Abstract

An analytical reverse solution and actual examples are given to show how to direct a laser beam from a pair of orthogonal prisms to given targets in free space. Considering the influences of double-prism structural parameters, a lookup table method to seek the numerical reverse solution of each prism’s tilting angle is also proposed for steering the double-prism orientation to track a target position located in the near field. Some case studies, as well as a specified elliptical target trajectory scanned by the cam-based driving double prisms, exhibit the significant application values of the theoretical derivation. The analytic reverse and numerical solutions can be generalized to investigate the synthesis of scanning patterns and the controlling strategy of double-prism tilting motion, the potentials of which can be explored to perform the orientation and position tracking functions in applications of precision engineering fields.

© 2014 Optical Society of America

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  1. L. Liu, “Coherent and incoherent synthetic-aperture imaging ladars and laboratory-space experimental demonstrations [Invited],” Appl. Opt. 52, 579–599 (2013).
    [CrossRef]
  2. L. Liu, L. Wang, J. Sun, Y. Zhou, X. Zhong, D. Liu, A. Yan, and N. Xu, “An integrated test-bed for PAT testing and verification of inter-satellite lasercom terminals,” Proc. SPIE 6709, 41–45 (2007).
    [CrossRef]
  3. G. C. Boisset, B. Robertson, and H. S. Hinton, “Design and construction of an active alignment demonstrator for a free-space optical interconnect,” IEEE Photon. Technol. Lett. 7, 676–678 (1995).
    [CrossRef]
  4. V. F. Duma, J. P. Rolland, and A. G. Podoleanu, “Perspectives of optical scanning in OCT,” Proc. SPIE 75560B, 1–12 (2010).
  5. F. A. Rosell, “Prism scanners,” J. Opt. Soc. Am. 50, 521–526 (1960).
    [CrossRef]
  6. N. Hagen and T. S. Tkaczyk, “Compound prism design principles, I,” Appl. Opt. 50, 4998–5011 (2011).
    [CrossRef]
  7. A. Schitea, M. Tuef, V. Duma, and A. M. Vlaicu, “Modeling of Risley prisms devices for exact scan patterns,” Proc. SPIE 8789, 878912 (2013).
  8. C. T. Amirault and C. A. DiMarzio, “Precision pointing using a dual-wedge scanner,” Appl. Opt. 24, 1302–1308 (1985).
    [CrossRef]
  9. Y. Yang, “Analytic solution of free space optical beam steering using Risley prisms,” J. Lightwave Technol. 26, 3576–3583 (2008).
    [CrossRef]
  10. Y. Li, “Third-order theory of Risley-prism based beam steering system,” Appl. Opt. 50, 679–686 (2011).
    [CrossRef]
  11. Y. Li, “Closed form analytical inverse solutions for Risley-prism-based beam steering systems in different configurations,” Appl. Opt. 50, 4302–4309 (2011).
    [CrossRef]
  12. A. H. Li, L. R. Liu, J. F. Sun, X. H. Zhong, L. J. Wang, D. A. Liu, and Z. Luan, “Research on a scanner for tilting orthogonal double prisms,” Appl. Opt. 45, 8063–8069 (2006).
    [CrossRef]
  13. A. H. Li, X. C. Jiang, J. F. Sun, L. J. Wang, Z. Z. Li, and L. R. Liu, “Laser coarse-fine coupling scanning method by steering double prisms,” Appl. Opt. 51, 356–364 (2012).
    [CrossRef]
  14. M. Tirabassi and S. J. Rothberg, “Scanning LDV using wedge prisms,” Opt. Laser Eng. 47, 454–460 (2009).
    [CrossRef]
  15. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999), Sect. 3.2.2.

2013 (2)

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

L. Liu, “Coherent and incoherent synthetic-aperture imaging ladars and laboratory-space experimental demonstrations [Invited],” Appl. Opt. 52, 579–599 (2013).
[CrossRef]

2012 (1)

2011 (3)

2010 (1)

V. F. Duma, J. P. Rolland, and A. G. Podoleanu, “Perspectives of optical scanning in OCT,” Proc. SPIE 75560B, 1–12 (2010).

2009 (1)

M. Tirabassi and S. J. Rothberg, “Scanning LDV using wedge prisms,” Opt. Laser Eng. 47, 454–460 (2009).
[CrossRef]

2008 (1)

2007 (1)

L. Liu, L. Wang, J. Sun, Y. Zhou, X. Zhong, D. Liu, A. Yan, and N. Xu, “An integrated test-bed for PAT testing and verification of inter-satellite lasercom terminals,” Proc. SPIE 6709, 41–45 (2007).
[CrossRef]

2006 (1)

1995 (1)

G. C. Boisset, B. Robertson, and H. S. Hinton, “Design and construction of an active alignment demonstrator for a free-space optical interconnect,” IEEE Photon. Technol. Lett. 7, 676–678 (1995).
[CrossRef]

1985 (1)

1960 (1)

Amirault, C. T.

Boisset, G. C.

G. C. Boisset, B. Robertson, and H. S. Hinton, “Design and construction of an active alignment demonstrator for a free-space optical interconnect,” IEEE Photon. Technol. Lett. 7, 676–678 (1995).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999), Sect. 3.2.2.

DiMarzio, C. A.

Duma, V.

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

Duma, V. F.

V. F. Duma, J. P. Rolland, and A. G. Podoleanu, “Perspectives of optical scanning in OCT,” Proc. SPIE 75560B, 1–12 (2010).

Hagen, N.

Hinton, H. S.

G. C. Boisset, B. Robertson, and H. S. Hinton, “Design and construction of an active alignment demonstrator for a free-space optical interconnect,” IEEE Photon. Technol. Lett. 7, 676–678 (1995).
[CrossRef]

Jiang, X. C.

Li, A. H.

Li, Y.

Li, Z. Z.

Liu, D.

L. Liu, L. Wang, J. Sun, Y. Zhou, X. Zhong, D. Liu, A. Yan, and N. Xu, “An integrated test-bed for PAT testing and verification of inter-satellite lasercom terminals,” Proc. SPIE 6709, 41–45 (2007).
[CrossRef]

Liu, D. A.

Liu, L.

L. Liu, “Coherent and incoherent synthetic-aperture imaging ladars and laboratory-space experimental demonstrations [Invited],” Appl. Opt. 52, 579–599 (2013).
[CrossRef]

L. Liu, L. Wang, J. Sun, Y. Zhou, X. Zhong, D. Liu, A. Yan, and N. Xu, “An integrated test-bed for PAT testing and verification of inter-satellite lasercom terminals,” Proc. SPIE 6709, 41–45 (2007).
[CrossRef]

Liu, L. R.

Luan, Z.

Podoleanu, A. G.

V. F. Duma, J. P. Rolland, and A. G. Podoleanu, “Perspectives of optical scanning in OCT,” Proc. SPIE 75560B, 1–12 (2010).

Robertson, B.

G. C. Boisset, B. Robertson, and H. S. Hinton, “Design and construction of an active alignment demonstrator for a free-space optical interconnect,” IEEE Photon. Technol. Lett. 7, 676–678 (1995).
[CrossRef]

Rolland, J. P.

V. F. Duma, J. P. Rolland, and A. G. Podoleanu, “Perspectives of optical scanning in OCT,” Proc. SPIE 75560B, 1–12 (2010).

Rosell, F. A.

Rothberg, S. J.

M. Tirabassi and S. J. Rothberg, “Scanning LDV using wedge prisms,” Opt. Laser Eng. 47, 454–460 (2009).
[CrossRef]

Schitea, A.

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

Sun, J.

L. Liu, L. Wang, J. Sun, Y. Zhou, X. Zhong, D. Liu, A. Yan, and N. Xu, “An integrated test-bed for PAT testing and verification of inter-satellite lasercom terminals,” Proc. SPIE 6709, 41–45 (2007).
[CrossRef]

Sun, J. F.

Tirabassi, M.

M. Tirabassi and S. J. Rothberg, “Scanning LDV using wedge prisms,” Opt. Laser Eng. 47, 454–460 (2009).
[CrossRef]

Tkaczyk, T. S.

Tuef, M.

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

Vlaicu, A. M.

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

Wang, L.

L. Liu, L. Wang, J. Sun, Y. Zhou, X. Zhong, D. Liu, A. Yan, and N. Xu, “An integrated test-bed for PAT testing and verification of inter-satellite lasercom terminals,” Proc. SPIE 6709, 41–45 (2007).
[CrossRef]

Wang, L. J.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999), Sect. 3.2.2.

Xu, N.

L. Liu, L. Wang, J. Sun, Y. Zhou, X. Zhong, D. Liu, A. Yan, and N. Xu, “An integrated test-bed for PAT testing and verification of inter-satellite lasercom terminals,” Proc. SPIE 6709, 41–45 (2007).
[CrossRef]

Yan, A.

L. Liu, L. Wang, J. Sun, Y. Zhou, X. Zhong, D. Liu, A. Yan, and N. Xu, “An integrated test-bed for PAT testing and verification of inter-satellite lasercom terminals,” Proc. SPIE 6709, 41–45 (2007).
[CrossRef]

Yang, Y.

Zhong, X.

L. Liu, L. Wang, J. Sun, Y. Zhou, X. Zhong, D. Liu, A. Yan, and N. Xu, “An integrated test-bed for PAT testing and verification of inter-satellite lasercom terminals,” Proc. SPIE 6709, 41–45 (2007).
[CrossRef]

Zhong, X. H.

Zhou, Y.

L. Liu, L. Wang, J. Sun, Y. Zhou, X. Zhong, D. Liu, A. Yan, and N. Xu, “An integrated test-bed for PAT testing and verification of inter-satellite lasercom terminals,” Proc. SPIE 6709, 41–45 (2007).
[CrossRef]

Appl. Opt. (7)

IEEE Photon. Technol. Lett. (1)

G. C. Boisset, B. Robertson, and H. S. Hinton, “Design and construction of an active alignment demonstrator for a free-space optical interconnect,” IEEE Photon. Technol. Lett. 7, 676–678 (1995).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

Opt. Laser Eng. (1)

M. Tirabassi and S. J. Rothberg, “Scanning LDV using wedge prisms,” Opt. Laser Eng. 47, 454–460 (2009).
[CrossRef]

Proc. SPIE (3)

V. F. Duma, J. P. Rolland, and A. G. Podoleanu, “Perspectives of optical scanning in OCT,” Proc. SPIE 75560B, 1–12 (2010).

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

L. Liu, L. Wang, J. Sun, Y. Zhou, X. Zhong, D. Liu, A. Yan, and N. Xu, “An integrated test-bed for PAT testing and verification of inter-satellite lasercom terminals,” Proc. SPIE 6709, 41–45 (2007).
[CrossRef]

Other (1)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999), Sect. 3.2.2.

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Figures (13)

Fig. 1.
Fig. 1.

Schematic diagram illustrating the tracking principle of tilting orthogonal double prisms.

Fig. 2.
Fig. 2.

Case 1: (a) Given tracking trajectory (a straight line parallel to the y axis); (b) two curves of tilting angles of double prisms; (c) curve of tilting angles of prism π1.

Fig. 3.
Fig. 3.

Case 2: (a) Given tracking trajectory (a straight line parallel to the x axis); (b) two curves of tilting angles of double prisms; (c) curve of tilting angles of prism π2.

Fig. 4.
Fig. 4.

Case 3: (a) Given tracking trajectory (an oblique line); (b) two curves of tilting angles of double prisms.

Fig. 5.
Fig. 5.

Case 4: (a) Given tracking trajectory (a parabolic curve); (b) two curves of tilting angles of double prisms.

Fig. 6.
Fig. 6.

Case 5: (a) Given tracking trajectory (a circle); (b) two curves of tilting angles of double prisms.

Fig. 7.
Fig. 7.

Case 6: (a) Given tracking trajectory (an oblique line); (b) two curves of tilting angles of double prisms.

Fig. 8.
Fig. 8.

Case 7: (a) Given tracking trajectory (a parabolic curve); (b) two curves of tilting angles of double prisms.

Fig. 9.
Fig. 9.

Case 8: (a) Given tracking trajectory (a circle); (b) two curves of tilting angles of double prisms.

Fig. 10.
Fig. 10.

Schematic diagram of the cam-driving system.

Fig. 11.
Fig. 11.

Example of an elliptical trajectory. (a) Target trajectory; (b) tilting angles of double prisms.

Fig. 12.
Fig. 12.

Relation between the tilting angles of each prism and the rotation angles of corresponding cam. (a) Tilting angle θt1 of prism Π1 and the rotation angle δ1 of the first cam. (b) Tilting angle θt2 of prism Π2, and the rotation angle δ2 of the second cam.

Fig. 13.
Fig. 13.

Configuration curves of two cams for driving double prisms. (a) First cam for driving prism Π1 to tilt around the horizontal axis. (b) Second cam for driving prism Π2 to tilt around the vertical axis (shown in Fig. 1).

Tables (2)

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Table 1. Coordination Values of Beam Intersection Points on a Receiving Screen Located in Far Field and Near Field

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Table 2. Polynomial Coefficients of Titling Angles of Two Prisms

Equations (8)

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

ρV=arctan(xtfztf)=arctancotβtcos(γtδ2),
ρH=arctan(ytfztf)=γtδ2,
θt1=k2π+(1)k2arcsin(n2l12+l22+12)+c12[θtmin,θtmax](k2Z),
δ2=θt2arcsin[sin(α+θt2)cosαsinαn¯22sin2(α+θt2)].
θt1=12(k2π+(1)k2arcsinn2l12+l22+12(l1l2)2+(l12+1l222)2+k1π+arctan(l12+1l222l1l2)),
θt2=12(k4π+(1)k4arcsinn¯22l32+l42+12(l3l4)2+(l32+1l422)22α+k3π+arctan(l32+1l422l3l4)),
{xp=(D1+D2zn)·xf/zf+xnyp=(D1+D2zn)·yf/zf+ynzp=D1+D2.
{xp=D2·xf/zfyp=D2·yf/zfzp=D1+D2.

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