Abstract

This paper presents a robust and low-cost roll angle measurement system (RAMS) on the basis of two parallel beams in association with two position detectors. The commonly occurring influences of beam drift, beam diameter, and intensity variations, and non-parallelism of dual-beam on the roll angular error measurement of precision linear stages are thoroughly considered and reduced. The effectiveness of the designed system and proposed methods were demonstrated by a series of experiments. It has been verified that the designed system’s measurement accuracy is within ± 1.2 arcsec over a measurement range of 1 m. The designed system is easy to construct both in the laboratory environment and factory field.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. H. Schwenke, W. Knapp, H. Haitjema, A. Weckenmann, R. Schmitt, and F. Delbressine, “Geometric error measurement and compensation of machines-an update,” CIRP Ann. 57(2), 660–675 (2008).
    [Crossref]
  2. Y. Huang, K. C. Fan, W. Sun, and S. Liu, “Low cost, compact 4-DOF measurement system with active compensation of beam angular drift error,” Opt. Express 26(13), 17185–17198 (2018).
    [Crossref] [PubMed]
  3. K. C. Fan, Y. T. Fei, X. F. Yu, Y. J. Chen, W. L. Wang, F. Chen, and Y. S. Liu, “Development of a low-cost micro-CMM for 3D micro/nano measurements,” Meas. Sci. Technol. 17(3), 524–532 (2006).
    [Crossref]
  4. W. Ye, M. Zhang, Y. Zhu, L. Wang, J. Hu, X. Li, and C. Hu, “Translational displacement computational algorithm of the grating interferometer without geometric error for the wafer stage in a photolithography scanner,” Opt. Express 26(26), 34734–34752 (2018).
    [Crossref] [PubMed]
  5. J. Torng, C. H. Wang, Z. N. Huang, and K. C. Fan, “A novel dual-axis optoelectronic level with refraction principle,” Meas. Sci. Technol. 24(3), 035902 (2013).
    [Crossref]
  6. Z. Y. Liu, D. J. Lin, H. Jiang, and C. Y. Yin, “Roll angle interferometer by means of wave plates,” Sens. Actuators A Phys. 104(2), 127–131 (2003).
    [Crossref]
  7. S. Tang, Z. Wang, M. Li, W. Zhang, F. Yang, and X. Zhang, “A small roll angle measurement method with enhanced resolution based on a heterodyne interferometer,” Rev. Sci. Instrum. 86(9), 096104 (2015).
    [Crossref] [PubMed]
  8. X. Chen, Z. Tao, C. Chen, C. Wang, L. Wang, H. Jiang, D. Fan, Y. Ekinci, and S. Liu, “All-dielectric metasurface-based roll-angle sensor,” Sens. Actuator A 279, 509–517 (2018).
    [Crossref]
  9. S. R. Gillmer, X. Yu, C. Wang, and J. D. Ellis, “Robust high-dynamic-range optical roll sensing,” Opt. Lett. 40(11), 2497–2500 (2015).
    [Crossref] [PubMed]
  10. Y. Zhai, Q. Feng, and B. Zhang, “A simple roll measurement method based on a rectangular-prism,” Opt. Laser Technol. 44(4), 839–843 (2012).
    [Crossref]
  11. Y. Zhu, S. Liu, C. Kuang, S. Li, and X. Liu, “Roll angle measurement based on common path compensation principle,” Opt. Lasers Eng. 67, 66–73 (2015).
    [Crossref]
  12. J. Ni and S. M. Wu, “An On-Line Measurement Technique for Machine Volumetric Error Compensation,” J. Eng. Ind. 115(1), 85–92 (1993).
    [Crossref]
  13. K. C. Fan, M. J. Chen, and W. M. Huang, “A six-degree-of-freedom measurement system for the motion accuracy of linear stages,” Int. J. Mach. Tools Manuf. 38(3), 155–164 (1998).
    [Crossref]
  14. K. C. Fan, H. Y. Wang, H. W. Yang, and L. M. Chen, “Techniques of multi-degree-of-freedom measurement on the linear motion error of precision machines,” Adv. Opt. Technol. 3(4), 375–386 (2014).
  15. C. Cui, Q. Feng, B. Zhang, and Y. Zhao, “System for simultaneously measuring 6DOF geometric motion errors using a polarization maintaining fiber-coupled dual-frequency laser,” Opt. Express 24(6), 6735–6748 (2016).
    [Crossref] [PubMed]
  16. W. Zhao, L. Qiu, Z. Feng, and C. Li, “Laser beam alignment by fast feedback control of both linear and angular drifts,” Optik (Stuttg.) 117(11), 505–510 (2006).
    [Crossref]
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  18. C. Cui, Q. Feng, and B. Zhang, “Compensation for straightness measurement systematic errors in six degree-of-freedom motion error simultaneous measurement system,” Appl. Opt. 54(11), 3122–3131 (2015).
    [Crossref] [PubMed]

2018 (3)

Y. Huang, K. C. Fan, W. Sun, and S. Liu, “Low cost, compact 4-DOF measurement system with active compensation of beam angular drift error,” Opt. Express 26(13), 17185–17198 (2018).
[Crossref] [PubMed]

W. Ye, M. Zhang, Y. Zhu, L. Wang, J. Hu, X. Li, and C. Hu, “Translational displacement computational algorithm of the grating interferometer without geometric error for the wafer stage in a photolithography scanner,” Opt. Express 26(26), 34734–34752 (2018).
[Crossref] [PubMed]

X. Chen, Z. Tao, C. Chen, C. Wang, L. Wang, H. Jiang, D. Fan, Y. Ekinci, and S. Liu, “All-dielectric metasurface-based roll-angle sensor,” Sens. Actuator A 279, 509–517 (2018).
[Crossref]

2016 (1)

C. Cui, Q. Feng, B. Zhang, and Y. Zhao, “System for simultaneously measuring 6DOF geometric motion errors using a polarization maintaining fiber-coupled dual-frequency laser,” Opt. Express 24(6), 6735–6748 (2016).
[Crossref] [PubMed]

2015 (4)

C. Cui, Q. Feng, and B. Zhang, “Compensation for straightness measurement systematic errors in six degree-of-freedom motion error simultaneous measurement system,” Appl. Opt. 54(11), 3122–3131 (2015).
[Crossref] [PubMed]

Y. Zhu, S. Liu, C. Kuang, S. Li, and X. Liu, “Roll angle measurement based on common path compensation principle,” Opt. Lasers Eng. 67, 66–73 (2015).
[Crossref]

S. R. Gillmer, X. Yu, C. Wang, and J. D. Ellis, “Robust high-dynamic-range optical roll sensing,” Opt. Lett. 40(11), 2497–2500 (2015).
[Crossref] [PubMed]

S. Tang, Z. Wang, M. Li, W. Zhang, F. Yang, and X. Zhang, “A small roll angle measurement method with enhanced resolution based on a heterodyne interferometer,” Rev. Sci. Instrum. 86(9), 096104 (2015).
[Crossref] [PubMed]

2014 (1)

K. C. Fan, H. Y. Wang, H. W. Yang, and L. M. Chen, “Techniques of multi-degree-of-freedom measurement on the linear motion error of precision machines,” Adv. Opt. Technol. 3(4), 375–386 (2014).

2013 (1)

J. Torng, C. H. Wang, Z. N. Huang, and K. C. Fan, “A novel dual-axis optoelectronic level with refraction principle,” Meas. Sci. Technol. 24(3), 035902 (2013).
[Crossref]

2012 (1)

Y. Zhai, Q. Feng, and B. Zhang, “A simple roll measurement method based on a rectangular-prism,” Opt. Laser Technol. 44(4), 839–843 (2012).
[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. 57(2), 660–675 (2008).
[Crossref]

2006 (2)

K. C. Fan, Y. T. Fei, X. F. Yu, Y. J. Chen, W. L. Wang, F. Chen, and Y. S. Liu, “Development of a low-cost micro-CMM for 3D micro/nano measurements,” Meas. Sci. Technol. 17(3), 524–532 (2006).
[Crossref]

W. Zhao, L. Qiu, Z. Feng, and C. Li, “Laser beam alignment by fast feedback control of both linear and angular drifts,” Optik (Stuttg.) 117(11), 505–510 (2006).
[Crossref]

2003 (1)

Z. Y. Liu, D. J. Lin, H. Jiang, and C. Y. Yin, “Roll angle interferometer by means of wave plates,” Sens. Actuators A Phys. 104(2), 127–131 (2003).
[Crossref]

1998 (1)

K. C. Fan, M. J. Chen, and W. M. Huang, “A six-degree-of-freedom measurement system for the motion accuracy of linear stages,” Int. J. Mach. Tools Manuf. 38(3), 155–164 (1998).
[Crossref]

1993 (1)

J. Ni and S. M. Wu, “An On-Line Measurement Technique for Machine Volumetric Error Compensation,” J. Eng. Ind. 115(1), 85–92 (1993).
[Crossref]

Chen, C.

X. Chen, Z. Tao, C. Chen, C. Wang, L. Wang, H. Jiang, D. Fan, Y. Ekinci, and S. Liu, “All-dielectric metasurface-based roll-angle sensor,” Sens. Actuator A 279, 509–517 (2018).
[Crossref]

Chen, F.

K. C. Fan, Y. T. Fei, X. F. Yu, Y. J. Chen, W. L. Wang, F. Chen, and Y. S. Liu, “Development of a low-cost micro-CMM for 3D micro/nano measurements,” Meas. Sci. Technol. 17(3), 524–532 (2006).
[Crossref]

Chen, L. M.

K. C. Fan, H. Y. Wang, H. W. Yang, and L. M. Chen, “Techniques of multi-degree-of-freedom measurement on the linear motion error of precision machines,” Adv. Opt. Technol. 3(4), 375–386 (2014).

Chen, M. J.

K. C. Fan, M. J. Chen, and W. M. Huang, “A six-degree-of-freedom measurement system for the motion accuracy of linear stages,” Int. J. Mach. Tools Manuf. 38(3), 155–164 (1998).
[Crossref]

Chen, X.

X. Chen, Z. Tao, C. Chen, C. Wang, L. Wang, H. Jiang, D. Fan, Y. Ekinci, and S. Liu, “All-dielectric metasurface-based roll-angle sensor,” Sens. Actuator A 279, 509–517 (2018).
[Crossref]

Chen, Y. J.

K. C. Fan, Y. T. Fei, X. F. Yu, Y. J. Chen, W. L. Wang, F. Chen, and Y. S. Liu, “Development of a low-cost micro-CMM for 3D micro/nano measurements,” Meas. Sci. Technol. 17(3), 524–532 (2006).
[Crossref]

Cui, C.

C. Cui, Q. Feng, B. Zhang, and Y. Zhao, “System for simultaneously measuring 6DOF geometric motion errors using a polarization maintaining fiber-coupled dual-frequency laser,” Opt. Express 24(6), 6735–6748 (2016).
[Crossref] [PubMed]

C. Cui, Q. Feng, and B. Zhang, “Compensation for straightness measurement systematic errors in six degree-of-freedom motion error simultaneous measurement system,” Appl. Opt. 54(11), 3122–3131 (2015).
[Crossref] [PubMed]

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(2), 660–675 (2008).
[Crossref]

Ekinci, Y.

X. Chen, Z. Tao, C. Chen, C. Wang, L. Wang, H. Jiang, D. Fan, Y. Ekinci, and S. Liu, “All-dielectric metasurface-based roll-angle sensor,” Sens. Actuator A 279, 509–517 (2018).
[Crossref]

Ellis, J. D.

S. R. Gillmer, X. Yu, C. Wang, and J. D. Ellis, “Robust high-dynamic-range optical roll sensing,” Opt. Lett. 40(11), 2497–2500 (2015).
[Crossref] [PubMed]

Fan, D.

X. Chen, Z. Tao, C. Chen, C. Wang, L. Wang, H. Jiang, D. Fan, Y. Ekinci, and S. Liu, “All-dielectric metasurface-based roll-angle sensor,” Sens. Actuator A 279, 509–517 (2018).
[Crossref]

Fan, K. C.

Y. Huang, K. C. Fan, W. Sun, and S. Liu, “Low cost, compact 4-DOF measurement system with active compensation of beam angular drift error,” Opt. Express 26(13), 17185–17198 (2018).
[Crossref] [PubMed]

K. C. Fan, H. Y. Wang, H. W. Yang, and L. M. Chen, “Techniques of multi-degree-of-freedom measurement on the linear motion error of precision machines,” Adv. Opt. Technol. 3(4), 375–386 (2014).

J. Torng, C. H. Wang, Z. N. Huang, and K. C. Fan, “A novel dual-axis optoelectronic level with refraction principle,” Meas. Sci. Technol. 24(3), 035902 (2013).
[Crossref]

K. C. Fan, Y. T. Fei, X. F. Yu, Y. J. Chen, W. L. Wang, F. Chen, and Y. S. Liu, “Development of a low-cost micro-CMM for 3D micro/nano measurements,” Meas. Sci. Technol. 17(3), 524–532 (2006).
[Crossref]

K. C. Fan, M. J. Chen, and W. M. Huang, “A six-degree-of-freedom measurement system for the motion accuracy of linear stages,” Int. J. Mach. Tools Manuf. 38(3), 155–164 (1998).
[Crossref]

Fei, Y. T.

K. C. Fan, Y. T. Fei, X. F. Yu, Y. J. Chen, W. L. Wang, F. Chen, and Y. S. Liu, “Development of a low-cost micro-CMM for 3D micro/nano measurements,” Meas. Sci. Technol. 17(3), 524–532 (2006).
[Crossref]

Feng, Q.

C. Cui, Q. Feng, B. Zhang, and Y. Zhao, “System for simultaneously measuring 6DOF geometric motion errors using a polarization maintaining fiber-coupled dual-frequency laser,” Opt. Express 24(6), 6735–6748 (2016).
[Crossref] [PubMed]

C. Cui, Q. Feng, and B. Zhang, “Compensation for straightness measurement systematic errors in six degree-of-freedom motion error simultaneous measurement system,” Appl. Opt. 54(11), 3122–3131 (2015).
[Crossref] [PubMed]

Y. Zhai, Q. Feng, and B. Zhang, “A simple roll measurement method based on a rectangular-prism,” Opt. Laser Technol. 44(4), 839–843 (2012).
[Crossref]

Feng, Z.

W. Zhao, L. Qiu, Z. Feng, and C. Li, “Laser beam alignment by fast feedback control of both linear and angular drifts,” Optik (Stuttg.) 117(11), 505–510 (2006).
[Crossref]

Gillmer, S. R.

S. R. Gillmer, X. Yu, C. Wang, and J. D. Ellis, “Robust high-dynamic-range optical roll sensing,” Opt. Lett. 40(11), 2497–2500 (2015).
[Crossref] [PubMed]

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(2), 660–675 (2008).
[Crossref]

Hu, C.

W. Ye, M. Zhang, Y. Zhu, L. Wang, J. Hu, X. Li, and C. Hu, “Translational displacement computational algorithm of the grating interferometer without geometric error for the wafer stage in a photolithography scanner,” Opt. Express 26(26), 34734–34752 (2018).
[Crossref] [PubMed]

Hu, J.

W. Ye, M. Zhang, Y. Zhu, L. Wang, J. Hu, X. Li, and C. Hu, “Translational displacement computational algorithm of the grating interferometer without geometric error for the wafer stage in a photolithography scanner,” Opt. Express 26(26), 34734–34752 (2018).
[Crossref] [PubMed]

Huang, W. M.

K. C. Fan, M. J. Chen, and W. M. Huang, “A six-degree-of-freedom measurement system for the motion accuracy of linear stages,” Int. J. Mach. Tools Manuf. 38(3), 155–164 (1998).
[Crossref]

Huang, Y.

Y. Huang, K. C. Fan, W. Sun, and S. Liu, “Low cost, compact 4-DOF measurement system with active compensation of beam angular drift error,” Opt. Express 26(13), 17185–17198 (2018).
[Crossref] [PubMed]

Huang, Z. N.

J. Torng, C. H. Wang, Z. N. Huang, and K. C. Fan, “A novel dual-axis optoelectronic level with refraction principle,” Meas. Sci. Technol. 24(3), 035902 (2013).
[Crossref]

Jiang, H.

X. Chen, Z. Tao, C. Chen, C. Wang, L. Wang, H. Jiang, D. Fan, Y. Ekinci, and S. Liu, “All-dielectric metasurface-based roll-angle sensor,” Sens. Actuator A 279, 509–517 (2018).
[Crossref]

Z. Y. Liu, D. J. Lin, H. Jiang, and C. Y. Yin, “Roll angle interferometer by means of wave plates,” Sens. Actuators A Phys. 104(2), 127–131 (2003).
[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(2), 660–675 (2008).
[Crossref]

Kuang, C.

Y. Zhu, S. Liu, C. Kuang, S. Li, and X. Liu, “Roll angle measurement based on common path compensation principle,” Opt. Lasers Eng. 67, 66–73 (2015).
[Crossref]

Li, C.

W. Zhao, L. Qiu, Z. Feng, and C. Li, “Laser beam alignment by fast feedback control of both linear and angular drifts,” Optik (Stuttg.) 117(11), 505–510 (2006).
[Crossref]

Li, M.

S. Tang, Z. Wang, M. Li, W. Zhang, F. Yang, and X. Zhang, “A small roll angle measurement method with enhanced resolution based on a heterodyne interferometer,” Rev. Sci. Instrum. 86(9), 096104 (2015).
[Crossref] [PubMed]

Li, S.

Y. Zhu, S. Liu, C. Kuang, S. Li, and X. Liu, “Roll angle measurement based on common path compensation principle,” Opt. Lasers Eng. 67, 66–73 (2015).
[Crossref]

Li, X.

W. Ye, M. Zhang, Y. Zhu, L. Wang, J. Hu, X. Li, and C. Hu, “Translational displacement computational algorithm of the grating interferometer without geometric error for the wafer stage in a photolithography scanner,” Opt. Express 26(26), 34734–34752 (2018).
[Crossref] [PubMed]

Lin, D. J.

Z. Y. Liu, D. J. Lin, H. Jiang, and C. Y. Yin, “Roll angle interferometer by means of wave plates,” Sens. Actuators A Phys. 104(2), 127–131 (2003).
[Crossref]

Liu, S.

X. Chen, Z. Tao, C. Chen, C. Wang, L. Wang, H. Jiang, D. Fan, Y. Ekinci, and S. Liu, “All-dielectric metasurface-based roll-angle sensor,” Sens. Actuator A 279, 509–517 (2018).
[Crossref]

Y. Huang, K. C. Fan, W. Sun, and S. Liu, “Low cost, compact 4-DOF measurement system with active compensation of beam angular drift error,” Opt. Express 26(13), 17185–17198 (2018).
[Crossref] [PubMed]

Y. Zhu, S. Liu, C. Kuang, S. Li, and X. Liu, “Roll angle measurement based on common path compensation principle,” Opt. Lasers Eng. 67, 66–73 (2015).
[Crossref]

Liu, X.

Y. Zhu, S. Liu, C. Kuang, S. Li, and X. Liu, “Roll angle measurement based on common path compensation principle,” Opt. Lasers Eng. 67, 66–73 (2015).
[Crossref]

Liu, Y. S.

K. C. Fan, Y. T. Fei, X. F. Yu, Y. J. Chen, W. L. Wang, F. Chen, and Y. S. Liu, “Development of a low-cost micro-CMM for 3D micro/nano measurements,” Meas. Sci. Technol. 17(3), 524–532 (2006).
[Crossref]

Liu, Z. Y.

Z. Y. Liu, D. J. Lin, H. Jiang, and C. Y. Yin, “Roll angle interferometer by means of wave plates,” Sens. Actuators A Phys. 104(2), 127–131 (2003).
[Crossref]

Ni, J.

J. Ni and S. M. Wu, “An On-Line Measurement Technique for Machine Volumetric Error Compensation,” J. Eng. Ind. 115(1), 85–92 (1993).
[Crossref]

Qiu, L.

W. Zhao, L. Qiu, Z. Feng, and C. Li, “Laser beam alignment by fast feedback control of both linear and angular drifts,” Optik (Stuttg.) 117(11), 505–510 (2006).
[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(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. 57(2), 660–675 (2008).
[Crossref]

Sun, W.

Y. Huang, K. C. Fan, W. Sun, and S. Liu, “Low cost, compact 4-DOF measurement system with active compensation of beam angular drift error,” Opt. Express 26(13), 17185–17198 (2018).
[Crossref] [PubMed]

Tang, S.

S. Tang, Z. Wang, M. Li, W. Zhang, F. Yang, and X. Zhang, “A small roll angle measurement method with enhanced resolution based on a heterodyne interferometer,” Rev. Sci. Instrum. 86(9), 096104 (2015).
[Crossref] [PubMed]

Tao, Z.

X. Chen, Z. Tao, C. Chen, C. Wang, L. Wang, H. Jiang, D. Fan, Y. Ekinci, and S. Liu, “All-dielectric metasurface-based roll-angle sensor,” Sens. Actuator A 279, 509–517 (2018).
[Crossref]

Torng, J.

J. Torng, C. H. Wang, Z. N. Huang, and K. C. Fan, “A novel dual-axis optoelectronic level with refraction principle,” Meas. Sci. Technol. 24(3), 035902 (2013).
[Crossref]

Wang, C.

X. Chen, Z. Tao, C. Chen, C. Wang, L. Wang, H. Jiang, D. Fan, Y. Ekinci, and S. Liu, “All-dielectric metasurface-based roll-angle sensor,” Sens. Actuator A 279, 509–517 (2018).
[Crossref]

S. R. Gillmer, X. Yu, C. Wang, and J. D. Ellis, “Robust high-dynamic-range optical roll sensing,” Opt. Lett. 40(11), 2497–2500 (2015).
[Crossref] [PubMed]

Wang, C. H.

J. Torng, C. H. Wang, Z. N. Huang, and K. C. Fan, “A novel dual-axis optoelectronic level with refraction principle,” Meas. Sci. Technol. 24(3), 035902 (2013).
[Crossref]

Wang, H. Y.

K. C. Fan, H. Y. Wang, H. W. Yang, and L. M. Chen, “Techniques of multi-degree-of-freedom measurement on the linear motion error of precision machines,” Adv. Opt. Technol. 3(4), 375–386 (2014).

Wang, L.

X. Chen, Z. Tao, C. Chen, C. Wang, L. Wang, H. Jiang, D. Fan, Y. Ekinci, and S. Liu, “All-dielectric metasurface-based roll-angle sensor,” Sens. Actuator A 279, 509–517 (2018).
[Crossref]

W. Ye, M. Zhang, Y. Zhu, L. Wang, J. Hu, X. Li, and C. Hu, “Translational displacement computational algorithm of the grating interferometer without geometric error for the wafer stage in a photolithography scanner,” Opt. Express 26(26), 34734–34752 (2018).
[Crossref] [PubMed]

Wang, W. L.

K. C. Fan, Y. T. Fei, X. F. Yu, Y. J. Chen, W. L. Wang, F. Chen, and Y. S. Liu, “Development of a low-cost micro-CMM for 3D micro/nano measurements,” Meas. Sci. Technol. 17(3), 524–532 (2006).
[Crossref]

Wang, Z.

S. Tang, Z. Wang, M. Li, W. Zhang, F. Yang, and X. Zhang, “A small roll angle measurement method with enhanced resolution based on a heterodyne interferometer,” Rev. Sci. Instrum. 86(9), 096104 (2015).
[Crossref] [PubMed]

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. 57(2), 660–675 (2008).
[Crossref]

Wu, S. M.

J. Ni and S. M. Wu, “An On-Line Measurement Technique for Machine Volumetric Error Compensation,” J. Eng. Ind. 115(1), 85–92 (1993).
[Crossref]

Yang, F.

S. Tang, Z. Wang, M. Li, W. Zhang, F. Yang, and X. Zhang, “A small roll angle measurement method with enhanced resolution based on a heterodyne interferometer,” Rev. Sci. Instrum. 86(9), 096104 (2015).
[Crossref] [PubMed]

Yang, H. W.

K. C. Fan, H. Y. Wang, H. W. Yang, and L. M. Chen, “Techniques of multi-degree-of-freedom measurement on the linear motion error of precision machines,” Adv. Opt. Technol. 3(4), 375–386 (2014).

Ye, W.

W. Ye, M. Zhang, Y. Zhu, L. Wang, J. Hu, X. Li, and C. Hu, “Translational displacement computational algorithm of the grating interferometer without geometric error for the wafer stage in a photolithography scanner,” Opt. Express 26(26), 34734–34752 (2018).
[Crossref] [PubMed]

Yin, C. Y.

Z. Y. Liu, D. J. Lin, H. Jiang, and C. Y. Yin, “Roll angle interferometer by means of wave plates,” Sens. Actuators A Phys. 104(2), 127–131 (2003).
[Crossref]

Yu, X.

S. R. Gillmer, X. Yu, C. Wang, and J. D. Ellis, “Robust high-dynamic-range optical roll sensing,” Opt. Lett. 40(11), 2497–2500 (2015).
[Crossref] [PubMed]

Yu, X. F.

K. C. Fan, Y. T. Fei, X. F. Yu, Y. J. Chen, W. L. Wang, F. Chen, and Y. S. Liu, “Development of a low-cost micro-CMM for 3D micro/nano measurements,” Meas. Sci. Technol. 17(3), 524–532 (2006).
[Crossref]

Zhai, Y.

Y. Zhai, Q. Feng, and B. Zhang, “A simple roll measurement method based on a rectangular-prism,” Opt. Laser Technol. 44(4), 839–843 (2012).
[Crossref]

Zhang, B.

C. Cui, Q. Feng, B. Zhang, and Y. Zhao, “System for simultaneously measuring 6DOF geometric motion errors using a polarization maintaining fiber-coupled dual-frequency laser,” Opt. Express 24(6), 6735–6748 (2016).
[Crossref] [PubMed]

C. Cui, Q. Feng, and B. Zhang, “Compensation for straightness measurement systematic errors in six degree-of-freedom motion error simultaneous measurement system,” Appl. Opt. 54(11), 3122–3131 (2015).
[Crossref] [PubMed]

Y. Zhai, Q. Feng, and B. Zhang, “A simple roll measurement method based on a rectangular-prism,” Opt. Laser Technol. 44(4), 839–843 (2012).
[Crossref]

Zhang, M.

W. Ye, M. Zhang, Y. Zhu, L. Wang, J. Hu, X. Li, and C. Hu, “Translational displacement computational algorithm of the grating interferometer without geometric error for the wafer stage in a photolithography scanner,” Opt. Express 26(26), 34734–34752 (2018).
[Crossref] [PubMed]

Zhang, W.

S. Tang, Z. Wang, M. Li, W. Zhang, F. Yang, and X. Zhang, “A small roll angle measurement method with enhanced resolution based on a heterodyne interferometer,” Rev. Sci. Instrum. 86(9), 096104 (2015).
[Crossref] [PubMed]

Zhang, X.

S. Tang, Z. Wang, M. Li, W. Zhang, F. Yang, and X. Zhang, “A small roll angle measurement method with enhanced resolution based on a heterodyne interferometer,” Rev. Sci. Instrum. 86(9), 096104 (2015).
[Crossref] [PubMed]

Zhao, W.

W. Zhao, L. Qiu, Z. Feng, and C. Li, “Laser beam alignment by fast feedback control of both linear and angular drifts,” Optik (Stuttg.) 117(11), 505–510 (2006).
[Crossref]

Zhao, Y.

C. Cui, Q. Feng, B. Zhang, and Y. Zhao, “System for simultaneously measuring 6DOF geometric motion errors using a polarization maintaining fiber-coupled dual-frequency laser,” Opt. Express 24(6), 6735–6748 (2016).
[Crossref] [PubMed]

Zhu, Y.

W. Ye, M. Zhang, Y. Zhu, L. Wang, J. Hu, X. Li, and C. Hu, “Translational displacement computational algorithm of the grating interferometer without geometric error for the wafer stage in a photolithography scanner,” Opt. Express 26(26), 34734–34752 (2018).
[Crossref] [PubMed]

Y. Zhu, S. Liu, C. Kuang, S. Li, and X. Liu, “Roll angle measurement based on common path compensation principle,” Opt. Lasers Eng. 67, 66–73 (2015).
[Crossref]

Adv. Opt. Technol. (1)

K. C. Fan, H. Y. Wang, H. W. Yang, and L. M. Chen, “Techniques of multi-degree-of-freedom measurement on the linear motion error of precision machines,” Adv. Opt. Technol. 3(4), 375–386 (2014).

Appl. Opt. (1)

C. Cui, Q. Feng, and B. Zhang, “Compensation for straightness measurement systematic errors in six degree-of-freedom motion error simultaneous measurement system,” Appl. Opt. 54(11), 3122–3131 (2015).
[Crossref] [PubMed]

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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(2), 660–675 (2008).
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W. Ye, M. Zhang, Y. Zhu, L. Wang, J. Hu, X. Li, and C. Hu, “Translational displacement computational algorithm of the grating interferometer without geometric error for the wafer stage in a photolithography scanner,” Opt. Express 26(26), 34734–34752 (2018).
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Y. Huang, K. C. Fan, W. Sun, and S. Liu, “Low cost, compact 4-DOF measurement system with active compensation of beam angular drift error,” Opt. Express 26(13), 17185–17198 (2018).
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C. Cui, Q. Feng, B. Zhang, and Y. Zhao, “System for simultaneously measuring 6DOF geometric motion errors using a polarization maintaining fiber-coupled dual-frequency laser,” Opt. Express 24(6), 6735–6748 (2016).
[Crossref] [PubMed]

Opt. Laser Technol. (1)

Y. Zhai, Q. Feng, and B. Zhang, “A simple roll measurement method based on a rectangular-prism,” Opt. Laser Technol. 44(4), 839–843 (2012).
[Crossref]

Opt. Lasers Eng. (1)

Y. Zhu, S. Liu, C. Kuang, S. Li, and X. Liu, “Roll angle measurement based on common path compensation principle,” Opt. Lasers Eng. 67, 66–73 (2015).
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Optik (Stuttg.) (1)

W. Zhao, L. Qiu, Z. Feng, and C. Li, “Laser beam alignment by fast feedback control of both linear and angular drifts,” Optik (Stuttg.) 117(11), 505–510 (2006).
[Crossref]

Rev. Sci. Instrum. (1)

S. Tang, Z. Wang, M. Li, W. Zhang, F. Yang, and X. Zhang, “A small roll angle measurement method with enhanced resolution based on a heterodyne interferometer,” Rev. Sci. Instrum. 86(9), 096104 (2015).
[Crossref] [PubMed]

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Figures (10)

Fig. 1
Fig. 1 Schematic of the RAMS for precision machines.
Fig. 2
Fig. 2 Measurement principles of (a) straightness errors and (b) roll angular error.
Fig. 3
Fig. 3 Compensation principle for error induced by non-parallelism of dual-beam at (a) do and (b) df.
Fig. 4
Fig. 4 Compensation principle for laser beam drift.
Fig. 5
Fig. 5 Calibration results of QPD1 for measurements of drifted angles.
Fig. 6
Fig. 6 Stability of the designed system with and without beam drift compensation.
Fig. 7
Fig. 7 Calibration results of QPD2 at do and df in the (a) X-direction and (b) Y-direction.
Fig. 8
Fig. 8 Sensitivity of QPD2 and measurement errors caused by sensitivity variation in the (a) X-direction and (b) Y-direction.
Fig. 9
Fig. 9 Sensitivity of QPD3 and measurement errors caused by sensitivity variation in the (a) X-direction and (b) Y-direction.
Fig. 10
Fig. 10 Measured results of roll angular error with and without compensation.

Equations (9)

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

δ x =Δ x 2 = k x2 ( I A2 + I D2 )( I B2 + I C2 ) I A2 + I B2 + I C2 + I D2 = k x2 Δ I x2
δ y =Δ y 2 = k y2 ( I A2 + I B2 )( I C2 + I D2 ) I A2 + I B2 + I C2 + I D2 = k y2 Δ I y2
θ roll = Δ y 2 Δ y 3 L = 1 L ( k y2 Δ I y2 k y3 Δ I y3 )
k mi_z = k mi_f k mi_o d f d o d z k mi_f k mi_o d f d o d o + k mi_o m=x,yi=2,3
θ o_R = (Δ y 2_o Δ y 3_o )+ θ p d o L = θ o_L + θ p d o L
θ f_R = (Δ y 2_f Δ y 3_f )+ θ p d f L = θ f_L + θ p d f L
θ p = ( θ f_R θ f_L )( θ o_R θ o_L ) d f d o L
θ z (z)= θ z_R θ p d z L
θ pitch = Δ x 1 2f and θ yaw = Δ y 1 2f

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