Abstract

A pair of orthogonal tilting double prisms with a tracking precision better than submicroradian order exhibits a good application potential in laser tracking fields. In the paper, the beam scanning performance determined by both the structure parameters and the tilting motions of two prisms is overall investigated. The functional relation between the structure parameters and the exact beam scanning range is established, the capability of high-accuracy beam steering is validated together with the investigation of the scanning error sources and the nonlinear control laws, and the beam shape distortion degree under multi-parameter combinations is demonstrated. These studies can provide important references for the development of tilting double prisms.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  16. 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]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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2016 (2)

2015 (1)

2014 (1)

2013 (2)

S. J. Rothberg and M. Tirabassi, “Development of a scanning head for laser Doppler vibrometry (LDV) using dual optical wedges,” Rev. Sci. Instrum. 84(12), 121704 (2013).
[Crossref] [PubMed]

A. Schitea, M. Tuef, V. F. Duma, and A. M. Vlaicu, “Modeling of Risley prisms devices for exact scan patterns,” Proc. SPIE 8789, 878912 (2013).
[Crossref]

2012 (1)

2011 (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]

E. Schundler, D. Carlson, R. Vaillancourt, J. R. Dupuis, and C. Schwarze, “Compact, wide field DRS explosive detector,” Proc. SPIE 8018, 80181O (2011).
[Crossref]

2010 (1)

V. F. Duma, J. P. Rolland, and A. G. Podoleanu, “Perspectives of optical scanning in OCT,” Proc. SPIE 7556, 75560B (2010).
[Crossref]

2008 (2)

2007 (2)

W. C. Warger and C. A. DiMarzio, “Dual-wedge scanning confocal reflectance microscope,” Opt. Lett. 32(15), 2140–2142 (2007).
[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]

2006 (2)

A. Li, L. Liu, J. Sun, X. Zhong, L. Wang, D. Liu, and Z. Luan, “Research on a scanner for tilting orthogonal double prisms,” Appl. Opt. 45(31), 8063–8069 (2006).
[Crossref] [PubMed]

J. Sun, L. Liu, M. Yun, L. Wan, and M. Zhang, “Distortion of beam shape by a rotating double prism wide-angle laser beam scanner,” Opt. Eng. 45(4), 043004 (2006).
[Crossref]

2005 (1)

A. Li, J. Sun, L. Wang, and L. Liu, “Submicroradian accuracy scanning system with a double-wedge rotating around the orthogonal axes,” Proc. SPIE 5892, 58921M (2005).
[Crossref]

1999 (2)

G. F. Marshall, “Risley prism scan patterns,” Proc. SPIE 3787, 74–86 (1999).
[Crossref]

W. Mao and Y. Xu, “Distortion of optical wedges with a large angle of incidence in a collimated beam,” Opt. Eng. 38(4), 580–585 (1999).
[Crossref]

1985 (1)

1960 (1)

Amirault, C. T.

Bian, Y.

Carlson, D.

E. Schundler, D. Carlson, R. Vaillancourt, J. R. Dupuis, and C. Schwarze, “Compact, wide field DRS explosive detector,” Proc. SPIE 8018, 80181O (2011).
[Crossref]

Cho, H.

DiMarzio, C. A.

Ding, Y.

Duma, V. F.

A. Schitea, M. Tuef, V. F. Duma, and A. M. Vlaicu, “Modeling of Risley prisms devices for exact scan patterns,” Proc. SPIE 8789, 878912 (2013).
[Crossref]

V. F. Duma, J. P. Rolland, and A. G. Podoleanu, “Perspectives of optical scanning in OCT,” Proc. SPIE 7556, 75560B (2010).
[Crossref]

Dupuis, J. R.

E. Schundler, D. Carlson, R. Vaillancourt, J. R. Dupuis, and C. Schwarze, “Compact, wide field DRS explosive detector,” Proc. SPIE 8018, 80181O (2011).
[Crossref]

Janabi-Sharifi, F.

Jiang, X.

Li, A.

Li, Y.

Li, Z.

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]

A. Li, L. Liu, J. Sun, X. Zhong, L. Wang, D. Liu, and Z. Luan, “Research on a scanner for tilting orthogonal double prisms,” Appl. Opt. 45(31), 8063–8069 (2006).
[Crossref] [PubMed]

Liu, L.

A. Li, W. Yi, W. Sun, and L. Liu, “Tilting double-prism scanner driven by cam-based mechanism,” Appl. Opt. 54(18), 5788–5796 (2015).
[Crossref] [PubMed]

A. Li, Y. Ding, Y. Bian, and L. Liu, “Inverse solutions for tilting orthogonal double prisms,” Appl. Opt. 53(17), 3712–3722 (2014).
[Crossref] [PubMed]

A. Li, X. Jiang, J. Sun, L. Wang, Z. Li, and L. Liu, “Laser coarse-fine coupling scanning method by steering double prisms,” Appl. Opt. 51(3), 356–364 (2012).
[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]

J. Sun, L. Liu, M. Yun, L. Wan, and M. Zhang, “Distortion of beam shape by a rotating double prism wide-angle laser beam scanner,” Opt. Eng. 45(4), 043004 (2006).
[Crossref]

A. Li, L. Liu, J. Sun, X. Zhong, L. Wang, D. Liu, and Z. Luan, “Research on a scanner for tilting orthogonal double prisms,” Appl. Opt. 45(31), 8063–8069 (2006).
[Crossref] [PubMed]

A. Li, J. Sun, L. Wang, and L. Liu, “Submicroradian accuracy scanning system with a double-wedge rotating around the orthogonal axes,” Proc. SPIE 5892, 58921M (2005).
[Crossref]

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]

A. Li, L. Liu, J. Sun, X. Zhong, L. Wang, D. Liu, and Z. Luan, “Research on a scanner for tilting orthogonal double prisms,” Appl. Opt. 45(31), 8063–8069 (2006).
[Crossref] [PubMed]

Mao, W.

W. Mao and Y. Xu, “Distortion of optical wedges with a large angle of incidence in a collimated beam,” Opt. Eng. 38(4), 580–585 (1999).
[Crossref]

Marshall, G. F.

G. F. Marshall, “Risley prism scan patterns,” Proc. SPIE 3787, 74–86 (1999).
[Crossref]

Podoleanu, A. G.

V. F. Duma, J. P. Rolland, and A. G. Podoleanu, “Perspectives of optical scanning in OCT,” Proc. SPIE 7556, 75560B (2010).
[Crossref]

Rolland, J. P.

V. F. Duma, J. P. Rolland, and A. G. Podoleanu, “Perspectives of optical scanning in OCT,” Proc. SPIE 7556, 75560B (2010).
[Crossref]

Rosell, F. A.

Rothberg, S. J.

S. J. Rothberg and M. Tirabassi, “Development of a scanning head for laser Doppler vibrometry (LDV) using dual optical wedges,” Rev. Sci. Instrum. 84(12), 121704 (2013).
[Crossref] [PubMed]

Schitea, A.

A. Schitea, M. Tuef, V. F. Duma, and A. M. Vlaicu, “Modeling of Risley prisms devices for exact scan patterns,” Proc. SPIE 8789, 878912 (2013).
[Crossref]

Schundler, E.

E. Schundler, D. Carlson, R. Vaillancourt, J. R. Dupuis, and C. Schwarze, “Compact, wide field DRS explosive detector,” Proc. SPIE 8018, 80181O (2011).
[Crossref]

Schwarze, C.

E. Schundler, D. Carlson, R. Vaillancourt, J. R. Dupuis, and C. Schwarze, “Compact, wide field DRS explosive detector,” Proc. SPIE 8018, 80181O (2011).
[Crossref]

Sun, J.

A. Li, X. Jiang, J. Sun, L. Wang, Z. Li, and L. Liu, “Laser coarse-fine coupling scanning method by steering double prisms,” Appl. Opt. 51(3), 356–364 (2012).
[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]

J. Sun, L. Liu, M. Yun, L. Wan, and M. Zhang, “Distortion of beam shape by a rotating double prism wide-angle laser beam scanner,” Opt. Eng. 45(4), 043004 (2006).
[Crossref]

A. Li, L. Liu, J. Sun, X. Zhong, L. Wang, D. Liu, and Z. Luan, “Research on a scanner for tilting orthogonal double prisms,” Appl. Opt. 45(31), 8063–8069 (2006).
[Crossref] [PubMed]

A. Li, J. Sun, L. Wang, and L. Liu, “Submicroradian accuracy scanning system with a double-wedge rotating around the orthogonal axes,” Proc. SPIE 5892, 58921M (2005).
[Crossref]

Sun, W.

Tao, X.

Tirabassi, M.

S. J. Rothberg and M. Tirabassi, “Development of a scanning head for laser Doppler vibrometry (LDV) using dual optical wedges,” Rev. Sci. Instrum. 84(12), 121704 (2013).
[Crossref] [PubMed]

Tuef, M.

A. Schitea, M. Tuef, V. F. Duma, and A. M. Vlaicu, “Modeling of Risley prisms devices for exact scan patterns,” Proc. SPIE 8789, 878912 (2013).
[Crossref]

Vaillancourt, R.

E. Schundler, D. Carlson, R. Vaillancourt, J. R. Dupuis, and C. Schwarze, “Compact, wide field DRS explosive detector,” Proc. SPIE 8018, 80181O (2011).
[Crossref]

Vlaicu, A. M.

A. Schitea, M. Tuef, V. F. Duma, and A. M. Vlaicu, “Modeling of Risley prisms devices for exact scan patterns,” Proc. SPIE 8789, 878912 (2013).
[Crossref]

Wan, L.

J. Sun, L. Liu, M. Yun, L. Wan, and M. Zhang, “Distortion of beam shape by a rotating double prism wide-angle laser beam scanner,” Opt. Eng. 45(4), 043004 (2006).
[Crossref]

Wang, L.

A. Li, X. Jiang, J. Sun, L. Wang, Z. Li, and L. Liu, “Laser coarse-fine coupling scanning method by steering double prisms,” Appl. Opt. 51(3), 356–364 (2012).
[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]

A. Li, L. Liu, J. Sun, X. Zhong, L. Wang, D. Liu, and Z. Luan, “Research on a scanner for tilting orthogonal double prisms,” Appl. Opt. 45(31), 8063–8069 (2006).
[Crossref] [PubMed]

A. Li, J. Sun, L. Wang, and L. Liu, “Submicroradian accuracy scanning system with a double-wedge rotating around the orthogonal axes,” Proc. SPIE 5892, 58921M (2005).
[Crossref]

Warger, W. C.

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]

Xu, Y.

W. Mao and Y. Xu, “Distortion of optical wedges with a large angle of incidence in a collimated beam,” Opt. Eng. 38(4), 580–585 (1999).
[Crossref]

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]

Yang, Y.

Yi, W.

Yun, M.

J. Sun, L. Liu, M. Yun, L. Wan, and M. Zhang, “Distortion of beam shape by a rotating double prism wide-angle laser beam scanner,” Opt. Eng. 45(4), 043004 (2006).
[Crossref]

Zhang, M.

J. Sun, L. Liu, M. Yun, L. Wan, and M. Zhang, “Distortion of beam shape by a rotating double prism wide-angle laser beam scanner,” Opt. Eng. 45(4), 043004 (2006).
[Crossref]

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]

A. Li, L. Liu, J. Sun, X. Zhong, L. Wang, D. Liu, and Z. Luan, “Research on a scanner for tilting orthogonal double prisms,” Appl. Opt. 45(31), 8063–8069 (2006).
[Crossref] [PubMed]

Zhou, Y.

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]

Zuo, Q.

Appl. Opt. (8)

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

Opt. Eng. (2)

W. Mao and Y. Xu, “Distortion of optical wedges with a large angle of incidence in a collimated beam,” Opt. Eng. 38(4), 580–585 (1999).
[Crossref]

J. Sun, L. Liu, M. Yun, L. Wan, and M. Zhang, “Distortion of beam shape by a rotating double prism wide-angle laser beam scanner,” Opt. Eng. 45(4), 043004 (2006).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (6)

V. F. Duma, J. P. Rolland, and A. G. Podoleanu, “Perspectives of optical scanning in OCT,” Proc. SPIE 7556, 75560B (2010).
[Crossref]

G. F. Marshall, “Risley prism scan patterns,” Proc. SPIE 3787, 74–86 (1999).
[Crossref]

A. Schitea, M. Tuef, V. F. Duma, and A. M. Vlaicu, “Modeling of Risley prisms devices for exact scan patterns,” Proc. SPIE 8789, 878912 (2013).
[Crossref]

E. Schundler, D. Carlson, R. Vaillancourt, J. R. Dupuis, and C. Schwarze, “Compact, wide field DRS explosive detector,” Proc. SPIE 8018, 80181O (2011).
[Crossref]

A. Li, J. Sun, L. Wang, and L. Liu, “Submicroradian accuracy scanning system with a double-wedge rotating around the orthogonal axes,” Proc. SPIE 5892, 58921M (2005).
[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]

Rev. Sci. Instrum. (1)

S. J. Rothberg and M. Tirabassi, “Development of a scanning head for laser Doppler vibrometry (LDV) using dual optical wedges,” Rev. Sci. Instrum. 84(12), 121704 (2013).
[Crossref] [PubMed]

Other (2)

G. F. Marshall, Handbook of Optical and Laser Scanning, 2nd ed. (CRC Press, 2011).

C. R. Schwarze, R. Vaillancourt, D. Carlson, E. Schundler, T. Evans, and J. R. Engeletc, “Risley-prism based compact laser beam steering for IRCM, laser communications, and laser radar,” http://www.optra.com/images/TP-Compact_Beam_Steering.pdf .

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Figures (10)

Fig. 1
Fig. 1 Schematic diagram illustrating the tracking principle of tilting orthogonal double prisms.
Fig. 2
Fig. 2 The field angle of the emergent beam. (a) the vertical field angle ρV; (b) the horizontal field angle ρH.
Fig. 3
Fig. 3 Experimental setup, mainly including tilting double prism scanner, receiving screen, prism controller, laser source, laser controller and guide.
Fig. 4
Fig. 4 The change laws of the partial derivatives between the field angles and the tilting angles. (a) and (b) represent the influences of θt1 on ρ V θ t1 and ρ H θ t1 ; (c) and (d) represent the influences of θt2 on ρ V θ t2 and ρ H θ t2 , respectively.
Fig. 5
Fig. 5 The nonlinear relations between the tilting angles θt1 and θt2 of two prisms and the deviation angle ρ of the final emergent beam. (a) θt1 corresponding to ρV and ρH; (b) θt2 corresponding to ρV and ρH.
Fig. 6
Fig. 6 The nonlinear relation between the tilting angular velocities of prisms and the change rate of deviation angle dθ/dρ. (a) ρV corresponding to dθt1/dρV and dθt2/dρV; (b) ρH corresponding to dθt1/dρH and dθt2/dρH.
Fig. 7
Fig. 7 Beam scanning trajectories with different tilting angular velocities, where the red arrows show the moving direction of the scanning point. These tilting angular velocities are chosen arbitrarily, while in practice the tilting angles and velocities should be determined based on specific applications. (a) uniform ωt1, uniform ωt2 and ωt2 = 2ωt1; (b) and (c) uniform ωt1, uniform ωt2 and ωt2 = 4ωt1; (d) sine function for ωt1 and uniform ωt2; (e) sine function for ωt1 and cosine function for ωt2.
Fig. 8
Fig. 8 The scanning field of a tilting double-prism scanner. The area enclosed by the red rectangle, which is the largest rectangle within the parallelogram-like area, is taken as the scanning field of this scanner.
Fig. 9
Fig. 9 The beam shape distortion induced by double prisms with different tilting angle combinations. Red curves with “°” signs and blue curves with “×” signs represent the original beam shapes and the distorted ones, respectively. (a) θt1 = 0°, θt2 = 0°; (b) θt1 = 0°, θt2 = 5°; (c) θt1 = 0°, θt2 = 10°; (d) θt1 = 10°, θt2 = 10°.
Fig. 10
Fig. 10 The influence of system parameters on beam distortion. (a) refractive index n; (b) wedge angle α; (c) thickness of the thinnest end d0; (d) distance D1 between O and O2.

Tables (2)

Tables Icon

Table 1 Parameters of Scanning Field under Different D1 (mm)

Tables Icon

Table 2 Parameters of Scanning Field under Different d0 (mm)

Equations (15)

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

N 11 = ( sin θ t1 ,0,cos θ t1 ) T , N 21 = ( sin( α+ θ t1 ),0,cos( α+ θ t1 ) ) T , N 21 = ( 0,sin( α+ θ t2 ),cos( α+ θ t2 ) ) T , N 22 = ( sin θ t2 ,0,cos θ t2 ) T .
A tf = ( cos β t ,sin β t sin( γ t δ 2 ),sin β t cos( γ t δ 2 ) ) T = ( x tf , y tf , z tf ) T ,
ρ V =arctan( x tf z tf )=arctan cot β t cos( γ t δ 2 ) =arctan tan δ 1 cos δ 2 ,
ρ H =arctan( y tf z tf )= γ t δ 2 = δ 2 .
{ x tk = x t1 t 1 y tk = y t1 t 1 z tk = z t1 t 1 ,{ x tm = x t2 t 2 + x tk y tm = y t2 t 2 + y tk z tm = z t2 t 2 + z tk ,{ x tn = x t3 t 3 + x tm y tn = y t3 t 3 + y tm z tn = z t3 t 3 + z tm ,{ x tp = x tf t 4 + x tn y tp = y tf t 4 + y tn z tp = z tf t 4 + z tn ,
t 1 = sin( α+ θ t1 )( dsin θ t1 )+cos( α+ θ t1 )( dcos θ t1 ) x t1 sin( α+ θ t1 )+ z t1 cos( α+ θ t1 )
t 2 = sin( α+ θ t2 )( y tk dsin θ t2 )cos( α+ θ t2 )[ z tk ( D 1 dcos θ t2 ) ] y t2 sin( α+ θ t2 )+ z t2 cos( α+ θ t2 )
t 3 = sin θ t2 y tm cos θ t2 ( z tm D 1 ) y t3 sin θ t2 + z t3 cos θ t2
t 4 = D 1 + D 2 z tn z tf
ρ V =arctan( x D 2 ), ρ H =arctan( y D 2 )
δ V =| ρ V θ t1 | δ θ t1 +| ρ V θ t2 | δ θ t2 +| ρ V α | δ α +| ρ V n | δ n ,
δ H =| ρ H θ t1 | δ θ t1 +| ρ H θ t2 | δ θ t2 +| ρ H α | δ α +| ρ H n | δ n ,
δ V δ θ t1 ×5.42%+ δ θ t2 ×0.0317%,
δ H δ θ t1 ×0.0822%+ δ θ t2 ×0.339%,
{ x=20cos(θ) y=10+20sin(θ) z=0 ,

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