Abstract

This article proposes a novel optical method for three-dimensional (3D) angle measurement. Using a simple and compact measurement system, the 3D angle can be determined simultaneously in real time based on geometric relation transformation and autocollimation. Additionally, the crosstalk error can be avoided between the three angles. In order to enable 3D angle measurement and simplify the system, a compact combined target with transmission grating and mirror group is designed. Theoretically, the relationship between the 3D angle and the light spot displacement on the PSD (position sensitive detector) has been deduced to demonstrate the possibility of this method. Practically, the verification experiments have been carried out to verify the feasibility of this approach, and the results fit well with the theoretical analysis.

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

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
  5. F. Siewert, J. Buchheim, S. Boutet, G. J. Williams, P. A. Montanez, J. Krzywinski, and R. Signorato, “Ultra-precise characterization of LCLS hard X-ray focusing mirrors by high resolution slope measuring deflectometry,” Opt. Express 20(4), 4525–4536 (2012).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  20. Y. Lou, L. Yan, B. Chen, and S. Zhang, “Laser homodyne straightness interferometer with simultaneous measurement of six degrees of freedom motion errors for precision linear stage metrology,” Opt. Express 25(6), 6805–6821 (2017).
    [Crossref]

2019 (1)

2018 (2)

L. Huang, J. Xue, B. Gao, and M. Idir, “One-dimensional angular-measurement-based stitching interferometry,” Opt. Express 26(8), 9882–9892 (2018).
[Crossref]

S. R. Gillmer, J. Martínez-Rincón, and J. D. Ellis, “Anomalous vibration suppression in a weak-value-emulated heterodyne roll interferometer,” Opt. Lett. 26(22), 29311–29318 (2018).
[Crossref]

2017 (2)

2016 (1)

2015 (3)

2014 (1)

2013 (2)

2012 (2)

2011 (1)

W. Gao, Y. Saito, H. Muto, Y. Arai, and Y. Shimizu, “A three-axis autocollimator for detection of angular error motions of a precision Stage,” CIRP Ann. 60(1), 515–518 (2011).
[Crossref]

2009 (2)

Y. Saito, Y. Arai, and W. Gao, “Detection of three-axis angles by an optical sensor,” Sens. Actuators, A 150(2), 175–183 (2009).
[Crossref]

C. Liu, H. Huang, and H. Lee, “Five-degrees-of-freedom diffractive laser encoder,” Appl. Opt. 48(14), 2767–2777 (2009).
[Crossref]

2008 (1)

D. Zheng, X. Wang, and Z. Li, “Accuracy analysis of parallel plate interferometer for angular displacement measurement,” Opt. Laser Technol. 40(1), 6–12 (2008).
[Crossref]

2007 (1)

R. Cowsik, R. Srinivasan, S. Kasturirengan, A. Senthil Kumar, and K. Wagoner, “Design and performance of a sub-nanoradian resolution autocollimating optical lever,” Rev. Sci. Instrum. 78(3), 035105 (2007).
[Crossref]

2003 (1)

J. Yuan and X. Long, “CCD-area-based autocollimator for precision small-angle measurement,” Rev. Sci. Instrum. 74(3), 1362–1365 (2003).
[Crossref]

Arai, Y.

W. Gao, Y. Saito, H. Muto, Y. Arai, and Y. Shimizu, “A three-axis autocollimator for detection of angular error motions of a precision Stage,” CIRP Ann. 60(1), 515–518 (2011).
[Crossref]

Y. Saito, Y. Arai, and W. Gao, “Detection of three-axis angles by an optical sensor,” Sens. Actuators, A 150(2), 175–183 (2009).
[Crossref]

Boutet, S.

Buchheim, J.

Chen, B.

Cowsik, R.

R. Cowsik, R. Srinivasan, S. Kasturirengan, A. Senthil Kumar, and K. Wagoner, “Design and performance of a sub-nanoradian resolution autocollimating optical lever,” Rev. Sci. Instrum. 78(3), 035105 (2007).
[Crossref]

Cui, C.

Cui, J.

Di, K.

Ellis, J. D.

S. R. Gillmer, J. Martínez-Rincón, and J. D. Ellis, “Anomalous vibration suppression in a weak-value-emulated heterodyne roll interferometer,” Opt. Lett. 26(22), 29311–29318 (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]

Feng, Q.

Gao, B.

Gao, W.

W. Gao, Y. Saito, H. Muto, Y. Arai, and Y. Shimizu, “A three-axis autocollimator for detection of angular error motions of a precision Stage,” CIRP Ann. 60(1), 515–518 (2011).
[Crossref]

Y. Saito, Y. Arai, and W. Gao, “Detection of three-axis angles by an optical sensor,” Sens. Actuators, A 150(2), 175–183 (2009).
[Crossref]

Gao, Y.

Gillmer, S. R.

S. R. Gillmer, J. Martínez-Rincón, and J. D. Ellis, “Anomalous vibration suppression in a weak-value-emulated heterodyne roll interferometer,” Opt. Lett. 26(22), 29311–29318 (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]

Guo, J.

Hou, W.

Hsieh, H. L.

Hu, C.

Hu, K.

Huang, H.

Huang, L.

Huang, Z.

Idir, M.

Jeong, H. S.

Kasturirengan, S.

R. Cowsik, R. Srinivasan, S. Kasturirengan, A. Senthil Kumar, and K. Wagoner, “Design and performance of a sub-nanoradian resolution autocollimating optical lever,” Rev. Sci. Instrum. 78(3), 035105 (2007).
[Crossref]

Kim, K. H.

Kim, S. H.

Konyakhin, I.

Krzywinski, J.

Kuang, C.

P. Zhang, Y. Wang, C. Kuang, S. Li, and X. Liu, “Measuring roll angle displacement based on ellipticity with high resolution and large range,” Opt. Laser Technol. 65, 126–130 (2015).
[Crossref]

Le, Y.

Lee, H.

Li, R.

Li, S.

P. Zhang, Y. Wang, C. Kuang, S. Li, and X. Liu, “Measuring roll angle displacement based on ellipticity with high resolution and large range,” Opt. Laser Technol. 65, 126–130 (2015).
[Crossref]

Li, Z.

D. Zheng, X. Wang, and Z. Li, “Accuracy analysis of parallel plate interferometer for angular displacement measurement,” Opt. Laser Technol. 40(1), 6–12 (2008).
[Crossref]

Liu, C.

Liu, X.

P. Zhang, Y. Wang, C. Kuang, S. Li, and X. Liu, “Measuring roll angle displacement based on ellipticity with high resolution and large range,” Opt. Laser Technol. 65, 126–130 (2015).
[Crossref]

Liu, Y.

Long, X.

J. Yuan and X. Long, “CCD-area-based autocollimator for precision small-angle measurement,” Rev. Sci. Instrum. 74(3), 1362–1365 (2003).
[Crossref]

Lou, Y.

Lu, Y.

Martínez-Rincón, J.

S. R. Gillmer, J. Martínez-Rincón, and J. D. Ellis, “Anomalous vibration suppression in a weak-value-emulated heterodyne roll interferometer,” Opt. Lett. 26(22), 29311–29318 (2018).
[Crossref]

Montanez, P. A.

Muto, H.

W. Gao, Y. Saito, H. Muto, Y. Arai, and Y. Shimizu, “A three-axis autocollimator for detection of angular error motions of a precision Stage,” CIRP Ann. 60(1), 515–518 (2011).
[Crossref]

Pan, S. W.

Saito, Y.

W. Gao, Y. Saito, H. Muto, Y. Arai, and Y. Shimizu, “A three-axis autocollimator for detection of angular error motions of a precision Stage,” CIRP Ann. 60(1), 515–518 (2011).
[Crossref]

Y. Saito, Y. Arai, and W. Gao, “Detection of three-axis angles by an optical sensor,” Sens. Actuators, A 150(2), 175–183 (2009).
[Crossref]

Senthil Kumar, A.

R. Cowsik, R. Srinivasan, S. Kasturirengan, A. Senthil Kumar, and K. Wagoner, “Design and performance of a sub-nanoradian resolution autocollimating optical lever,” Rev. Sci. Instrum. 78(3), 035105 (2007).
[Crossref]

Shi, K.

Shimizu, Y.

W. Gao, Y. Saito, H. Muto, Y. Arai, and Y. Shimizu, “A three-axis autocollimator for detection of angular error motions of a precision Stage,” CIRP Ann. 60(1), 515–518 (2011).
[Crossref]

Siewert, F.

Signorato, R.

Srinivasan, R.

R. Cowsik, R. Srinivasan, S. Kasturirengan, A. Senthil Kumar, and K. Wagoner, “Design and performance of a sub-nanoradian resolution autocollimating optical lever,” Rev. Sci. Instrum. 78(3), 035105 (2007).
[Crossref]

Tan, J.

Wagoner, K.

R. Cowsik, R. Srinivasan, S. Kasturirengan, A. Senthil Kumar, and K. Wagoner, “Design and performance of a sub-nanoradian resolution autocollimating optical lever,” Rev. Sci. Instrum. 78(3), 035105 (2007).
[Crossref]

Wang, C.

Wang, X.

Y. Gao, X. Wang, Z. Huang, D. Zhan, and C. Hu, “High-precision rolling angle measurement for a three-dimensional collimator,” Appl. Opt. 53(29), 6629–6634 (2014).
[Crossref]

D. Zheng, X. Wang, and Z. Li, “Accuracy analysis of parallel plate interferometer for angular displacement measurement,” Opt. Laser Technol. 40(1), 6–12 (2008).
[Crossref]

Wang, Y.

P. Zhang, Y. Wang, C. Kuang, S. Li, and X. Liu, “Measuring roll angle displacement based on ellipticity with high resolution and large range,” Opt. Laser Technol. 65, 126–130 (2015).
[Crossref]

Williams, G. J.

Xue, J.

Yan, L.

Yu, X.

Yuan, J.

J. Yuan and X. Long, “CCD-area-based autocollimator for precision small-angle measurement,” Rev. Sci. Instrum. 74(3), 1362–1365 (2003).
[Crossref]

Yun, H. G.

Zhan, D.

Zhang, B.

Zhang, P.

P. Zhang, Y. Wang, C. Kuang, S. Li, and X. Liu, “Measuring roll angle displacement based on ellipticity with high resolution and large range,” Opt. Laser Technol. 65, 126–130 (2015).
[Crossref]

Zhang, S.

Zhao, Y.

Zheng, D.

D. Zheng, X. Wang, and Z. Li, “Accuracy analysis of parallel plate interferometer for angular displacement measurement,” Opt. Laser Technol. 40(1), 6–12 (2008).
[Crossref]

Zhou, M.

Zhu, F.

Appl. Opt. (3)

CIRP Ann. (1)

W. Gao, Y. Saito, H. Muto, Y. Arai, and Y. Shimizu, “A three-axis autocollimator for detection of angular error motions of a precision Stage,” CIRP Ann. 60(1), 515–518 (2011).
[Crossref]

Opt. Express (8)

L. Huang, J. Xue, B. Gao, and M. Idir, “One-dimensional angular-measurement-based stitching interferometry,” Opt. Express 26(8), 9882–9892 (2018).
[Crossref]

R. Li, M. Zhou, I. Konyakhin, K. Di, Y. Lu, J. Guo, and Y. Liu, “Cube-corner autocollimator with expanded measurement range,” Opt. Express 27(5), 6389–6403 (2019).
[Crossref]

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]

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]

F. Siewert, J. Buchheim, S. Boutet, G. J. Williams, P. A. Montanez, J. Krzywinski, and R. Signorato, “Ultra-precise characterization of LCLS hard X-ray focusing mirrors by high resolution slope measuring deflectometry,” Opt. Express 20(4), 4525–4536 (2012).
[Crossref]

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]

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]

Y. Lou, L. Yan, B. Chen, and S. Zhang, “Laser homodyne straightness interferometer with simultaneous measurement of six degrees of freedom motion errors for precision linear stage metrology,” Opt. Express 25(6), 6805–6821 (2017).
[Crossref]

Opt. Laser Technol. (2)

D. Zheng, X. Wang, and Z. Li, “Accuracy analysis of parallel plate interferometer for angular displacement measurement,” Opt. Laser Technol. 40(1), 6–12 (2008).
[Crossref]

P. Zhang, Y. Wang, C. Kuang, S. Li, and X. Liu, “Measuring roll angle displacement based on ellipticity with high resolution and large range,” Opt. Laser Technol. 65, 126–130 (2015).
[Crossref]

Opt. Lett. (3)

Rev. Sci. Instrum. (2)

J. Yuan and X. Long, “CCD-area-based autocollimator for precision small-angle measurement,” Rev. Sci. Instrum. 74(3), 1362–1365 (2003).
[Crossref]

R. Cowsik, R. Srinivasan, S. Kasturirengan, A. Senthil Kumar, and K. Wagoner, “Design and performance of a sub-nanoradian resolution autocollimating optical lever,” Rev. Sci. Instrum. 78(3), 035105 (2007).
[Crossref]

Sens. Actuators, A (1)

Y. Saito, Y. Arai, and W. Gao, “Detection of three-axis angles by an optical sensor,” Sens. Actuators, A 150(2), 175–183 (2009).
[Crossref]

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Figures (7)

Fig. 1.
Fig. 1. Schematic of 3D measurement system.
Fig. 2.
Fig. 2. The motion trail of the light spots on transmission grating. The dashed circle is the motion trail
Fig. 3.
Fig. 3. Schematic of beam path inside of the combined target with yaw angle α
Fig. 4.
Fig. 4. (a) change of motion trail when α exists. (b) change of motion trail when β exists
Fig. 5.
Fig. 5. Measurement results of verification experiments. (a) yaw; (b) pitch; (c) roll.
Fig. 6.
Fig. 6. Roll measurement with different yaw and pitch. Residual1 is the difference between first curve and second curve, Residual2 is the difference between first curve and third curve.
Fig. 7.
Fig. 7. 3D angular displacements measurement of a precision linear stage. (a) yaw; (b) pitch; (c) roll.

Equations (10)

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

sin 2 α = Δ x 1 f
sin 2 β = Δ y 1 f
sin γ = Δ y 2 Δ y 3 d
sin θ + 1 = λ g sin α
sin θ + 1 = λ g sin α
sin α 2 = λ g sin θ + 1 = sin α
Δ y 2 = l × sin(2 β ) + Δ y 2 × cos ( 2 β )
Δ y 3 = l × sin(2 β ) + Δ y 3 × cos ( 2 β )
sin γ = Δ y 2 Δ y 3 d cos 2 β
sin γ = Δ y 2 Δ y 3 d 1 ( Δ y 1 / f ) 2