Abstract

In this paper, the error analysis model for the three-element Risley-prism scan system (TRSS) is established, and categories of error sources are redefined. The impact of each error on the pointing accuracy is graphically presented with analytical and numerical results. The analysis method can be implemented to any Risley-prism beam scan system. For thin prisms, an error compensation algorithm for the TRSS is developed to accomplish high-accuracy beam scanning, which can be referred to the error calibration of the TRSS.

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

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References

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    [Crossref]
  2. Y. Li, “Closed form analytical inverse solutions for Risley-prism-based beam steering systems in different configurations,” Appl. Opt. 50(22), 4302–4309 (2011).
    [Crossref] [PubMed]
  3. J. Li, Q. Peng, K. Chen, and C. Fu, “High precision pointing system based on Risley prism: analysis and simulation,” Proc. SPIE 9255, 1–7 (2015).
  4. A. Li, W. Sun, W. Yi, and Q. Zuo, “Investigation of beam steering performances in rotation Risley-prism scanner,” Opt. Express 24(12), 12840–12850 (2016).
    [Crossref] [PubMed]
  5. L. Liu, L. Wang, J. Sun, Y. Zhou, X. Zhong, Z. Luan, D. Liu, A. Yan, and N. Xu, “An integrated test-bed for PAT testing and verification of inter-satellite lasercom terminals,” Proc. SPIE 6709, 670904 (2007).
    [Crossref]
  6. V. Lavigne and B. Ricard, “Fast Risley prisms camera steering system: calibration and image distortions correction through the use of a three-dimensional refraction model,” Opt. Eng. 46(4), 043201 (2007).
    [Crossref]
  7. F. Souvestre, M. Hafez, and S. Régnier, “DMD-based multi-target laser tracking for motion capturing,” Proc. SPIE 7596, 75960B (2010).
    [Crossref]
  8. X. Tao, H. Cho, and F. Janabi-Sharifi, “Active optical system for variable view imaging of micro objects with emphasis on kinematic analysis,” Appl. Opt. 47(22), 4121–4132 (2008).
    [Crossref] [PubMed]
  9. S. Jianfeng, L. Liren, Y. Maojin, W. Lingyu, and Z. Mingli, “The effect of the rotating double-prism wide-angle laser beam scanner on the beam shape,” Optik (Stuttg.) 116(12), 553–556 (2005).
    [Crossref]
  10. J. L. Gibson, B. D. Duncan, P. Bos, and V. Sergen, “Wide-angle achromatic prism beam steering for infrared countermeasure applications,” Opt. Eng. 42(4), 1038–1047 (2003).
    [Crossref]
  11. A. Li, X. Liu, and W. Sun, “Forward and inverse solutions for three-element Risley prism beam scanners,” Opt. Express 25(7), 7677–7688 (2017).
    [Crossref] [PubMed]
  12. M. Sánchez and D. Gutow, “Control laws for a 3-element Risley prism optical beam pointer,” Proc. SPIE 6304, 630403 (2006).
    [Crossref]
  13. J. L. Gibson, B. D. Duncan, P. Bos, and V. Sergen, “Wide angle beam steering for infrared countermeasures applications,” Proc. SPIE 4723, 100–111 (2002).
    [Crossref]
  14. M. Ostaszewski, S. Harford, N. Doughty, C. Hoffman, M. Sanchez, D. Gutow, and R. Pierce, “Risley prism beam pointer,” Proc. SPIE 6304, 630406 (2006).
    [Crossref]
  15. J. S. Horng and Y. Li, “Error sources and their impact on the performance of dual-wedge beam steering systems,” Appl. Opt. 51(18), 4168–4175 (2012).
    [Crossref] [PubMed]
  16. Y. Zhao and Y. Yuan, “First-order approximation error analysis of Risley-prism-based beam directing system,” Appl. Opt. 53(34), 8020–8031 (2014).
    [Crossref] [PubMed]
  17. Y. Zhou, Y. Lu, M. Hei, G. Liu, and D. Fan, “Pointing error analysis of Risley-prism-based beam steering system,” Appl. Opt. 53(25), 5775–5783 (2014).
    [Crossref] [PubMed]
  18. B. Bravo-Medina, M. Strojnik, G. Garcia-Torales, H. Torres-Ortega, R. Estrada-Marmolejo, A. Beltrán-González, and J. L. Flores, “Error compensation in a pointing system based on Risley prisms,” Appl. Opt. 56(8), 2209–2216 (2017).
    [Crossref] [PubMed]
  19. J. Li, K. Chen, Q. Peng, Z. Wang, Y. Jiang, C. Fu, and G. Ren, “Improvement of pointing accuracy for Risley prisms by parameter identification,” Appl. Opt. 56(26), 7358–7366 (2017).
    [Crossref] [PubMed]
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  21. H. Zhang, Y. Yuan, L. Su, and F. Huang, “Error modeling and analysis of Risley-prism system based on ray direction deviation in light refraction,” Appl. Opt. 37, 61307020 (2015).
  22. A. Li, Q. Zou, Y. Bian, H. Liu, and L. Liu, “Assembly error analysis of laser tracking steering prisms with sub-microradian order accuracy,” J. Mechan. Engin. 52(10), 9–12 (2016).
    [Crossref]
  23. L. Zhang and Y. Li, “Error analysis of spherical 2-DOF parallel manipulator with actuation redundancy,” J. Mechan. Engin. 49(7), 148–154 (2013).
    [Crossref]
  24. J. Sun, L. Liu, A. Li, and D. Xu, “Submicroradian laser beam angular scan precision measurement by interference method,” Opt. Eng. 48(7), 705–709 (2009).
    [Crossref]
  25. Y. Ge, J. Liu, F. Xue, E. Guan, W. Yan, and Y. Zhao, “Effect of mechanical error on dual-wedge laser scanning system and error correction,” Appl. Opt. 57(21), 6047–6054 (2018).
    [Crossref] [PubMed]

2018 (1)

2017 (3)

2016 (2)

A. Li, W. Sun, W. Yi, and Q. Zuo, “Investigation of beam steering performances in rotation Risley-prism scanner,” Opt. Express 24(12), 12840–12850 (2016).
[Crossref] [PubMed]

A. Li, Q. Zou, Y. Bian, H. Liu, and L. Liu, “Assembly error analysis of laser tracking steering prisms with sub-microradian order accuracy,” J. Mechan. Engin. 52(10), 9–12 (2016).
[Crossref]

2015 (2)

H. Zhang, Y. Yuan, L. Su, and F. Huang, “Error modeling and analysis of Risley-prism system based on ray direction deviation in light refraction,” Appl. Opt. 37, 61307020 (2015).

J. Li, Q. Peng, K. Chen, and C. Fu, “High precision pointing system based on Risley prism: analysis and simulation,” Proc. SPIE 9255, 1–7 (2015).

2014 (2)

2013 (1)

L. Zhang and Y. Li, “Error analysis of spherical 2-DOF parallel manipulator with actuation redundancy,” J. Mechan. Engin. 49(7), 148–154 (2013).
[Crossref]

2012 (1)

2011 (1)

2010 (1)

F. Souvestre, M. Hafez, and S. Régnier, “DMD-based multi-target laser tracking for motion capturing,” Proc. SPIE 7596, 75960B (2010).
[Crossref]

2009 (1)

J. Sun, L. Liu, A. Li, and D. Xu, “Submicroradian laser beam angular scan precision measurement by interference method,” Opt. Eng. 48(7), 705–709 (2009).
[Crossref]

2008 (1)

2007 (2)

L. Liu, L. Wang, J. Sun, Y. Zhou, X. Zhong, Z. Luan, D. Liu, A. Yan, and N. Xu, “An integrated test-bed for PAT testing and verification of inter-satellite lasercom terminals,” Proc. SPIE 6709, 670904 (2007).
[Crossref]

V. Lavigne and B. Ricard, “Fast Risley prisms camera steering system: calibration and image distortions correction through the use of a three-dimensional refraction model,” Opt. Eng. 46(4), 043201 (2007).
[Crossref]

2006 (2)

M. Ostaszewski, S. Harford, N. Doughty, C. Hoffman, M. Sanchez, D. Gutow, and R. Pierce, “Risley prism beam pointer,” Proc. SPIE 6304, 630406 (2006).
[Crossref]

M. Sánchez and D. Gutow, “Control laws for a 3-element Risley prism optical beam pointer,” Proc. SPIE 6304, 630403 (2006).
[Crossref]

2005 (1)

S. Jianfeng, L. Liren, Y. Maojin, W. Lingyu, and Z. Mingli, “The effect of the rotating double-prism wide-angle laser beam scanner on the beam shape,” Optik (Stuttg.) 116(12), 553–556 (2005).
[Crossref]

2003 (1)

J. L. Gibson, B. D. Duncan, P. Bos, and V. Sergen, “Wide-angle achromatic prism beam steering for infrared countermeasure applications,” Opt. Eng. 42(4), 1038–1047 (2003).
[Crossref]

2002 (1)

J. L. Gibson, B. D. Duncan, P. Bos, and V. Sergen, “Wide angle beam steering for infrared countermeasures applications,” Proc. SPIE 4723, 100–111 (2002).
[Crossref]

1960 (1)

Beltrán-González, A.

Bian, Y.

A. Li, Q. Zou, Y. Bian, H. Liu, and L. Liu, “Assembly error analysis of laser tracking steering prisms with sub-microradian order accuracy,” J. Mechan. Engin. 52(10), 9–12 (2016).
[Crossref]

Bos, P.

J. L. Gibson, B. D. Duncan, P. Bos, and V. Sergen, “Wide-angle achromatic prism beam steering for infrared countermeasure applications,” Opt. Eng. 42(4), 1038–1047 (2003).
[Crossref]

J. L. Gibson, B. D. Duncan, P. Bos, and V. Sergen, “Wide angle beam steering for infrared countermeasures applications,” Proc. SPIE 4723, 100–111 (2002).
[Crossref]

Bravo-Medina, B.

Chen, K.

J. Li, K. Chen, Q. Peng, Z. Wang, Y. Jiang, C. Fu, and G. Ren, “Improvement of pointing accuracy for Risley prisms by parameter identification,” Appl. Opt. 56(26), 7358–7366 (2017).
[Crossref] [PubMed]

J. Li, Q. Peng, K. Chen, and C. Fu, “High precision pointing system based on Risley prism: analysis and simulation,” Proc. SPIE 9255, 1–7 (2015).

Cho, H.

Doughty, N.

M. Ostaszewski, S. Harford, N. Doughty, C. Hoffman, M. Sanchez, D. Gutow, and R. Pierce, “Risley prism beam pointer,” Proc. SPIE 6304, 630406 (2006).
[Crossref]

Duncan, B. D.

J. L. Gibson, B. D. Duncan, P. Bos, and V. Sergen, “Wide-angle achromatic prism beam steering for infrared countermeasure applications,” Opt. Eng. 42(4), 1038–1047 (2003).
[Crossref]

J. L. Gibson, B. D. Duncan, P. Bos, and V. Sergen, “Wide angle beam steering for infrared countermeasures applications,” Proc. SPIE 4723, 100–111 (2002).
[Crossref]

Estrada-Marmolejo, R.

Fan, D.

Flores, J. L.

Fu, C.

J. Li, K. Chen, Q. Peng, Z. Wang, Y. Jiang, C. Fu, and G. Ren, “Improvement of pointing accuracy for Risley prisms by parameter identification,” Appl. Opt. 56(26), 7358–7366 (2017).
[Crossref] [PubMed]

J. Li, Q. Peng, K. Chen, and C. Fu, “High precision pointing system based on Risley prism: analysis and simulation,” Proc. SPIE 9255, 1–7 (2015).

Garcia-Torales, G.

Ge, Y.

Gibson, J. L.

J. L. Gibson, B. D. Duncan, P. Bos, and V. Sergen, “Wide-angle achromatic prism beam steering for infrared countermeasure applications,” Opt. Eng. 42(4), 1038–1047 (2003).
[Crossref]

J. L. Gibson, B. D. Duncan, P. Bos, and V. Sergen, “Wide angle beam steering for infrared countermeasures applications,” Proc. SPIE 4723, 100–111 (2002).
[Crossref]

Guan, E.

Gutow, D.

M. Sánchez and D. Gutow, “Control laws for a 3-element Risley prism optical beam pointer,” Proc. SPIE 6304, 630403 (2006).
[Crossref]

M. Ostaszewski, S. Harford, N. Doughty, C. Hoffman, M. Sanchez, D. Gutow, and R. Pierce, “Risley prism beam pointer,” Proc. SPIE 6304, 630406 (2006).
[Crossref]

Hafez, M.

F. Souvestre, M. Hafez, and S. Régnier, “DMD-based multi-target laser tracking for motion capturing,” Proc. SPIE 7596, 75960B (2010).
[Crossref]

Harford, S.

M. Ostaszewski, S. Harford, N. Doughty, C. Hoffman, M. Sanchez, D. Gutow, and R. Pierce, “Risley prism beam pointer,” Proc. SPIE 6304, 630406 (2006).
[Crossref]

Hei, M.

Hoffman, C.

M. Ostaszewski, S. Harford, N. Doughty, C. Hoffman, M. Sanchez, D. Gutow, and R. Pierce, “Risley prism beam pointer,” Proc. SPIE 6304, 630406 (2006).
[Crossref]

Horng, J. S.

Huang, F.

H. Zhang, Y. Yuan, L. Su, and F. Huang, “Error modeling and analysis of Risley-prism system based on ray direction deviation in light refraction,” Appl. Opt. 37, 61307020 (2015).

Janabi-Sharifi, F.

Jianfeng, S.

S. Jianfeng, L. Liren, Y. Maojin, W. Lingyu, and Z. Mingli, “The effect of the rotating double-prism wide-angle laser beam scanner on the beam shape,” Optik (Stuttg.) 116(12), 553–556 (2005).
[Crossref]

Jiang, Y.

Lavigne, V.

V. Lavigne and B. Ricard, “Fast Risley prisms camera steering system: calibration and image distortions correction through the use of a three-dimensional refraction model,” Opt. Eng. 46(4), 043201 (2007).
[Crossref]

Li, A.

A. Li, X. Liu, and W. Sun, “Forward and inverse solutions for three-element Risley prism beam scanners,” Opt. Express 25(7), 7677–7688 (2017).
[Crossref] [PubMed]

A. Li, W. Sun, W. Yi, and Q. Zuo, “Investigation of beam steering performances in rotation Risley-prism scanner,” Opt. Express 24(12), 12840–12850 (2016).
[Crossref] [PubMed]

A. Li, Q. Zou, Y. Bian, H. Liu, and L. Liu, “Assembly error analysis of laser tracking steering prisms with sub-microradian order accuracy,” J. Mechan. Engin. 52(10), 9–12 (2016).
[Crossref]

J. Sun, L. Liu, A. Li, and D. Xu, “Submicroradian laser beam angular scan precision measurement by interference method,” Opt. Eng. 48(7), 705–709 (2009).
[Crossref]

Li, J.

J. Li, K. Chen, Q. Peng, Z. Wang, Y. Jiang, C. Fu, and G. Ren, “Improvement of pointing accuracy for Risley prisms by parameter identification,” Appl. Opt. 56(26), 7358–7366 (2017).
[Crossref] [PubMed]

J. Li, Q. Peng, K. Chen, and C. Fu, “High precision pointing system based on Risley prism: analysis and simulation,” Proc. SPIE 9255, 1–7 (2015).

Li, Y.

Lingyu, W.

S. Jianfeng, L. Liren, Y. Maojin, W. Lingyu, and Z. Mingli, “The effect of the rotating double-prism wide-angle laser beam scanner on the beam shape,” Optik (Stuttg.) 116(12), 553–556 (2005).
[Crossref]

Liren, L.

S. Jianfeng, L. Liren, Y. Maojin, W. Lingyu, and Z. Mingli, “The effect of the rotating double-prism wide-angle laser beam scanner on the beam shape,” Optik (Stuttg.) 116(12), 553–556 (2005).
[Crossref]

Liu, D.

L. Liu, L. Wang, J. Sun, Y. Zhou, X. Zhong, Z. Luan, D. Liu, A. Yan, and N. Xu, “An integrated test-bed for PAT testing and verification of inter-satellite lasercom terminals,” Proc. SPIE 6709, 670904 (2007).
[Crossref]

Liu, G.

Liu, H.

A. Li, Q. Zou, Y. Bian, H. Liu, and L. Liu, “Assembly error analysis of laser tracking steering prisms with sub-microradian order accuracy,” J. Mechan. Engin. 52(10), 9–12 (2016).
[Crossref]

Liu, J.

Liu, L.

A. Li, Q. Zou, Y. Bian, H. Liu, and L. Liu, “Assembly error analysis of laser tracking steering prisms with sub-microradian order accuracy,” J. Mechan. Engin. 52(10), 9–12 (2016).
[Crossref]

J. Sun, L. Liu, A. Li, and D. Xu, “Submicroradian laser beam angular scan precision measurement by interference method,” Opt. Eng. 48(7), 705–709 (2009).
[Crossref]

L. Liu, L. Wang, J. Sun, Y. Zhou, X. Zhong, Z. Luan, D. Liu, A. Yan, and N. Xu, “An integrated test-bed for PAT testing and verification of inter-satellite lasercom terminals,” Proc. SPIE 6709, 670904 (2007).
[Crossref]

Liu, X.

Lu, Y.

Luan, Z.

L. Liu, L. Wang, J. Sun, Y. Zhou, X. Zhong, Z. Luan, D. Liu, A. Yan, and N. Xu, “An integrated test-bed for PAT testing and verification of inter-satellite lasercom terminals,” Proc. SPIE 6709, 670904 (2007).
[Crossref]

Maojin, Y.

S. Jianfeng, L. Liren, Y. Maojin, W. Lingyu, and Z. Mingli, “The effect of the rotating double-prism wide-angle laser beam scanner on the beam shape,” Optik (Stuttg.) 116(12), 553–556 (2005).
[Crossref]

Mingli, Z.

S. Jianfeng, L. Liren, Y. Maojin, W. Lingyu, and Z. Mingli, “The effect of the rotating double-prism wide-angle laser beam scanner on the beam shape,” Optik (Stuttg.) 116(12), 553–556 (2005).
[Crossref]

Ostaszewski, M.

M. Ostaszewski, S. Harford, N. Doughty, C. Hoffman, M. Sanchez, D. Gutow, and R. Pierce, “Risley prism beam pointer,” Proc. SPIE 6304, 630406 (2006).
[Crossref]

Peng, Q.

J. Li, K. Chen, Q. Peng, Z. Wang, Y. Jiang, C. Fu, and G. Ren, “Improvement of pointing accuracy for Risley prisms by parameter identification,” Appl. Opt. 56(26), 7358–7366 (2017).
[Crossref] [PubMed]

J. Li, Q. Peng, K. Chen, and C. Fu, “High precision pointing system based on Risley prism: analysis and simulation,” Proc. SPIE 9255, 1–7 (2015).

Pierce, R.

M. Ostaszewski, S. Harford, N. Doughty, C. Hoffman, M. Sanchez, D. Gutow, and R. Pierce, “Risley prism beam pointer,” Proc. SPIE 6304, 630406 (2006).
[Crossref]

Régnier, S.

F. Souvestre, M. Hafez, and S. Régnier, “DMD-based multi-target laser tracking for motion capturing,” Proc. SPIE 7596, 75960B (2010).
[Crossref]

Ren, G.

Ricard, B.

V. Lavigne and B. Ricard, “Fast Risley prisms camera steering system: calibration and image distortions correction through the use of a three-dimensional refraction model,” Opt. Eng. 46(4), 043201 (2007).
[Crossref]

Rosell, F. A.

Sanchez, M.

M. Ostaszewski, S. Harford, N. Doughty, C. Hoffman, M. Sanchez, D. Gutow, and R. Pierce, “Risley prism beam pointer,” Proc. SPIE 6304, 630406 (2006).
[Crossref]

Sánchez, M.

M. Sánchez and D. Gutow, “Control laws for a 3-element Risley prism optical beam pointer,” Proc. SPIE 6304, 630403 (2006).
[Crossref]

Sergen, V.

J. L. Gibson, B. D. Duncan, P. Bos, and V. Sergen, “Wide-angle achromatic prism beam steering for infrared countermeasure applications,” Opt. Eng. 42(4), 1038–1047 (2003).
[Crossref]

J. L. Gibson, B. D. Duncan, P. Bos, and V. Sergen, “Wide angle beam steering for infrared countermeasures applications,” Proc. SPIE 4723, 100–111 (2002).
[Crossref]

Souvestre, F.

F. Souvestre, M. Hafez, and S. Régnier, “DMD-based multi-target laser tracking for motion capturing,” Proc. SPIE 7596, 75960B (2010).
[Crossref]

Strojnik, M.

Su, L.

H. Zhang, Y. Yuan, L. Su, and F. Huang, “Error modeling and analysis of Risley-prism system based on ray direction deviation in light refraction,” Appl. Opt. 37, 61307020 (2015).

Sun, J.

J. Sun, L. Liu, A. Li, and D. Xu, “Submicroradian laser beam angular scan precision measurement by interference method,” Opt. Eng. 48(7), 705–709 (2009).
[Crossref]

L. Liu, L. Wang, J. Sun, Y. Zhou, X. Zhong, Z. Luan, D. Liu, A. Yan, and N. Xu, “An integrated test-bed for PAT testing and verification of inter-satellite lasercom terminals,” Proc. SPIE 6709, 670904 (2007).
[Crossref]

Sun, W.

Tao, X.

Torres-Ortega, H.

Wang, L.

L. Liu, L. Wang, J. Sun, Y. Zhou, X. Zhong, Z. Luan, D. Liu, A. Yan, and N. Xu, “An integrated test-bed for PAT testing and verification of inter-satellite lasercom terminals,” Proc. SPIE 6709, 670904 (2007).
[Crossref]

Wang, Z.

Xu, D.

J. Sun, L. Liu, A. Li, and D. Xu, “Submicroradian laser beam angular scan precision measurement by interference method,” Opt. Eng. 48(7), 705–709 (2009).
[Crossref]

Xu, N.

L. Liu, L. Wang, J. Sun, Y. Zhou, X. Zhong, Z. Luan, D. Liu, A. Yan, and N. Xu, “An integrated test-bed for PAT testing and verification of inter-satellite lasercom terminals,” Proc. SPIE 6709, 670904 (2007).
[Crossref]

Xue, F.

Yan, A.

L. Liu, L. Wang, J. Sun, Y. Zhou, X. Zhong, Z. Luan, D. Liu, A. Yan, and N. Xu, “An integrated test-bed for PAT testing and verification of inter-satellite lasercom terminals,” Proc. SPIE 6709, 670904 (2007).
[Crossref]

Yan, W.

Yi, W.

Yuan, Y.

H. Zhang, Y. Yuan, L. Su, and F. Huang, “Error modeling and analysis of Risley-prism system based on ray direction deviation in light refraction,” Appl. Opt. 37, 61307020 (2015).

Y. Zhao and Y. Yuan, “First-order approximation error analysis of Risley-prism-based beam directing system,” Appl. Opt. 53(34), 8020–8031 (2014).
[Crossref] [PubMed]

Zhang, H.

H. Zhang, Y. Yuan, L. Su, and F. Huang, “Error modeling and analysis of Risley-prism system based on ray direction deviation in light refraction,” Appl. Opt. 37, 61307020 (2015).

Zhang, L.

L. Zhang and Y. Li, “Error analysis of spherical 2-DOF parallel manipulator with actuation redundancy,” J. Mechan. Engin. 49(7), 148–154 (2013).
[Crossref]

Zhao, Y.

Zhong, X.

L. Liu, L. Wang, J. Sun, Y. Zhou, X. Zhong, Z. Luan, D. Liu, A. Yan, and N. Xu, “An integrated test-bed for PAT testing and verification of inter-satellite lasercom terminals,” Proc. SPIE 6709, 670904 (2007).
[Crossref]

Zhou, Y.

Y. Zhou, Y. Lu, M. Hei, G. Liu, and D. Fan, “Pointing error analysis of Risley-prism-based beam steering system,” Appl. Opt. 53(25), 5775–5783 (2014).
[Crossref] [PubMed]

L. Liu, L. Wang, J. Sun, Y. Zhou, X. Zhong, Z. Luan, D. Liu, A. Yan, and N. Xu, “An integrated test-bed for PAT testing and verification of inter-satellite lasercom terminals,” Proc. SPIE 6709, 670904 (2007).
[Crossref]

Zou, Q.

A. Li, Q. Zou, Y. Bian, H. Liu, and L. Liu, “Assembly error analysis of laser tracking steering prisms with sub-microradian order accuracy,” J. Mechan. Engin. 52(10), 9–12 (2016).
[Crossref]

Zuo, Q.

Appl. Opt. (9)

Y. Li, “Closed form analytical inverse solutions for Risley-prism-based beam steering systems in different configurations,” Appl. Opt. 50(22), 4302–4309 (2011).
[Crossref] [PubMed]

X. Tao, H. Cho, and F. Janabi-Sharifi, “Active optical system for variable view imaging of micro objects with emphasis on kinematic analysis,” Appl. Opt. 47(22), 4121–4132 (2008).
[Crossref] [PubMed]

J. S. Horng and Y. Li, “Error sources and their impact on the performance of dual-wedge beam steering systems,” Appl. Opt. 51(18), 4168–4175 (2012).
[Crossref] [PubMed]

Y. Zhao and Y. Yuan, “First-order approximation error analysis of Risley-prism-based beam directing system,” Appl. Opt. 53(34), 8020–8031 (2014).
[Crossref] [PubMed]

Y. Zhou, Y. Lu, M. Hei, G. Liu, and D. Fan, “Pointing error analysis of Risley-prism-based beam steering system,” Appl. Opt. 53(25), 5775–5783 (2014).
[Crossref] [PubMed]

B. Bravo-Medina, M. Strojnik, G. Garcia-Torales, H. Torres-Ortega, R. Estrada-Marmolejo, A. Beltrán-González, and J. L. Flores, “Error compensation in a pointing system based on Risley prisms,” Appl. Opt. 56(8), 2209–2216 (2017).
[Crossref] [PubMed]

J. Li, K. Chen, Q. Peng, Z. Wang, Y. Jiang, C. Fu, and G. Ren, “Improvement of pointing accuracy for Risley prisms by parameter identification,” Appl. Opt. 56(26), 7358–7366 (2017).
[Crossref] [PubMed]

H. Zhang, Y. Yuan, L. Su, and F. Huang, “Error modeling and analysis of Risley-prism system based on ray direction deviation in light refraction,” Appl. Opt. 37, 61307020 (2015).

Y. Ge, J. Liu, F. Xue, E. Guan, W. Yan, and Y. Zhao, “Effect of mechanical error on dual-wedge laser scanning system and error correction,” Appl. Opt. 57(21), 6047–6054 (2018).
[Crossref] [PubMed]

J. Mechan. Engin. (2)

A. Li, Q. Zou, Y. Bian, H. Liu, and L. Liu, “Assembly error analysis of laser tracking steering prisms with sub-microradian order accuracy,” J. Mechan. Engin. 52(10), 9–12 (2016).
[Crossref]

L. Zhang and Y. Li, “Error analysis of spherical 2-DOF parallel manipulator with actuation redundancy,” J. Mechan. Engin. 49(7), 148–154 (2013).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Eng. (3)

J. Sun, L. Liu, A. Li, and D. Xu, “Submicroradian laser beam angular scan precision measurement by interference method,” Opt. Eng. 48(7), 705–709 (2009).
[Crossref]

J. L. Gibson, B. D. Duncan, P. Bos, and V. Sergen, “Wide-angle achromatic prism beam steering for infrared countermeasure applications,” Opt. Eng. 42(4), 1038–1047 (2003).
[Crossref]

V. Lavigne and B. Ricard, “Fast Risley prisms camera steering system: calibration and image distortions correction through the use of a three-dimensional refraction model,” Opt. Eng. 46(4), 043201 (2007).
[Crossref]

Opt. Express (2)

Optik (Stuttg.) (1)

S. Jianfeng, L. Liren, Y. Maojin, W. Lingyu, and Z. Mingli, “The effect of the rotating double-prism wide-angle laser beam scanner on the beam shape,” Optik (Stuttg.) 116(12), 553–556 (2005).
[Crossref]

Proc. SPIE (6)

F. Souvestre, M. Hafez, and S. Régnier, “DMD-based multi-target laser tracking for motion capturing,” Proc. SPIE 7596, 75960B (2010).
[Crossref]

L. Liu, L. Wang, J. Sun, Y. Zhou, X. Zhong, Z. Luan, D. Liu, A. Yan, and N. Xu, “An integrated test-bed for PAT testing and verification of inter-satellite lasercom terminals,” Proc. SPIE 6709, 670904 (2007).
[Crossref]

J. Li, Q. Peng, K. Chen, and C. Fu, “High precision pointing system based on Risley prism: analysis and simulation,” Proc. SPIE 9255, 1–7 (2015).

M. Sánchez and D. Gutow, “Control laws for a 3-element Risley prism optical beam pointer,” Proc. SPIE 6304, 630403 (2006).
[Crossref]

J. L. Gibson, B. D. Duncan, P. Bos, and V. Sergen, “Wide angle beam steering for infrared countermeasures applications,” Proc. SPIE 4723, 100–111 (2002).
[Crossref]

M. Ostaszewski, S. Harford, N. Doughty, C. Hoffman, M. Sanchez, D. Gutow, and R. Pierce, “Risley prism beam pointer,” Proc. SPIE 6304, 630406 (2006).
[Crossref]

Other (1)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), Sec. 3.2.2.

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Figures (13)

Fig. 1
Fig. 1 Schematic diagram of the TRSS. All prism surfaces are marked as ∑ with the first subscript “1”, “2” or “3” to distinguish each prism and the second subscript “1” or “2” indicating the incident or emergent surface of the prism. It is notable that ∑11, ∑22 and ∑32 are plane surfaces exactly perpendicular to Z-axis, whereas ∑12, ∑21 and ∑31 are wedge surfaces inclined to those plane surfaces, respectively.
Fig. 2
Fig. 2 Schematic of the incident beam direction deviation.
Fig. 3
Fig. 3 Impact of direction deviation of the incident beam on the pointing accuracy. (a) SΔAr0 as a function of Δθ12 and Δθ23; (b) SΔAr0 as a function of Δθ12 and Δθ23 with different wedge angles.
Fig. 4
Fig. 4 Schematic of the assembly error of the prism. (a) Prism tilt deviation around the Y-axis. The tilt angle δY is the separated angle of the tilted principle section relative to the theoretical one in the XOZ plane. (b) Prism tilt deviation around the X-axis. The tilt angle δX is the separated angle of the position of the tilted prism relative to the theoretical one in the YOZ plane. (taking prism 1 as an example)
Fig. 5
Fig. 5 Impact of prism tilt deviation on the pointing accuracy. (a) SδX for prism 1 tilting around the X-axis, (b) SδX for prism 2 tilting around the X-axis, (c) SδX for prism 3 tilting around the X-axis, (d) SδY for prism 1 tilting around the Y-axis, (e) SδY for prism 2 tilting around the Y-axis and (f) SδY for prism 3 tilting around the Y-axis.
Fig. 6
Fig. 6 Schematic of the assembly error of the bearing. (a) Bearing axis tilting around the Y-axis with the magnitude of ξY, which is the separated angle of the tilted bearing axis relative to the theoretical one in the XOZ plane. (b) Bearing axis tilting around the X-axis with the magnitude of ξX, which is the separated angle of the tilted bearing axis relative to the theoretical one in the YOZ plane. (taking prism 1 as an example)
Fig. 7
Fig. 7 Impact of bearing tilt deviation on the pointing accuracy. (a) SξX for the bearing axis of prism 1 tilting around the X-axis, (b) SξX for the bearing axis of prism 2 tilting around the X-axis, (c) SξX for the bearing axis of prism 3 tilting around the X-axis, (d) SξY for the bearing axis of prism 1 tilting around the Y-axis, (e) SξY for the bearing axis of prism 2 tilting around the Y-axis and (f) SξY for the bearing axis of prism 3 tilting around the Y-axis.
Fig. 8
Fig. 8 Impact of prisms rotational error on the pointing accuracy. (a) SΔθr1 for rotational error of prism 1, (b) SΔθr2 for rotational error of prism 2 and (c) SΔθr3 for rotational error of prism 3.
Fig. 9
Fig. 9 Beam scan trajectories under different angular velocity ratios of three prisms, where ω1: ω2: ω3 equals to (a) 1: 2: 1, (b) 1: 1.5: 2, (c) 1: −1.5: 1 and (d) 1: 2: −1.5.
Fig. 10
Fig. 10 Schematic of error-compensation model for the TRSS, where the stationary orientations are θ'r1 = 90°, θ'r2 = 0° and θ'r3 = 30°. The position of each circle center depends on the stationary orientations of other two prisms. d10, d20 and d30 represent the separate deviations produced by three prisms at their initial positions, which are defined as the vectors that connect the three circle centers with P1, respectively.
Fig. 11
Fig. 11 Take the average of four radii of the circle to improve accuracy, where Δxy is the distance difference between the actual point and the theoretical one.
Fig. 12
Fig. 12 Optimized radius by the genetic algorithm to improve the pointing accuracy.
Fig. 13
Fig. 13 Improvement of error compensation method for pointing accuracy.

Tables (1)

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Table 1 Simulation result of pointing error for each method.

Equations (22)

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N 11 = ( 0,0,1 ) T , N 12 = ( cos θ r1 sinα,sin θ r1 sinα,cosα ) T , N 21 = ( cos θ r2 sinα,sin θ r2 sinα,cosα ) T , N 22 = ( 0,0,1 ) T , N 31 = ( cos θ r3 sinα,sin θ r3 sinα,cosα ) T , N 32 = ( 0,0,1 ) T .
A rj+1 = n j n j+1 [ A rj ( N A rj )N ]+N 1 ( n j n j+1 ) 2 [ 1 (N A rj ) 2 ] .
Δ A rj+1 = n j n j+1 Δ A rj + k j+1 ΔN+ h j+1 ( ΔN A rj +NΔ A rj )N where k j+1 = 1 ( n j n j+1 ) 2 [ 1 ( N A rj ) 2 ] n j n j+1 ( N A rj ) and h j+1 = ( n j n j+1 ) 2 ( N A rj ) 1 ( n j n j+1 ) 2 [ 1 ( N A rj ) 2 ] n j n j+1 .
A r0 ' = ( sin δ Z sin δ Y ,sin δ Z cos δ Y , 1 ( sin δ Z sin δ Y ) 2 ( sin δ Z cos δ Y ) 2 ) T .
S Δ A r0 = | Δ A r6 | | Δ A r0 | .
N 11 ' =Rot(Z, θ r1 )Rot(Y, δ Y ) (0,0,1) T ,
N 12 ' =Rot(Z, θ r1 )Rot(Y, δ Y ) (sinα,0,cosα) T .
S δ i = | Δ A r6 | | δ i | , =X,Y.
( u x ' , u y ' , u z ' ) T =Rot(Y, ξ Y )Rot(X, ξ X ) ( u x , u y , u z ) T = (sin ξ Y cos ξ X ,sin ξ X ,cos ξ Y cos ξ X ) T .
M b = A b +cos θ r1 (I A b )+sin θ r1 B b .
A b =[ u x '2 u x ' u y ' u x ' u z ' u y ' u x ' u y '2 u y ' u z ' u z ' u x ' u z ' u y ' u z '2 ],
B b =[ 0 u z ' u y ' u z ' 0 u x ' u y ' u x ' 0 ].
N 11 ' = M b ( 0,0,1 ) T
N 12 ' = M b ( sinα,0,cosα ) T
S ξ i = | Δ A r6 | | ξ X |+| ξ Y | .
N 12 ' = [ cos( θ r1 +Δ θ r1 )sinα,sin( θ r1 +Δ θ r1 )sinα,cosα ] T .
Δ N 12 = N 12 ' N 12 Δ θ r1 ( sin θ r1 sinα,cos θ r1 sinα,0 ) T .
S Δ θ ri = | Δ A r6 | | Δ θ ri | , i=1,2,3.
d T = d 1 + d 2 + d 3 + d E .
d E = d V d 120 = d V d 10 d 20 .
ω i0 ={ arcttan( y 1 y O i x 1 x O i ), x 1 x O i 0 π+arctan( y 1 y O i x 1 x O i ), x 1 x O i <0 (i=1,2,3)
d i =[| d i |cos( ϕ i ω i0 ),| d i |sin( ϕ i ω i0 )], i=1,2,3.

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