Abstract

A high resolution roll measurement heterodyne interferometer with differential configurations is proposed in this paper. The proposed interferometer is composed of a pair of measurement beams providing environmental noise immunity. The structure is designed and the mathematic model based on Jones’ matrix for measuring the roll angle is established. Sensitivity is enhanced dramatically because of the opposite phase shift directions of two signals. An experimental setup is built and an amplification factor of 270 is obtained. Correspondingly, a roll angle resolution of 0.13 arcsec is attained using a phase meter with detecting resolution of 0.01°.

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

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  24. Z. Liu, D. Lin, H. Jiang, and C. Yin, “Roll angle interferometer by means of wave plates,” Sens. Actuators A Phys. 104(2), 127–131 (2003).
    [Crossref]
  25. C.-M. Wu and Y.-T. Chuang, “Roll angular displacement measurement system with microradian accuracy,” Sens. Actuators A Phys. 116(1), 145–149 (2004).
    [Crossref]
  26. S. Tang, Z. Wang, M. Li, W. Zhang, F. Yang, and X. Zhang, “Note: 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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    [Crossref] [PubMed]

2017 (4)

T. Jin, H. Ji, W. Hou, Y. Le, and L. Shen, “Measurement of straightness without Abbe error using an enhanced differential plane mirror interferometer,” Appl. Opt. 56(3), 607–610 (2017).
[Crossref] [PubMed]

B. Chen, L. Cheng, L. Yan, E. Zhang, and Y. Lou, “A heterodyne straightness and displacement measuring interferometer with laser beam drift compensation for long-travel linear stage metrology,” Rev. Sci. Instrum. 88(3), 035114 (2017).
[Crossref] [PubMed]

Y. Zhao, B. Zhang, and Q. Feng, “Measurement system and model for simultaneously measuring 6DOF geometric errors,” Opt. Express 25(18), 20993–21007 (2017).
[Crossref] [PubMed]

T. Jin, G. Xia, W. Hou, Y. Le, and S. Han, “High resolution and stability roll angle measurement method for precision linear displacement stages,” Rev. Sci. Instrum. 88(2), 023102 (2017).
[Crossref] [PubMed]

2016 (4)

J. Qi, Z. Wang, J. Huang, B. Yu, and J. Gao, “A field calibration method to eliminate the error caused by relative tilt on roll angle measurement,” Proc. SPIE 10023, 1002360B (2016).

J. Qi, Z. Wang, J. H. Huang, B. Yu, J. Gao, and S. Donati, “Note: Enhancing the sensitivity of roll-angle measurement with a novel interferometric configuration based on waveplates and folding mirror,” Rev. Sci. Instrum. 87(3), 036106 (2016).
[Crossref] [PubMed]

Y. Yin, S. Cai, and Y. Qiao, “Design, fabrication, and verification of a three-dimensional autocollimator,” Appl. Opt. 55(35), 9986–9991 (2016).
[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]

2015 (7)

H.-L. Hsieh and S.-W. Pan, “Development of a grating-based interferometer for six-degree-of-freedom displacement and angle measurements,” Opt. Express 23(3), 2451–2465 (2015).
[Crossref] [PubMed]

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

Z. Yusheng, Z. Zhifeng, S. Yuling, W. Xinjie, and F. Qibo, “A high-precision roll angle measurement method,” Optik (Stuttg.) 126(24), 4837–4840 (2015).
[Crossref]

S. Zhao, H. 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]

S. Donati, D. Rossi, and M. Norgia, “Single Channel Self-Mixing Interferometer Measures Simultaneously Displacement and Tilt and Yaw Angles of a Reflective Target,” IEEE J. Quantum Electron. 51(12), 1–8 (2015).
[Crossref]

A. Ju, W. Hou, and Y. Le, “Enhanced roll-angle measurement interferometer,” Opt. Eng. 54(3), 034101 (2015).
[Crossref]

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

2014 (2)

S. Tang, Z. Wang, J. Gao, and J. Guo, “Measurement method for roll angular displacement with a high resolution by using diffraction gratings and a heterodyne interferometer,” Rev. Sci. Instrum. 85(4), 045110 (2014).
[Crossref] [PubMed]

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]

2013 (1)

2011 (1)

2010 (2)

2009 (1)

I. Rahneberg, F. Baldini, H. J. Büchner, J. Homola, R. A. Lieberman, and G. Jäger,” “Optical system for the simultaneous measurement of two-dimensional straightness errors and the roll angle,” Proc. SPIE 7356, 73560S (2009).

2008 (1)

2007 (1)

C. Kuang, E. Hong, and J. Ni, “A high-precision five-degree-of-freedom measurement system based on laser collimator and interferometry techniques,” Rev. Sci. Instrum. 78(9), 095105 (2007).
[Crossref] [PubMed]

2005 (1)

C.-H. Liu, W.-Y. Jywe, C.-C. Hsu, and T.-H. Hsu, “Development of a laser-based high-precision six-degrees-of-freedom motion errors measuring system for linear stage,” Rev. Sci. Instrum. 76(5), 055110 (2005).
[Crossref]

2004 (1)

C.-M. Wu and Y.-T. Chuang, “Roll angular displacement measurement system with microradian accuracy,” Sens. Actuators A Phys. 116(1), 145–149 (2004).
[Crossref]

2003 (1)

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

2000 (1)

H. Jiang and C. Yin, “Sensitivity enhanced roll angle measurement,” Opt. Eng. 39(2), 516–519 (2000).
[Crossref]

Baldini, F.

I. Rahneberg, F. Baldini, H. J. Büchner, J. Homola, R. A. Lieberman, and G. Jäger,” “Optical system for the simultaneous measurement of two-dimensional straightness errors and the roll angle,” Proc. SPIE 7356, 73560S (2009).

Bin, Z.

Büchner, H. J.

I. Rahneberg, F. Baldini, H. J. Büchner, J. Homola, R. A. Lieberman, and G. Jäger,” “Optical system for the simultaneous measurement of two-dimensional straightness errors and the roll angle,” Proc. SPIE 7356, 73560S (2009).

Buice, E. S.

Cai, S.

Chatterjee, S.

Chen, B.

Cheng, L.

B. Chen, L. Cheng, L. Yan, E. Zhang, and Y. Lou, “A heterodyne straightness and displacement measuring interferometer with laser beam drift compensation for long-travel linear stage metrology,” Rev. Sci. Instrum. 88(3), 035114 (2017).
[Crossref] [PubMed]

Chiu, C. S.

Chuang, Y.-T.

C.-M. Wu and Y.-T. Chuang, “Roll angular displacement measurement system with microradian accuracy,” Sens. Actuators A Phys. 116(1), 145–149 (2004).
[Crossref]

Cuifang, K.

Cunxing, C.

Donati, S.

J. Qi, Z. Wang, J. H. Huang, B. Yu, J. Gao, and S. Donati, “Note: Enhancing the sensitivity of roll-angle measurement with a novel interferometric configuration based on waveplates and folding mirror,” Rev. Sci. Instrum. 87(3), 036106 (2016).
[Crossref] [PubMed]

S. Donati, D. Rossi, and M. Norgia, “Single Channel Self-Mixing Interferometer Measures Simultaneously Displacement and Tilt and Yaw Angles of a Reflective Target,” IEEE J. Quantum Electron. 51(12), 1–8 (2015).
[Crossref]

Dong, W.

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]

K.-N. Joo, J. D. Ellis, E. S. Buice, J. W. Spronck, and R. H. M. Schmidt, “High resolution heterodyne interferometer without detectable periodic nonlinearity,” Opt. Express 18(2), 1159–1165 (2010).
[Crossref] [PubMed]

Feng, Q.

Fenglin, Y.

Gao, J.

J. Qi, Z. Wang, J. Huang, B. Yu, and J. Gao, “A field calibration method to eliminate the error caused by relative tilt on roll angle measurement,” Proc. SPIE 10023, 1002360B (2016).

J. Qi, Z. Wang, J. H. Huang, B. Yu, J. Gao, and S. Donati, “Note: Enhancing the sensitivity of roll-angle measurement with a novel interferometric configuration based on waveplates and folding mirror,” Rev. Sci. Instrum. 87(3), 036106 (2016).
[Crossref] [PubMed]

S. Tang, Z. Wang, J. Gao, and J. Guo, “Measurement method for roll angular displacement with a high resolution by using diffraction gratings and a heterodyne interferometer,” Rev. Sci. Instrum. 85(4), 045110 (2014).
[Crossref] [PubMed]

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]

Guo, J.

S. Tang, Z. Wang, J. Gao, and J. Guo, “Measurement method for roll angular displacement with a high resolution by using diffraction gratings and a heterodyne interferometer,” Rev. Sci. Instrum. 85(4), 045110 (2014).
[Crossref] [PubMed]

Han, S.

T. Jin, G. Xia, W. Hou, Y. Le, and S. Han, “High resolution and stability roll angle measurement method for precision linear displacement stages,” Rev. Sci. Instrum. 88(2), 023102 (2017).
[Crossref] [PubMed]

Hao, Q.

Homola, J.

I. Rahneberg, F. Baldini, H. J. Büchner, J. Homola, R. A. Lieberman, and G. Jäger,” “Optical system for the simultaneous measurement of two-dimensional straightness errors and the roll angle,” Proc. SPIE 7356, 73560S (2009).

Hong, E.

C. Kuang, E. Hong, and J. Ni, “A high-precision five-degree-of-freedom measurement system based on laser collimator and interferometry techniques,” Rev. Sci. Instrum. 78(9), 095105 (2007).
[Crossref] [PubMed]

Hou, W.

T. Jin, H. Ji, W. Hou, Y. Le, and L. Shen, “Measurement of straightness without Abbe error using an enhanced differential plane mirror interferometer,” Appl. Opt. 56(3), 607–610 (2017).
[Crossref] [PubMed]

T. Jin, G. Xia, W. Hou, Y. Le, and S. Han, “High resolution and stability roll angle measurement method for precision linear displacement stages,” Rev. Sci. Instrum. 88(2), 023102 (2017).
[Crossref] [PubMed]

A. Ju, W. Hou, and Y. Le, “Enhanced roll-angle measurement interferometer,” Opt. Eng. 54(3), 034101 (2015).
[Crossref]

Hsieh, H.-L.

Hsu, C.-C.

C.-H. Liu, W.-Y. Jywe, C.-C. Hsu, and T.-H. Hsu, “Development of a laser-based high-precision six-degrees-of-freedom motion errors measuring system for linear stage,” Rev. Sci. Instrum. 76(5), 055110 (2005).
[Crossref]

Hsu, T.-H.

C.-H. Liu, W.-Y. Jywe, C.-C. Hsu, and T.-H. Hsu, “Development of a laser-based high-precision six-degrees-of-freedom motion errors measuring system for linear stage,” Rev. Sci. Instrum. 76(5), 055110 (2005).
[Crossref]

Huang, J.

J. Qi, Z. Wang, J. Huang, B. Yu, and J. Gao, “A field calibration method to eliminate the error caused by relative tilt on roll angle measurement,” Proc. SPIE 10023, 1002360B (2016).

Huang, J. H.

J. Qi, Z. Wang, J. H. Huang, B. Yu, J. Gao, and S. Donati, “Note: Enhancing the sensitivity of roll-angle measurement with a novel interferometric configuration based on waveplates and folding mirror,” Rev. Sci. Instrum. 87(3), 036106 (2016).
[Crossref] [PubMed]

Huang, M. S.

Jäger, G.

I. Rahneberg, F. Baldini, H. J. Büchner, J. Homola, R. A. Lieberman, and G. Jäger,” “Optical system for the simultaneous measurement of two-dimensional straightness errors and the roll angle,” Proc. SPIE 7356, 73560S (2009).

Ji, H.

Jiang, H.

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

H. Jiang and C. Yin, “Sensitivity enhanced roll angle measurement,” Opt. Eng. 39(2), 516–519 (2000).
[Crossref]

Jin, T.

T. Jin, G. Xia, W. Hou, Y. Le, and S. Han, “High resolution and stability roll angle measurement method for precision linear displacement stages,” Rev. Sci. Instrum. 88(2), 023102 (2017).
[Crossref] [PubMed]

T. Jin, H. Ji, W. Hou, Y. Le, and L. Shen, “Measurement of straightness without Abbe error using an enhanced differential plane mirror interferometer,” Appl. Opt. 56(3), 607–610 (2017).
[Crossref] [PubMed]

Joo, K.-N.

Ju, A.

A. Ju, W. Hou, and Y. Le, “Enhanced roll-angle measurement interferometer,” Opt. Eng. 54(3), 034101 (2015).
[Crossref]

Jywe, W.-Y.

C.-H. Liu, W.-Y. Jywe, C.-C. Hsu, and T.-H. Hsu, “Development of a laser-based high-precision six-degrees-of-freedom motion errors measuring system for linear stage,” Rev. Sci. Instrum. 76(5), 055110 (2005).
[Crossref]

Kuang, C.

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

C. Kuang, E. Hong, and J. Ni, “A high-precision five-degree-of-freedom measurement system based on laser collimator and interferometry techniques,” Rev. Sci. Instrum. 78(9), 095105 (2007).
[Crossref] [PubMed]

Kumar, Y. P.

Le, Y.

T. Jin, H. Ji, W. Hou, Y. Le, and L. Shen, “Measurement of straightness without Abbe error using an enhanced differential plane mirror interferometer,” Appl. Opt. 56(3), 607–610 (2017).
[Crossref] [PubMed]

T. Jin, G. Xia, W. Hou, Y. Le, and S. Han, “High resolution and stability roll angle measurement method for precision linear displacement stages,” Rev. Sci. Instrum. 88(2), 023102 (2017).
[Crossref] [PubMed]

A. Ju, W. Hou, and Y. Le, “Enhanced roll-angle measurement interferometer,” Opt. Eng. 54(3), 034101 (2015).
[Crossref]

Li, C.

Li, D.

Li, M.

S. Tang, Z. Wang, M. Li, W. Zhang, F. Yang, and X. Zhang, “Note: 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. Eng. 67, 66–73 (2015).
[Crossref]

Li, Y.

S. Zhao, H. 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]

Lieberman, R. A.

I. Rahneberg, F. Baldini, H. J. Büchner, J. Homola, R. A. Lieberman, and G. Jäger,” “Optical system for the simultaneous measurement of two-dimensional straightness errors and the roll angle,” Proc. SPIE 7356, 73560S (2009).

Lin, D.

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

Lin, S. T.

Liu, C.-H.

C.-H. Liu, W.-Y. Jywe, C.-C. Hsu, and T.-H. Hsu, “Development of a laser-based high-precision six-degrees-of-freedom motion errors measuring system for linear stage,” Rev. Sci. Instrum. 76(5), 055110 (2005).
[Crossref]

Liu, S.

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

Liu, Y.

Liu, Z.

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

Lou, Y.

B. Chen, L. Cheng, L. Yan, E. Zhang, and Y. Lou, “A heterodyne straightness and displacement measuring interferometer with laser beam drift compensation for long-travel linear stage metrology,” Rev. Sci. Instrum. 88(3), 035114 (2017).
[Crossref] [PubMed]

Ni, J.

C. Kuang, E. Hong, and J. Ni, “A high-precision five-degree-of-freedom measurement system based on laser collimator and interferometry techniques,” Rev. Sci. Instrum. 78(9), 095105 (2007).
[Crossref] [PubMed]

Norgia, M.

S. Donati, D. Rossi, and M. Norgia, “Single Channel Self-Mixing Interferometer Measures Simultaneously Displacement and Tilt and Yaw Angles of a Reflective Target,” IEEE J. Quantum Electron. 51(12), 1–8 (2015).
[Crossref]

Pan, S.-W.

Qi, J.

J. Qi, Z. Wang, J. H. Huang, B. Yu, J. Gao, and S. Donati, “Note: Enhancing the sensitivity of roll-angle measurement with a novel interferometric configuration based on waveplates and folding mirror,” Rev. Sci. Instrum. 87(3), 036106 (2016).
[Crossref] [PubMed]

J. Qi, Z. Wang, J. Huang, B. Yu, and J. Gao, “A field calibration method to eliminate the error caused by relative tilt on roll angle measurement,” Proc. SPIE 10023, 1002360B (2016).

Qiao, Y.

Qibo, F.

Rahneberg, I.

I. Rahneberg, F. Baldini, H. J. Büchner, J. Homola, R. A. Lieberman, and G. Jäger,” “Optical system for the simultaneous measurement of two-dimensional straightness errors and the roll angle,” Proc. SPIE 7356, 73560S (2009).

Rossi, D.

S. Donati, D. Rossi, and M. Norgia, “Single Channel Self-Mixing Interferometer Measures Simultaneously Displacement and Tilt and Yaw Angles of a Reflective Target,” IEEE J. Quantum Electron. 51(12), 1–8 (2015).
[Crossref]

Schmidt, R. H. M.

Shen, L.

Spronck, J. W.

Tang, S.

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

S. Tang, Z. Wang, J. Gao, and J. Guo, “Measurement method for roll angular displacement with a high resolution by using diffraction gratings and a heterodyne interferometer,” Rev. Sci. Instrum. 85(4), 045110 (2014).
[Crossref] [PubMed]

Tang, W.

Wang, Z.

J. Qi, Z. Wang, J. Huang, B. Yu, and J. Gao, “A field calibration method to eliminate the error caused by relative tilt on roll angle measurement,” Proc. SPIE 10023, 1002360B (2016).

J. Qi, Z. Wang, J. H. Huang, B. Yu, J. Gao, and S. Donati, “Note: Enhancing the sensitivity of roll-angle measurement with a novel interferometric configuration based on waveplates and folding mirror,” Rev. Sci. Instrum. 87(3), 036106 (2016).
[Crossref] [PubMed]

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

S. Tang, Z. Wang, J. Gao, and J. Guo, “Measurement method for roll angular displacement with a high resolution by using diffraction gratings and a heterodyne interferometer,” Rev. Sci. Instrum. 85(4), 045110 (2014).
[Crossref] [PubMed]

Wei, H.

S. Zhao, H. 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]

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]

Wu, C.-M.

C.-M. Wu and Y.-T. Chuang, “Roll angular displacement measurement system with microradian accuracy,” Sens. Actuators A Phys. 116(1), 145–149 (2004).
[Crossref]

Xia, G.

T. Jin, G. Xia, W. Hou, Y. Le, and S. Han, “High resolution and stability roll angle measurement method for precision linear displacement stages,” Rev. Sci. Instrum. 88(2), 023102 (2017).
[Crossref] [PubMed]

Xinjie, W.

Z. Yusheng, Z. Zhifeng, S. Yuling, W. Xinjie, and F. Qibo, “A high-precision roll angle measurement method,” Optik (Stuttg.) 126(24), 4837–4840 (2015).
[Crossref]

Yan, L.

Yang, F.

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

Yang, T.

Yao, X.

Yeh, S. L.

Yin, C.

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

H. Jiang and C. Yin, “Sensitivity enhanced roll angle measurement,” Opt. Eng. 39(2), 516–519 (2000).
[Crossref]

Yin, Y.

Yu, B.

J. Qi, Z. Wang, J. H. Huang, B. Yu, J. Gao, and S. Donati, “Note: Enhancing the sensitivity of roll-angle measurement with a novel interferometric configuration based on waveplates and folding mirror,” Rev. Sci. Instrum. 87(3), 036106 (2016).
[Crossref] [PubMed]

J. Qi, Z. Wang, J. Huang, B. Yu, and J. Gao, “A field calibration method to eliminate the error caused by relative tilt on roll angle measurement,” Proc. SPIE 10023, 1002360B (2016).

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]

Yuling, S.

Z. Yusheng, Z. Zhifeng, S. Yuling, W. Xinjie, and F. Qibo, “A high-precision roll angle measurement method,” Optik (Stuttg.) 126(24), 4837–4840 (2015).
[Crossref]

Yusheng, Z.

Zhang, B.

Zhang, E.

B. Chen, L. Cheng, L. Yan, E. Zhang, and Y. Lou, “A heterodyne straightness and displacement measuring interferometer with laser beam drift compensation for long-travel linear stage metrology,” Rev. Sci. Instrum. 88(3), 035114 (2017).
[Crossref] [PubMed]

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]

Zhang, W.

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

Zhao, S.

S. Zhao, H. 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]

Zhao, Y.

Zhifeng, Z.

Z. Yusheng, Z. Zhifeng, S. Yuling, W. Xinjie, and F. Qibo, “A high-precision roll angle measurement method,” Optik (Stuttg.) 126(24), 4837–4840 (2015).
[Crossref]

Zhu, Y.

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

Appl. Opt. (3)

IEEE J. Quantum Electron. (1)

S. Donati, D. Rossi, and M. Norgia, “Single Channel Self-Mixing Interferometer Measures Simultaneously Displacement and Tilt and Yaw Angles of a Reflective Target,” IEEE J. Quantum Electron. 51(12), 1–8 (2015).
[Crossref]

Opt. Eng. (4)

S. Zhao, H. 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]

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

A. Ju, W. Hou, and Y. Le, “Enhanced roll-angle measurement interferometer,” Opt. Eng. 54(3), 034101 (2015).
[Crossref]

H. Jiang and C. Yin, “Sensitivity enhanced roll angle measurement,” Opt. Eng. 39(2), 516–519 (2000).
[Crossref]

Opt. Express (7)

Y. Zhao, B. Zhang, and Q. Feng, “Measurement system and model for simultaneously measuring 6DOF geometric errors,” Opt. Express 25(18), 20993–21007 (2017).
[Crossref] [PubMed]

K.-N. Joo, J. D. Ellis, E. S. Buice, J. W. Spronck, and R. H. M. Schmidt, “High resolution heterodyne interferometer without detectable periodic nonlinearity,” Opt. Express 18(2), 1159–1165 (2010).
[Crossref] [PubMed]

B. Chen, L. Yan, X. Yao, T. Yang, D. Li, W. Dong, C. Li, and W. Tang, “Development of a laser synthetic wavelength interferometer for large displacement measurement with nanometer accuracy,” Opt. Express 18(3), 3000–3010 (2010).
[Crossref] [PubMed]

S. T. Lin, S. L. Yeh, C. S. Chiu, and M. S. Huang, “A calibrator based on the use of low-coherent light source straightness interferometer and compensation method,” Opt. Express 19(22), 21929–21937 (2011).
[Crossref] [PubMed]

F. Qibo, Z. Bin, C. Cunxing, K. Cuifang, Z. Yusheng, and Y. Fenglin, “Development of a simple system for simultaneously measuring 6DOF geometric motion errors of a linear guide,” Opt. Express 21(22), 25805–25819 (2013).
[Crossref] [PubMed]

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]

H.-L. Hsieh and S.-W. Pan, “Development of a grating-based interferometer for six-degree-of-freedom displacement and angle measurements,” Opt. Express 23(3), 2451–2465 (2015).
[Crossref] [PubMed]

Optik (Stuttg.) (1)

Z. Yusheng, Z. Zhifeng, S. Yuling, W. Xinjie, and F. Qibo, “A high-precision roll angle measurement method,” Optik (Stuttg.) 126(24), 4837–4840 (2015).
[Crossref]

Proc. SPIE (2)

I. Rahneberg, F. Baldini, H. J. Büchner, J. Homola, R. A. Lieberman, and G. Jäger,” “Optical system for the simultaneous measurement of two-dimensional straightness errors and the roll angle,” Proc. SPIE 7356, 73560S (2009).

J. Qi, Z. Wang, J. Huang, B. Yu, and J. Gao, “A field calibration method to eliminate the error caused by relative tilt on roll angle measurement,” Proc. SPIE 10023, 1002360B (2016).

Rev. Sci. Instrum. (8)

J. Qi, Z. Wang, J. H. Huang, B. Yu, J. Gao, and S. Donati, “Note: Enhancing the sensitivity of roll-angle measurement with a novel interferometric configuration based on waveplates and folding mirror,” Rev. Sci. Instrum. 87(3), 036106 (2016).
[Crossref] [PubMed]

C.-H. Liu, W.-Y. Jywe, C.-C. Hsu, and T.-H. Hsu, “Development of a laser-based high-precision six-degrees-of-freedom motion errors measuring system for linear stage,” Rev. Sci. Instrum. 76(5), 055110 (2005).
[Crossref]

C. Kuang, E. Hong, and J. Ni, “A high-precision five-degree-of-freedom measurement system based on laser collimator and interferometry techniques,” Rev. Sci. Instrum. 78(9), 095105 (2007).
[Crossref] [PubMed]

S. Tang, Z. Wang, J. Gao, and J. Guo, “Measurement method for roll angular displacement with a high resolution by using diffraction gratings and a heterodyne interferometer,” Rev. Sci. Instrum. 85(4), 045110 (2014).
[Crossref] [PubMed]

T. Jin, G. Xia, W. Hou, Y. Le, and S. Han, “High resolution and stability roll angle measurement method for precision linear displacement stages,” Rev. Sci. Instrum. 88(2), 023102 (2017).
[Crossref] [PubMed]

B. Chen, L. Cheng, L. Yan, E. Zhang, and Y. Lou, “A heterodyne straightness and displacement measuring interferometer with laser beam drift compensation for long-travel linear stage metrology,” Rev. Sci. Instrum. 88(3), 035114 (2017).
[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]

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

Sens. Actuators A Phys. (2)

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

C.-M. Wu and Y.-T. Chuang, “Roll angular displacement measurement system with microradian accuracy,” Sens. Actuators A Phys. 116(1), 145–149 (2004).
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 Schematic of the single-path heterodyne interferometer for roll measurement.
Fig. 2
Fig. 2 Differential heterodyne interferometer for roll angle measurement.
Fig. 3
Fig. 3 Calculated phase difference versus roll angle for the differential interferometer and single-path interferometer
Fig. 4
Fig. 4 Schematic configuration of differential roll angle measurement system.
Fig. 5
Fig. 5 Experimental setup for roll angle measurement with same structure in Fig. 2.
Fig. 6
Fig. 6 Experimental results of the differential interferometer and single-path interferometer in the range of 90°.
Fig. 7
Fig. 7 Experimental result of the phase difference versus roll angle in the sensitive area.
Fig. 8
Fig. 8 The roll obtained from the differential interferometer against that from the XL-80 interferometer and the residual between them.
Fig. 9
Fig. 9 Measured roll angle error of a precision translation stage.

Equations (15)

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

ψ= tan 1 ( tanθtan4α )+ tan 1 ( cotθtan4α ).
I A = k A cos[ 2π( f 1 f 2 )t+( φ A 1 φ A2 ) ].
I B = k B cos[ 2π( f 1 f 2 )t+( φ B1 φ B2 ) ].
φ=( φ A1 φ A2 )( φ B1 φ B2 ) =( 2π f 1 L A n c 2π f 2 L A n c )( 2π f 1 L B n c 2π f 2 L B n c ). = 2π( f 1 f 2 )( L A L B ) c n
B 1 = B 2 =[ Eexp[ i( ω 1 t+ φ 1 ) ] Eexp[ i( ω 2 t+ φ 2 ) ] ], Q 1 =[ cos 2 θ+i sin 2 θ (1i)sinθcosθ (1i)sinθcosθ sin 2 θ+i cos 2 θ ], Q 2 =[ cos 2 θ+i sin 2 θ (i1)sinθcosθ (i1)sinθcosθ sin 2 θ+i cos 2 θ ],H( α )=[ cos2α sin2α sin2α cos2α ], P 1 =[ cos θ 1 sin θ 1 ], P 2 =[ cos θ 2 sin θ 2 ]
E 2 1 = P 2 1 H(α)H(α) Q 2 1 B 2 1 .
E 1 =E ( cosθcos4α ) 2 + ( sinθsin4α ) 2 exp[ ω 1 t+ φ 1 + tan 1 ( tanθtan4α ) ] +E ( sinθcos4α ) 2 + ( cosθsin4α ) 2 exp[ ω 2 t+ φ 2 + tan 1 ( cotθtan4α ) ].
E 2 =E ( sinθcos4α ) 2 + ( cosθsin4α ) 2 exp[ ω 1 t+ φ 1 + tan 1 ( cotθtan4α ) ] +E ( cosθcos4α ) 2 + ( sinθsin4α ) 2 exp[ ω 2 t+ φ 2 + tan 1 ( tanθtan4α ) ].
I 1 =Ecos[ ( ω 1 ω 2 )t+( φ 1 φ 2 )+ tan 1 ( tanθtan4α )+ tan 1 ( cotθtan4α ) ].
I 2 =Ecos[ ( ω 1 ω 2 )t+( φ 1 φ 2 ) tan 1 ( tanθtan4α ) tan 1 ( cotθtan4α ) ].
ψ=2[ tan 1 ( tanθtan4α )+ tan 1 ( cotθtan4α ) ].
A= Δ{ 2[ arctan( tanθtan4α )+arctan( cotθtan4α ) ] }/ Δα = 2( tanθ/k k4nΔα+ cotθ/k k4nΔα )/ Δα . =8( tanθ+cotθ )
Δα= Δψ A = Δψ 8( tanθ+cotθ ) .
B 1 =[ Eexp[ i( ω 1 t+ φ 1 ) ] Eexp[ i( ω 2 t+ φ 2 ) ] ], B 2 =[ Eexp[ i( ω 2 t+ φ 2 ) ] Eexp[ i( ω 1 t+ φ 1 ) ] ], Q=[ cos 2 θ+i sin 2 θ (1i)sinθcosθ (1i)sinθcosθ sin 2 θ+i cos 2 θ ],H( α )=[ cos2α sin2α sin2α cos2α ],P= 2 2 [ 1 1 ]
E Ι Ι Ι =PH(α)H(α)Q B 2 1 .

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