Abstract

A laser heterodyne interferometer with rotational error compensation is proposed for precision displacement measurement. In this interferometer, the rotational error of the measured object is obtained by using an angle detecting unit which is composed of a semi-reflective film, a polarizing beam splitter, a quarter-wave plate, a convex lens and a two-dimensional position sensitive detector. And the obtained rotational angle is used for compensating its influence on displacement measurement result. The optical configuration of the proposed interferometer is designed, and the mathematical model for displacement measurement with rotational error compensation is established. The coupling effect of axial displacement on rotational angle measurement and the rotational angle range used for compensation on displacement measurement are discussed in detail. To verify feasibility of the proposed interferometer, the experimental setup was constructed and several verification experiments were performed.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9(7), 1024–1030 (1998).
    [Crossref]
  2. N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4(9), 907–926 (1993).
    [Crossref]
  3. 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(2), 660–675 (2008).
    [Crossref]
  4. Z. Y. He, J. Z. Fu, L. C. Zhang, and X. H. Yao, “A new error measurement method to identify all six error parameters of a rotational axis of a machine tool,” Int. J. Mach. Tools Manuf. 88, 1–8 (2015).
    [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. G. M. Harry, “Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quantum Gravity 27(8), 084006 (2010).
    [Crossref]
  7. P. de Groot, J. Biegen, J. Clark, X. Colonna de Lega, and D. Grigg, “Optical interferometry for measurement of the geometric dimensions of industrial parts,” Appl. Opt. 41(19), 3853–3860 (2002).
    [Crossref] [PubMed]
  8. H. F. F. Castro and M. Burdekin, “Dynamic calibration of the positioning accuracy of machine tools and coordinate measuring machines using a laser interferometer,” Int. J. Mach. Tools Manuf. 43(9), 947–954 (2003).
    [Crossref]
  9. A. J. H. Meskers, D. Voigt, and J. W. Spronck, “Relative optical wavefront measurement in displacement measuring interferometer systems with sub-nm precision,” Opt. Express 21(15), 17920–17930 (2013).
    [Crossref] [PubMed]
  10. Zygo Corp., “A primer on displacement measuring interferometers,” Zygo Corp. Technical Document (1999).
  11. J. A. Kim, J. W. Kim, C. S. Kang, J. H. Jin, and T. B. Eom, “An interferometric calibration system for various linear artefacts using active compensation of angular motion errors,” Meas. Sci. Technol. 22(7), 075304 (2011).
    [Crossref]
  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. L. Clark, B. Shirinzadeh, Y. L. Tian, and D. Oetomo, “Laser-based sensing, measurement, and misalignment control of coupled linear and angular motion for ultrahigh precision movement,” IEEE/ASME Trans. Mechatron. 20(1), 84–92 (2015).
    [Crossref]
  14. X. Yu, S. R. Gillmer, S. C. Woody, and J. D. Ellis, “Development of a compact, fiber-coupled, six degree-of-freedom measurement system for precision linear stage metrology,” Rev. Sci. Instrum. 87(6), 065109 (2016).
    [Crossref] [PubMed]
  15. F. Zhu, J. Tan, and J. Cui, “Common-path design criteria for laser datum based measurement of small angle deviations and laser autocollimation method in compliance with the criteria with high accuracy and stability,” Opt. Express 21(9), 11391–11403 (2013).
    [Crossref] [PubMed]
  16. 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]
  17. E. Zhang, Q. Hao, B. Chen, L. Yan, and Y. Liu, “Laser heterodyne interferometer for simultaneous measuring displacement and angle based on the Faraday effect,” Opt. Express 22(21), 25587–25598 (2014).
    [Crossref] [PubMed]
  18. Q. B. Feng, Optical Measurement Techniques and Applications (Tsinghua University, 2008).

2016 (1)

X. Yu, S. R. Gillmer, S. C. Woody, and J. D. Ellis, “Development of a compact, fiber-coupled, six degree-of-freedom measurement system for precision linear stage metrology,” Rev. Sci. Instrum. 87(6), 065109 (2016).
[Crossref] [PubMed]

2015 (3)

L. Clark, B. Shirinzadeh, Y. L. Tian, and D. Oetomo, “Laser-based sensing, measurement, and misalignment control of coupled linear and angular motion for ultrahigh precision movement,” IEEE/ASME Trans. Mechatron. 20(1), 84–92 (2015).
[Crossref]

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]

Z. Y. He, J. Z. Fu, L. C. Zhang, and X. H. Yao, “A new error measurement method to identify all six error parameters of a rotational axis of a machine tool,” Int. J. Mach. Tools Manuf. 88, 1–8 (2015).
[Crossref]

2014 (2)

E. Zhang, Q. Hao, B. Chen, L. Yan, and Y. Liu, “Laser heterodyne interferometer for simultaneous measuring displacement and angle based on the Faraday effect,” Opt. Express 22(21), 25587–25598 (2014).
[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]

2013 (2)

2011 (1)

J. A. Kim, J. W. Kim, C. S. Kang, J. H. Jin, and T. B. Eom, “An interferometric calibration system for various linear artefacts using active compensation of angular motion errors,” Meas. Sci. Technol. 22(7), 075304 (2011).
[Crossref]

2010 (1)

G. M. Harry, “Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quantum Gravity 27(8), 084006 (2010).
[Crossref]

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(2), 660–675 (2008).
[Crossref]

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)

H. F. F. Castro and M. Burdekin, “Dynamic calibration of the positioning accuracy of machine tools and coordinate measuring machines using a laser interferometer,” Int. J. Mach. Tools Manuf. 43(9), 947–954 (2003).
[Crossref]

2002 (1)

1998 (1)

F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9(7), 1024–1030 (1998).
[Crossref]

1993 (1)

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

Biegen, J.

Bobroff, N.

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

Burdekin, M.

H. F. F. Castro and M. Burdekin, “Dynamic calibration of the positioning accuracy of machine tools and coordinate measuring machines using a laser interferometer,” Int. J. Mach. Tools Manuf. 43(9), 947–954 (2003).
[Crossref]

Castro, H. F. F.

H. F. F. Castro and M. Burdekin, “Dynamic calibration of the positioning accuracy of machine tools and coordinate measuring machines using a laser interferometer,” Int. J. Mach. Tools Manuf. 43(9), 947–954 (2003).
[Crossref]

Chen, B.

Clark, J.

Clark, L.

L. Clark, B. Shirinzadeh, Y. L. Tian, and D. Oetomo, “Laser-based sensing, measurement, and misalignment control of coupled linear and angular motion for ultrahigh precision movement,” IEEE/ASME Trans. Mechatron. 20(1), 84–92 (2015).
[Crossref]

Colonna de Lega, X.

Cui, J.

de Groot, P.

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(2), 660–675 (2008).
[Crossref]

Demarest, F. C.

F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9(7), 1024–1030 (1998).
[Crossref]

Ellis, J. D.

X. Yu, S. R. Gillmer, S. C. Woody, and J. D. Ellis, “Development of a compact, fiber-coupled, six degree-of-freedom measurement system for precision linear stage metrology,” Rev. Sci. Instrum. 87(6), 065109 (2016).
[Crossref] [PubMed]

Eom, T. B.

J. A. Kim, J. W. Kim, C. S. Kang, J. H. Jin, and T. B. Eom, “An interferometric calibration system for various linear artefacts using active compensation of angular motion errors,” Meas. Sci. Technol. 22(7), 075304 (2011).
[Crossref]

Fu, J. Z.

Z. Y. He, J. Z. Fu, L. C. Zhang, and X. H. Yao, “A new error measurement method to identify all six error parameters of a rotational axis of a machine tool,” Int. J. Mach. Tools Manuf. 88, 1–8 (2015).
[Crossref]

Gillmer, S. R.

X. Yu, S. R. Gillmer, S. C. Woody, and J. D. Ellis, “Development of a compact, fiber-coupled, six degree-of-freedom measurement system for precision linear stage metrology,” Rev. Sci. Instrum. 87(6), 065109 (2016).
[Crossref] [PubMed]

Grigg, D.

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(2), 660–675 (2008).
[Crossref]

Hao, Q.

Harry, G. M.

G. M. Harry, “Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quantum Gravity 27(8), 084006 (2010).
[Crossref]

He, Z. Y.

Z. Y. He, J. Z. Fu, L. C. Zhang, and X. H. Yao, “A new error measurement method to identify all six error parameters of a rotational axis of a machine tool,” Int. J. Mach. Tools Manuf. 88, 1–8 (2015).
[Crossref]

Jin, J. H.

J. A. Kim, J. W. Kim, C. S. Kang, J. H. Jin, and T. B. Eom, “An interferometric calibration system for various linear artefacts using active compensation of angular motion errors,” Meas. Sci. Technol. 22(7), 075304 (2011).
[Crossref]

Kang, C. S.

J. A. Kim, J. W. Kim, C. S. Kang, J. H. Jin, and T. B. Eom, “An interferometric calibration system for various linear artefacts using active compensation of angular motion errors,” Meas. Sci. Technol. 22(7), 075304 (2011).
[Crossref]

Kim, J. A.

J. A. Kim, J. W. Kim, C. S. Kang, J. H. Jin, and T. B. Eom, “An interferometric calibration system for various linear artefacts using active compensation of angular motion errors,” Meas. Sci. Technol. 22(7), 075304 (2011).
[Crossref]

Kim, J. W.

J. A. Kim, J. W. Kim, C. S. Kang, J. H. Jin, and T. B. Eom, “An interferometric calibration system for various linear artefacts using active compensation of angular motion errors,” Meas. Sci. Technol. 22(7), 075304 (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(2), 660–675 (2008).
[Crossref]

Liu, Y.

Meskers, A. J. H.

Oetomo, D.

L. Clark, B. Shirinzadeh, Y. L. Tian, and D. Oetomo, “Laser-based sensing, measurement, and misalignment control of coupled linear and angular motion for ultrahigh precision movement,” IEEE/ASME Trans. Mechatron. 20(1), 84–92 (2015).
[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(2), 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(2), 660–675 (2008).
[Crossref]

Shirinzadeh, B.

L. Clark, B. Shirinzadeh, Y. L. Tian, and D. Oetomo, “Laser-based sensing, measurement, and misalignment control of coupled linear and angular motion for ultrahigh precision movement,” IEEE/ASME Trans. Mechatron. 20(1), 84–92 (2015).
[Crossref]

Spronck, J. W.

Tan, J.

Tian, Y. L.

L. Clark, B. Shirinzadeh, Y. L. Tian, and D. Oetomo, “Laser-based sensing, measurement, and misalignment control of coupled linear and angular motion for ultrahigh precision movement,” IEEE/ASME Trans. Mechatron. 20(1), 84–92 (2015).
[Crossref]

Voigt, D.

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(2), 660–675 (2008).
[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]

Woody, S. C.

X. Yu, S. R. Gillmer, S. C. Woody, and J. D. Ellis, “Development of a compact, fiber-coupled, six degree-of-freedom measurement system for precision linear stage metrology,” Rev. Sci. Instrum. 87(6), 065109 (2016).
[Crossref] [PubMed]

Xu, B.

Yan, L.

Yao, X. H.

Z. Y. He, J. Z. Fu, L. C. Zhang, and X. H. Yao, “A new error measurement method to identify all six error parameters of a rotational axis of a machine tool,” Int. J. Mach. Tools Manuf. 88, 1–8 (2015).
[Crossref]

Yu, X.

X. Yu, S. R. Gillmer, S. C. Woody, and J. D. Ellis, “Development of a compact, fiber-coupled, six degree-of-freedom measurement system for precision linear stage metrology,” Rev. Sci. Instrum. 87(6), 065109 (2016).
[Crossref] [PubMed]

Zhang, E.

Zhang, L. C.

Z. Y. He, J. Z. Fu, L. C. Zhang, and X. H. Yao, “A new error measurement method to identify all six error parameters of a rotational axis of a machine tool,” Int. J. Mach. Tools Manuf. 88, 1–8 (2015).
[Crossref]

Zhu, F.

Appl. Opt. (1)

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(2), 660–675 (2008).
[Crossref]

Class. Quantum Gravity (1)

G. M. Harry, “Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quantum Gravity 27(8), 084006 (2010).
[Crossref]

IEEE/ASME Trans. Mechatron. (1)

L. Clark, B. Shirinzadeh, Y. L. Tian, and D. Oetomo, “Laser-based sensing, measurement, and misalignment control of coupled linear and angular motion for ultrahigh precision movement,” IEEE/ASME Trans. Mechatron. 20(1), 84–92 (2015).
[Crossref]

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

Z. Y. He, J. Z. Fu, L. C. Zhang, and X. H. Yao, “A new error measurement method to identify all six error parameters of a rotational axis of a machine tool,” Int. J. Mach. Tools Manuf. 88, 1–8 (2015).
[Crossref]

H. F. F. Castro and M. Burdekin, “Dynamic calibration of the positioning accuracy of machine tools and coordinate measuring machines using a laser interferometer,” Int. J. Mach. Tools Manuf. 43(9), 947–954 (2003).
[Crossref]

Meas. Sci. Technol. (4)

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]

F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol. 9(7), 1024–1030 (1998).
[Crossref]

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

J. A. Kim, J. W. Kim, C. S. Kang, J. H. Jin, and T. B. Eom, “An interferometric calibration system for various linear artefacts using active compensation of angular motion errors,” Meas. Sci. Technol. 22(7), 075304 (2011).
[Crossref]

Opt. Express (4)

Rev. Sci. Instrum. (2)

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]

X. Yu, S. R. Gillmer, S. C. Woody, and J. D. Ellis, “Development of a compact, fiber-coupled, six degree-of-freedom measurement system for precision linear stage metrology,” Rev. Sci. Instrum. 87(6), 065109 (2016).
[Crossref] [PubMed]

Other (2)

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

Zygo Corp., “A primer on displacement measuring interferometers,” Zygo Corp. Technical Document (1999).

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Figures (9)

Fig. 1
Fig. 1 Schematic of the proposed interferometer with rotational error compensation for displacement measurement.
Fig. 2
Fig. 2 Schematic for measuring displacement with rotational error compensation.
Fig. 3
Fig. 3 Schematic of rotational angle measurement with a displacement.
Fig. 4
Fig. 4 Simulation result of the maximum measurement angle when SR has yaw motion.
Fig. 5
Fig. 5 Simulation result of the maximum measurement angle when SR has pitch motion.
Fig. 6
Fig. 6 Experimental setup.
Fig. 7
Fig. 7 Experimental results of angle measurement comparison.
Fig. 8
Fig. 8 Experimental results of displacement measurement with rotational angle compensation
Fig. 9
Fig. 9 Experimental results of displacement measurement with rotational error compensation. (a) Rotational error measurement. (b) Displacement measurement comparison. To make the plots visible, the red dot line presenting displacement and deviation are shifted by 10 mm and 0.1 μm from actual values, respectively.

Equations (7)

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

Δ L in ( θ )= 4H n 1- ( nsinθ n ) 2 -4H n
Δ L out ( θ )=4nHsinθtan( arcsin( nsinθ n ) )
L=( N+ε ) λ 4n +Hsinθtan( arcsin( nsinθ n ) ) n H n 1- ( nsinθ n ) 2 + n H n
θ= 1 2 arctan( ( Δ x PSD ) 2 + ( Δ y PSD ) 2 f CL )
θ Yaw+ =arctan[ 2( S 1 + S 2 ) 4 ( S 1 + S 2 ) 2 8dΔR+4Δ R 2 4d2ΔR ]
θ Yaw- =arctan[ -2( S 1 + S 2 )+ 4 ( S 1 + S 2 ) 2 +8dΔR+4Δ R 2 4d+2ΔR ]
θ Pitch± =± 1 2 arctan( ΔR S 1 + S 2 )

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