. Montoya, C. H. Chang, R. K. Heilmann, and M. L. Schattenburg, “Doppler writing and linewidth control for scanning beam interference lithography,” J. Vac. Sci. Technol. B 23(6), 2640–2645 (2005).
[Crossref]

Chen, C. G.

R. K. Heilmann, C. G. Chen, P. T. Konkola, and M. L. Schattenburg, “Dimensional metrology for nanometre-scale science and engineering: towards sub-nanometre accurate encoders,” Nat. Nanotechnol. 15(10), 504 (2004).
[Crossref]

Cheng, W.

W. Cheng, J. Zhu, Y. Zhang, A. Zeng, and H. Huang, “Status and Development of Scanning Beam Interference Lithography System,” Laser Optoelectronics Prog. 52, 1–12 (2015).

Feng, S.

H. Yu, X. Li, J. Zhu, H. Yu, X. Qi, and S. Feng, “Reducing the line curvature error of mechanically ruled gratings by interferometric control,” Appl. Phys. B 117(1), 279–286 (2014).
[Crossref]

Gao, W.

W. Gao, J. C. Lee, Y. Arai, C. H. Park, W. Gao, J. C. Lee, Y. Arai, and C. H. Park, “An Improved Three-Probe Method for Precision Measurement of Straightness Verbesserung der Drei-Sensoren-Methode für die Präzisions-Geradheitsmessung,” Plattform Für Methoden Systeme Und Anwendungen Der Messtechnik 76, 259–265 (2009).

W. Gao, J. C. Lee, Y. Arai, C. H. Park, W. Gao, J. C. Lee, Y. Arai, and C. H. Park, “An Improved Three-Probe Method for Precision Measurement of Straightness Verbesserung der Drei-Sensoren-Methode für die Präzisions-Geradheitsmessung,” Plattform Für Methoden Systeme Und Anwendungen Der Messtechnik 76, 259–265 (2009).

J. Hwang, C. H. Park, W. Gao, and S. W. Kim, “A three-probe system for measuring the parallelism and straightness of a pair of rails for ultra-precision guideways,” Int. J. Mach. Tools Manuf. 47(7-8), 1053–1058 (2007).
[Crossref]

W. Gao, J. Yokoyama, S. Kiyono, and N. Hitomi, “A scanning multiprobe straightness measurement system for alignment of linear collider accelerator,” Key Eng. Mater. 295, 253–258 (2005).
[Crossref]

W. Gao, J. Yokoyama, H. Kojima, and S. Kiyono, “Precision measurement of cylinder straightness using a scanning multi-probe system,” Precis. Eng. 26(3), 279–288 (2002).
[Crossref]

S. Kiyono and W. Gao, “Profile measurement of machined surface with a new differential method,” Precis. Eng. 16(3), 212–218 (1994).
[Crossref]

Gruhler, N.

M. Schumann, T. Bückmann, N. Gruhler, M. Wegener, and W. Pernice, “Hybrid 2D-3D optical devices for integrated optics by direct laser writing,” Light Sci. Appl. 3(6), 175 (2014).
[Crossref]

He, L.

L. He, X. Wang, and M. Ma, “Non- Flatness Measurement of Wafer Stage Mirrors in a Step-and-Scan Lithographic Tool,” Chin. J. Lasers 34, 519–525 (2007).

Heilmann, R. K.

J. C. Montoya, C. H. Chang, R. K. Heilmann, and M. L. Schattenburg, “Doppler writing and linewidth control for scanning beam interference lithography,” J. Vac. Sci. Technol. B 23(6), 2640–2645 (2005).
[Crossref]

R. K. Heilmann, C. G. Chen, P. T. Konkola, and M. L. Schattenburg, “Dimensional metrology for nanometre-scale science and engineering: towards sub-nanometre accurate encoders,” Nat. Nanotechnol. 15(10), 504 (2004).
[Crossref]

Hitomi, N.

W. Gao, J. Yokoyama, S. Kiyono, and N. Hitomi, “A scanning multiprobe straightness measurement system for alignment of linear collider accelerator,” Key Eng. Mater. 295, 253–258 (2005).
[Crossref]

Huang, H.

W. Cheng, J. Zhu, Y. Zhang, A. Zeng, and H. Huang, “Status and Development of Scanning Beam Interference Lithography System,” Laser Optoelectronics Prog. 52, 1–12 (2015).

Hwang, J.

J. Hwang, C. H. Park, W. Gao, and S. W. Kim, “A three-probe system for measuring the parallelism and straightness of a pair of rails for ultra-precision guideways,” Int. J. Mach. Tools Manuf. 47(7-8), 1053–1058 (2007).
[Crossref]

Jiang, S.

Z. Liu, W. Li, J. Wang, S. Jiang, Y. Song, M. Pan, and Bayanheshig, “Online detection of profile deviation for nano precision 2-D stage mirror,” Opt. Precision Eng. 24, 40–47 (2016).

S. Jiang, M. Bayanheshig, W. Pan, Li, and Y. Song, “An Accurate Method for Measuring Interference Fringe Period in Scanning Beam Interference Lithography System,” Acta Opt. Sin. 35, 55–64 (2015).

Kim, S. W.

J. Hwang, C. H. Park, W. Gao, and S. W. Kim, “A three-probe system for measuring the parallelism and straightness of a pair of rails for ultra-precision guideways,” Int. J. Mach. Tools Manuf. 47(7-8), 1053–1058 (2007).
[Crossref]

Kiyono, S.

W. Gao, J. Yokoyama, S. Kiyono, and N. Hitomi, “A scanning multiprobe straightness measurement system for alignment of linear collider accelerator,” Key Eng. Mater. 295, 253–258 (2005).
[Crossref]

W. Gao, J. Yokoyama, H. Kojima, and S. Kiyono, “Precision measurement of cylinder straightness using a scanning multi-probe system,” Precis. Eng. 26(3), 279–288 (2002).
[Crossref]

S. Kiyono and W. Gao, “Profile measurement of machined surface with a new differential method,” Precis. Eng. 16(3), 212–218 (1994).
[Crossref]

Kojima, H.

W. Gao, J. Yokoyama, H. Kojima, and S. Kiyono, “Precision measurement of cylinder straightness using a scanning multi-probe system,” Precis. Eng. 26(3), 279–288 (2002).
[Crossref]

Konkola, P. T.

R. K. Heilmann, C. G. Chen, P. T. Konkola, and M. L. Schattenburg, “Dimensional metrology for nanometre-scale science and engineering: towards sub-nanometre accurate encoders,” Nat. Nanotechnol. 15(10), 504 (2004).
[Crossref]

Lee, J. C.

W. Gao, J. C. Lee, Y. Arai, C. H. Park, W. Gao, J. C. Lee, Y. Arai, and C. H. Park, “An Improved Three-Probe Method for Precision Measurement of Straightness Verbesserung der Drei-Sensoren-Methode für die Präzisions-Geradheitsmessung,” Plattform Für Methoden Systeme Und Anwendungen Der Messtechnik 76, 259–265 (2009).

W. Gao, J. C. Lee, Y. Arai, C. H. Park, W. Gao, J. C. Lee, Y. Arai, and C. H. Park, “An Improved Three-Probe Method for Precision Measurement of Straightness Verbesserung der Drei-Sensoren-Methode für die Präzisions-Geradheitsmessung,” Plattform Für Methoden Systeme Und Anwendungen Der Messtechnik 76, 259–265 (2009).

Li,

S. Jiang, M. Bayanheshig, W. Pan, Li, and Y. Song, “An Accurate Method for Measuring Interference Fringe Period in Scanning Beam Interference Lithography System,” Acta Opt. Sin. 35, 55–64 (2015).

Li, S. Y.

Z. Q. Yin and S. Y. Li, “High accuracy error separation technique for on-machine measuring straightness,” Precis. Eng. 30(2), 192–200 (2006).
[Crossref]

Li, W.

Q. Lv, W. Li, Y. Bayanheshig, Z. Bai, Liu, and W. Wang, “Interferometric precision displacement measurement system based on diffraction grating,” Chin. Opt. 10(1), 39-50 (2016).

Z. Liu, W. Li, J. Wang, S. Jiang, Y. Song, M. Pan, and Bayanheshig, “Online detection of profile deviation for nano precision 2-D stage mirror,” Opt. Precision Eng. 24, 40–47 (2016).

Li, X.

Q. Zhou, X. Li, K. Ni, R. Tian, and J. Pang, “Holographic fabrication of large-constant concave gratings for wide-range flat-field spectrometers with the addition of a concave lens,” Opt. Express 24(2), 732–738 (2016).
[Crossref] [PubMed]

H. Yu, X. Li, J. Zhu, H. Yu, X. Qi, and S. Feng, “Reducing the line curvature error of mechanically ruled gratings by interferometric control,” Appl. Phys. B 117(1), 279–286 (2014).
[Crossref]

Liu,

Q. Lv, W. Li, Y. Bayanheshig, Z. Bai, Liu, and W. Wang, “Interferometric precision displacement measurement system based on diffraction grating,” Chin. Opt. 10(1), 39-50 (2016).

Liu, Z.

Z. Liu, W. Li, J. Wang, S. Jiang, Y. Song, M. Pan, and Bayanheshig, “Online detection of profile deviation for nano precision 2-D stage mirror,” Opt. Precision Eng. 24, 40–47 (2016).

Lv, Q.

Q. Lv, W. Li, Y. Bayanheshig, Z. Bai, Liu, and W. Wang, “Interferometric precision displacement measurement system based on diffraction grating,” Chin. Opt. 10(1), 39-50 (2016).

Ma, H.

H. Ma, C. Zhuang, and Z. Xiong, “Multipoint Recursive Sequential Three-point Method for On-machine Roundness Measurement,” Procedia Cirp 31, 459–464 (2015).
[Crossref]

Ma, M.

L. He, X. Wang, and M. Ma, “Non- Flatness Measurement of Wafer Stage Mirrors in a Step-and-Scan Lithographic Tool,” Chin. J. Lasers 34, 519–525 (2007).

Montoya, J. C.

J. C. Montoya, C. H. Chang, R. K. Heilmann, and M. L. Schattenburg, “Doppler writing and linewidth control for scanning beam interference lithography,” J. Vac. Sci. Technol. B 23(6), 2640–2645 (2005).
[Crossref]

Ni, K.

Osawa, S.

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Calibration for multiple motion errors of X-Y table on micro-coordinate measuring machine (M-CMM) by utilizing multi-probe scanning method,” Isupen 8, 1–6 (2013).

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Multi-probe scanning system comprising three laser interferometers and one autocollimator for measuring flat bar mirror profile with nanometer accuracy,” Precis. Eng. 35(4), 686–692 (2011).
[Crossref]

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Development of high-precision micro-coordinate measuring machine: Multi-probe measurement system for measuring yaw and straightness motion error of linear stage,” Precis. Eng. 35(3), 424–430 (2011).
[Crossref]

Pan, M.

Z. Liu, W. Li, J. Wang, S. Jiang, Y. Song, M. Pan, and Bayanheshig, “Online detection of profile deviation for nano precision 2-D stage mirror,” Opt. Precision Eng. 24, 40–47 (2016).

Pan, W.

S. Jiang, M. Bayanheshig, W. Pan, Li, and Y. Song, “An Accurate Method for Measuring Interference Fringe Period in Scanning Beam Interference Lithography System,” Acta Opt. Sin. 35, 55–64 (2015).

Pang, J.

Park, C. H.

W. Gao, J. C. Lee, Y. Arai, C. H. Park, W. Gao, J. C. Lee, Y. Arai, and C. H. Park, “An Improved Three-Probe Method for Precision Measurement of Straightness Verbesserung der Drei-Sensoren-Methode für die Präzisions-Geradheitsmessung,” Plattform Für Methoden Systeme Und Anwendungen Der Messtechnik 76, 259–265 (2009).

W. Gao, J. C. Lee, Y. Arai, C. H. Park, W. Gao, J. C. Lee, Y. Arai, and C. H. Park, “An Improved Three-Probe Method for Precision Measurement of Straightness Verbesserung der Drei-Sensoren-Methode für die Präzisions-Geradheitsmessung,” Plattform Für Methoden Systeme Und Anwendungen Der Messtechnik 76, 259–265 (2009).

J. Hwang, C. H. Park, W. Gao, and S. W. Kim, “A three-probe system for measuring the parallelism and straightness of a pair of rails for ultra-precision guideways,” Int. J. Mach. Tools Manuf. 47(7-8), 1053–1058 (2007).
[Crossref]

Pernice, W.

M. Schumann, T. Bückmann, N. Gruhler, M. Wegener, and W. Pernice, “Hybrid 2D-3D optical devices for integrated optics by direct laser writing,” Light Sci. Appl. 3(6), 175 (2014).
[Crossref]

Qi, X.

H. Yu, X. Li, J. Zhu, H. Yu, X. Qi, and S. Feng, “Reducing the line curvature error of mechanically ruled gratings by interferometric control,” Appl. Phys. B 117(1), 279–286 (2014).
[Crossref]

Sato, O.

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Calibration for multiple motion errors of X-Y table on micro-coordinate measuring machine (M-CMM) by utilizing multi-probe scanning method,” Isupen 8, 1–6 (2013).

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Multi-probe scanning system comprising three laser interferometers and one autocollimator for measuring flat bar mirror profile with nanometer accuracy,” Precis. Eng. 35(4), 686–692 (2011).
[Crossref]

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Development of high-precision micro-coordinate measuring machine: Multi-probe measurement system for measuring yaw and straightness motion error of linear stage,” Precis. Eng. 35(3), 424–430 (2011).
[Crossref]

Schattenburg, M. L.

J. C. Montoya, C. H. Chang, R. K. Heilmann, and M. L. Schattenburg, “Doppler writing and linewidth control for scanning beam interference lithography,” J. Vac. Sci. Technol. B 23(6), 2640–2645 (2005).
[Crossref]

R. K. Heilmann, C. G. Chen, P. T. Konkola, and M. L. Schattenburg, “Dimensional metrology for nanometre-scale science and engineering: towards sub-nanometre accurate encoders,” Nat. Nanotechnol. 15(10), 504 (2004).
[Crossref]

Schumann, M.

M. Schumann, T. Bückmann, N. Gruhler, M. Wegener, and W. Pernice, “Hybrid 2D-3D optical devices for integrated optics by direct laser writing,” Light Sci. Appl. 3(6), 175 (2014).
[Crossref]

Song, Y.

Z. Liu, W. Li, J. Wang, S. Jiang, Y. Song, M. Pan, and Bayanheshig, “Online detection of profile deviation for nano precision 2-D stage mirror,” Opt. Precision Eng. 24, 40–47 (2016).

S. Jiang, M. Bayanheshig, W. Pan, Li, and Y. Song, “An Accurate Method for Measuring Interference Fringe Period in Scanning Beam Interference Lithography System,” Acta Opt. Sin. 35, 55–64 (2015).

Takahashi, S.

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Calibration for multiple motion errors of X-Y table on micro-coordinate measuring machine (M-CMM) by utilizing multi-probe scanning method,” Isupen 8, 1–6 (2013).

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Development of high-precision micro-coordinate measuring machine: Multi-probe measurement system for measuring yaw and straightness motion error of linear stage,” Precis. Eng. 35(3), 424–430 (2011).
[Crossref]

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Multi-probe scanning system comprising three laser interferometers and one autocollimator for measuring flat bar mirror profile with nanometer accuracy,” Precis. Eng. 35(4), 686–692 (2011).
[Crossref]

Takamasu, K.

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Calibration for multiple motion errors of X-Y table on micro-coordinate measuring machine (M-CMM) by utilizing multi-probe scanning method,” Isupen 8, 1–6 (2013).

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Multi-probe scanning system comprising three laser interferometers and one autocollimator for measuring flat bar mirror profile with nanometer accuracy,” Precis. Eng. 35(4), 686–692 (2011).
[Crossref]

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Development of high-precision micro-coordinate measuring machine: Multi-probe measurement system for measuring yaw and straightness motion error of linear stage,” Precis. Eng. 35(3), 424–430 (2011).
[Crossref]

Takamura, T.

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Calibration for multiple motion errors of X-Y table on micro-coordinate measuring machine (M-CMM) by utilizing multi-probe scanning method,” Isupen 8, 1–6 (2013).

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Development of high-precision micro-coordinate measuring machine: Multi-probe measurement system for measuring yaw and straightness motion error of linear stage,” Precis. Eng. 35(3), 424–430 (2011).
[Crossref]

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Multi-probe scanning system comprising three laser interferometers and one autocollimator for measuring flat bar mirror profile with nanometer accuracy,” Precis. Eng. 35(4), 686–692 (2011).
[Crossref]

Takatsuji, T.

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Calibration for multiple motion errors of X-Y table on micro-coordinate measuring machine (M-CMM) by utilizing multi-probe scanning method,” Isupen 8, 1–6 (2013).

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Multi-probe scanning system comprising three laser interferometers and one autocollimator for measuring flat bar mirror profile with nanometer accuracy,” Precis. Eng. 35(4), 686–692 (2011).
[Crossref]

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Development of high-precision micro-coordinate measuring machine: Multi-probe measurement system for measuring yaw and straightness motion error of linear stage,” Precis. Eng. 35(3), 424–430 (2011).
[Crossref]

Tian, R.

Wang, J.

Z. Liu, W. Li, J. Wang, S. Jiang, Y. Song, M. Pan, and Bayanheshig, “Online detection of profile deviation for nano precision 2-D stage mirror,” Opt. Precision Eng. 24, 40–47 (2016).

Wang, W.

Q. Lv, W. Li, Y. Bayanheshig, Z. Bai, Liu, and W. Wang, “Interferometric precision displacement measurement system based on diffraction grating,” Chin. Opt. 10(1), 39-50 (2016).

Wang, X.

L. He, X. Wang, and M. Ma, “Non- Flatness Measurement of Wafer Stage Mirrors in a Step-and-Scan Lithographic Tool,” Chin. J. Lasers 34, 519–525 (2007).

Wegener, M.

M. Schumann, T. Bückmann, N. Gruhler, M. Wegener, and W. Pernice, “Hybrid 2D-3D optical devices for integrated optics by direct laser writing,” Light Sci. Appl. 3(6), 175 (2014).
[Crossref]

Xiong, Z.

H. Ma, C. Zhuang, and Z. Xiong, “Multipoint Recursive Sequential Three-point Method for On-machine Roundness Measurement,” Procedia Cirp 31, 459–464 (2015).
[Crossref]

Yang, P.

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Calibration for multiple motion errors of X-Y table on micro-coordinate measuring machine (M-CMM) by utilizing multi-probe scanning method,” Isupen 8, 1–6 (2013).

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Development of high-precision micro-coordinate measuring machine: Multi-probe measurement system for measuring yaw and straightness motion error of linear stage,” Precis. Eng. 35(3), 424–430 (2011).
[Crossref]

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Multi-probe scanning system comprising three laser interferometers and one autocollimator for measuring flat bar mirror profile with nanometer accuracy,” Precis. Eng. 35(4), 686–692 (2011).
[Crossref]

Yin, Z. Q.

Z. Q. Yin and S. Y. Li, “High accuracy error separation technique for on-machine measuring straightness,” Precis. Eng. 30(2), 192–200 (2006).
[Crossref]

Yokoyama, J.

W. Gao, J. Yokoyama, S. Kiyono, and N. Hitomi, “A scanning multiprobe straightness measurement system for alignment of linear collider accelerator,” Key Eng. Mater. 295, 253–258 (2005).
[Crossref]

W. Gao, J. Yokoyama, H. Kojima, and S. Kiyono, “Precision measurement of cylinder straightness using a scanning multi-probe system,” Precis. Eng. 26(3), 279–288 (2002).
[Crossref]

Yu, H.

H. Yu, X. Li, J. Zhu, H. Yu, X. Qi, and S. Feng, “Reducing the line curvature error of mechanically ruled gratings by interferometric control,” Appl. Phys. B 117(1), 279–286 (2014).
[Crossref]

H. Yu, X. Li, J. Zhu, H. Yu, X. Qi, and S. Feng, “Reducing the line curvature error of mechanically ruled gratings by interferometric control,” Appl. Phys. B 117(1), 279–286 (2014).
[Crossref]

Zeng, A.

W. Cheng, J. Zhu, Y. Zhang, A. Zeng, and H. Huang, “Status and Development of Scanning Beam Interference Lithography System,” Laser Optoelectronics Prog. 52, 1–12 (2015).

Zhang, Y.

W. Cheng, J. Zhu, Y. Zhang, A. Zeng, and H. Huang, “Status and Development of Scanning Beam Interference Lithography System,” Laser Optoelectronics Prog. 52, 1–12 (2015).

Zhou, Q.

Zhu, J.

W. Cheng, J. Zhu, Y. Zhang, A. Zeng, and H. Huang, “Status and Development of Scanning Beam Interference Lithography System,” Laser Optoelectronics Prog. 52, 1–12 (2015).

H. Yu, X. Li, J. Zhu, H. Yu, X. Qi, and S. Feng, “Reducing the line curvature error of mechanically ruled gratings by interferometric control,” Appl. Phys. B 117(1), 279–286 (2014).
[Crossref]

Zhuang, C.

H. Ma, C. Zhuang, and Z. Xiong, “Multipoint Recursive Sequential Three-point Method for On-machine Roundness Measurement,” Procedia Cirp 31, 459–464 (2015).
[Crossref]

Acta Opt. Sin. (1)

S. Jiang, M. Bayanheshig, W. Pan, Li, and Y. Song, “An Accurate Method for Measuring Interference Fringe Period in Scanning Beam Interference Lithography System,” Acta Opt. Sin. 35, 55–64 (2015).

Appl. Phys. B (1)

H. Yu, X. Li, J. Zhu, H. Yu, X. Qi, and S. Feng, “Reducing the line curvature error of mechanically ruled gratings by interferometric control,” Appl. Phys. B 117(1), 279–286 (2014).
[Crossref]

Chin. J. Lasers (1)

L. He, X. Wang, and M. Ma, “Non- Flatness Measurement of Wafer Stage Mirrors in a Step-and-Scan Lithographic Tool,” Chin. J. Lasers 34, 519–525 (2007).

Chin. Opt. (1)

Q. Lv, W. Li, Y. Bayanheshig, Z. Bai, Liu, and W. Wang, “Interferometric precision displacement measurement system based on diffraction grating,” Chin. Opt. 10(1), 39-50 (2016).

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

J. Hwang, C. H. Park, W. Gao, and S. W. Kim, “A three-probe system for measuring the parallelism and straightness of a pair of rails for ultra-precision guideways,” Int. J. Mach. Tools Manuf. 47(7-8), 1053–1058 (2007).
[Crossref]

Isupen (1)

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Calibration for multiple motion errors of X-Y table on micro-coordinate measuring machine (M-CMM) by utilizing multi-probe scanning method,” Isupen 8, 1–6 (2013).

J. Vac. Sci. Technol. B (1)

J. C. Montoya, C. H. Chang, R. K. Heilmann, and M. L. Schattenburg, “Doppler writing and linewidth control for scanning beam interference lithography,” J. Vac. Sci. Technol. B 23(6), 2640–2645 (2005).
[Crossref]

Key Eng. Mater. (1)

W. Gao, J. Yokoyama, S. Kiyono, and N. Hitomi, “A scanning multiprobe straightness measurement system for alignment of linear collider accelerator,” Key Eng. Mater. 295, 253–258 (2005).
[Crossref]

Laser Optoelectronics Prog. (1)

W. Cheng, J. Zhu, Y. Zhang, A. Zeng, and H. Huang, “Status and Development of Scanning Beam Interference Lithography System,” Laser Optoelectronics Prog. 52, 1–12 (2015).

Light Sci. Appl. (1)

M. Schumann, T. Bückmann, N. Gruhler, M. Wegener, and W. Pernice, “Hybrid 2D-3D optical devices for integrated optics by direct laser writing,” Light Sci. Appl. 3(6), 175 (2014).
[Crossref]

Nat. Nanotechnol. (1)

R. K. Heilmann, C. G. Chen, P. T. Konkola, and M. L. Schattenburg, “Dimensional metrology for nanometre-scale science and engineering: towards sub-nanometre accurate encoders,” Nat. Nanotechnol. 15(10), 504 (2004).
[Crossref]

Opt. Express (1)

Opt. Precision Eng. (1)

Z. Liu, W. Li, J. Wang, S. Jiang, Y. Song, M. Pan, and Bayanheshig, “Online detection of profile deviation for nano precision 2-D stage mirror,” Opt. Precision Eng. 24, 40–47 (2016).

Plattform Für Methoden Systeme Und Anwendungen Der Messtechnik (1)

W. Gao, J. C. Lee, Y. Arai, C. H. Park, W. Gao, J. C. Lee, Y. Arai, and C. H. Park, “An Improved Three-Probe Method for Precision Measurement of Straightness Verbesserung der Drei-Sensoren-Methode für die Präzisions-Geradheitsmessung,” Plattform Für Methoden Systeme Und Anwendungen Der Messtechnik 76, 259–265 (2009).

Precis. Eng. (5)

W. Gao, J. Yokoyama, H. Kojima, and S. Kiyono, “Precision measurement of cylinder straightness using a scanning multi-probe system,” Precis. Eng. 26(3), 279–288 (2002).
[Crossref]

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Development of high-precision micro-coordinate measuring machine: Multi-probe measurement system for measuring yaw and straightness motion error of linear stage,” Precis. Eng. 35(3), 424–430 (2011).
[Crossref]

P. Yang, T. Takamura, S. Takahashi, K. Takamasu, O. Sato, S. Osawa, and T. Takatsuji, “Multi-probe scanning system comprising three laser interferometers and one autocollimator for measuring flat bar mirror profile with nanometer accuracy,” Precis. Eng. 35(4), 686–692 (2011).
[Crossref]

Z. Q. Yin and S. Y. Li, “High accuracy error separation technique for on-machine measuring straightness,” Precis. Eng. 30(2), 192–200 (2006).
[Crossref]

S. Kiyono and W. Gao, “Profile measurement of machined surface with a new differential method,” Precis. Eng. 16(3), 212–218 (1994).
[Crossref]

Procedia Cirp (1)

H. Ma, C. Zhuang, and Z. Xiong, “Multipoint Recursive Sequential Three-point Method for On-machine Roundness Measurement,” Procedia Cirp 31, 459–464 (2015).
[Crossref]

Other (1)

J. Montoya, R. Heilmann, and M. Schattenburg, “Measuring two-axis stage mirror non-flatness using linear/angular interferometers,” in ASPE(2004), pp. 382–385.

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Figures (8)

Fig. 1
Fig. 1 Illustrative diagram of three-point method of stage mirror profile measurement: (a) schematic of three-point method and (b) zero-adjustment errors.
Fig. 2
Fig. 2 Experimental setup of the three-point method.
Fig. 3
Fig. 3 Installation mode of stage mirror in the first condition.
Fig. 4
Fig. 4 Results of first condition: (a) interferometer outputs, (b) original evaluated profiles, (c) twenty-times-evaluated profile with zero adjustment, and (d) standard deviation of 20 times.
Fig. 5
Fig. 5 Installation mode of stage mirror in the second condition.
Fig. 6
Fig. 6 Results of the second condition: (a) interferometer outputs, (b) original evaluated profiles, (c) twenty-times-evaluated profile with zero adjustment and (d) standard deviation of 20 times.
Fig. 7
Fig. 7 Experimental setup of two-point method.
Fig. 8
Fig. 8 Results of contrast experiment: (a) twenty-times-evaluated profile using two-point method and (d) standard deviation of 20 times.

Equations (18)

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

x a ( y i ) = x ( y i ) + E x ( y i d ) d θ ( y i ) e a .
x b ( y i ) = x ( y i ) + E x ( y i ) e b .
x c ( y i ) = x ( y i ) + E x ( y i + d ) + d θ ( y i ) e c .
f ( y i ) = x c ( y i ) 2 x b ( y i ) + x a ( y i ) d 2 = E x ( y i + d ) 2 E x ( y i ) + E x ( y i d ) α d 2 .
E x ( y i ) = ( E x ( y i + d ) E x ( y i ) d E x ( y i ) E x ( y i d ) d ) 1 d = f ( y i ) + α d 2 , i = 1 , 2 n .
E x ( y i ) = E x ( y 0 ) + k = 1 i ( E x ( y 0 ) + j = 0 k 1 E x ( y j ) d ) d , i = 1 , 2 n + 1.
E x ( y 0 ) = x b ( y 1 ) x a ( y 1 ) d + β a b d .
E x ( y i ) = { 0 , i = 0 f ( y i ) + α 2 d 2 ( y i y 1 ) 2 + α 2 d ( y i y 1 ) + β a b d y i , i = 1 , 2 n + 1 .
f ( y i ) = { 0 , i = 0 E x ( y 0 ) + k = 1 i ( x b ( y 1 ) x a ( y 1 ) d + j = 0 k 1 f ( y j ) δ ) δ , i = 1 , 2 n + 1 .
f ( y i ) = { 0 , i = 0 E x ( y i ) α 2 d 2 ( y i y 1 ) 2 α 2 d ( y i y 1 ) β a b d y i , i = 1 , 2 n + 1 .
f o p p o s i t e ( y i ) = { E x ( y n + 1 ) = 0 , i = n + 1 E x ( y n + 1 ) + k = n i ( x b ( y n ) x c ( y n ) d + j = n + 1 k f ( y j ) δ ) δ , i = n , n 1 0 .
f o p p o s i t e ( y i ) = { E x ( y i ) α 2 d 2 ( y n y i ) 2 α 2 d ( y n y i ) + β b c d ( y n + 1 y i ) , i = 0 , 2 n 0 , i = n + 1 .
Δ f ( y i ) = f o p p o s i t e ( y i ) f ( y i ) = k y i + b , i = 0 , 1 n + 1.
k = ( n 1 ) α d .
b = ( n 2 ) ( n + 1 ) α 2 + ( n + 1 ) β a b .
α = k d n 1 .
β a b = b n + 1 + ( n 2 ) k d 2 ( n 1 ) .
E x ( y i ) = E x ( y 1 ) + k = 1 i 1 ( x c ( y i ) x b ( y i ) d y e ( y i ) y d ( y i ) d ) δ , i = 2 , 2 n +1 .

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