Abstract

This paper presents analytical and numerical results that elucidate the impact of error sources on the performance of dual-wedge beam steering systems. Different types of error sources are considered. Specifically, we investigate optical distortions in the pattern scanned out by a single ray through a pair of rotatable wedge elements with slightly different parameters. Case examples are given to reveal the difference between the distorted patterns and the patterns produced by a pair of perfectly equal wedge elements. Furthermore, nonparaxial ray tracing is performed to investigate the impact of assembly errors on the accuracy of steering a laser beam to a remote target. We found that a misalignment in a bearing axis of rotation with respect to the system optical axis will result in a change of beam deflection off-axis that gives rise to a severe decrease of pointing accuracy to a level well below the level that a tilted wedge prism may attain.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. A. Rosell, “Prism scanners,” J. Opt. Soc. Am. 50, 521–526 (1960).
    [CrossRef]
  2. W. L. Wolfe, “Optical-mechanical scanning techniques and devices,” in The Infrared HandbookW. L. Wolfe and G. J. Zissis, eds. (ERIM, 1989), Chap. 10.
  3. G. Garcia-Torales, M. Strojnik, and G. Paez, “Risley prisms to control wave-front tilt and displacement in a vectorial shearing interferometer,” Appl. Opt. 41, 1380–1384 (2002).
    [CrossRef]
  4. C. R. Schwarze, R. Vaillancourt, D. Carlson, E. Schundler, T. Evans, and J. R. Engel, “Risley-prism based compact laser beam steering for IRCM, laser communications, and laser radar,” http://www.optra.com/images/TP-Compact_Beam_Steering.pdf .
  5. R. C. Yates, Curves and Their Properties (National Council of Teachers of Math, 1974), p. 255.
  6. Y. Li and J. Katz, “Laser beam scanning by rotary mirrors. I. Modeling mirror-scanning devices,” Appl. Opt. 34, 6403–6416 (1995).
    [CrossRef]
  7. Y. Li, “Third-order theory of Risley-prism based beam steering system,” Appl. Opt. 50, 679–686 (2011).
    [CrossRef]
  8. Y. Li, “Closed form analytical inverse solutions for Risley-prism-based beam steering systems in different configurations,” Appl. Opt. 50, 4302–4309 (2011).
    [CrossRef]
  9. P. R. Yoder, Opto-Mechanical System Design2nd ed.(Marcel Dekker, 1993), p. 22.
  10. C. T. Amirault and C. A. DiMarzio, “Precision pointing using a dual-wedge scanner,” Appl. Opt. 24, 1302–1308(1985).
    [CrossRef]
  11. M. Saayman, “Materials for infrared optics,” http://www.optics.arizona.edu/optomech/student%20reports/tutorials/2009/Saayman%20521%20Tutorial.pdf .

2011 (2)

2002 (1)

1995 (1)

1985 (1)

1960 (1)

Amirault, C. T.

DiMarzio, C. A.

Garcia-Torales, G.

Katz, J.

Li, Y.

Paez, G.

Rosell, F. A.

Strojnik, M.

Wolfe, W. L.

W. L. Wolfe, “Optical-mechanical scanning techniques and devices,” in The Infrared HandbookW. L. Wolfe and G. J. Zissis, eds. (ERIM, 1989), Chap. 10.

Yates, R. C.

R. C. Yates, Curves and Their Properties (National Council of Teachers of Math, 1974), p. 255.

Yoder, P. R.

P. R. Yoder, Opto-Mechanical System Design2nd ed.(Marcel Dekker, 1993), p. 22.

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

Other (5)

W. L. Wolfe, “Optical-mechanical scanning techniques and devices,” in The Infrared HandbookW. L. Wolfe and G. J. Zissis, eds. (ERIM, 1989), Chap. 10.

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

R. C. Yates, Curves and Their Properties (National Council of Teachers of Math, 1974), p. 255.

P. R. Yoder, Opto-Mechanical System Design2nd ed.(Marcel Dekker, 1993), p. 22.

M. Saayman, “Materials for infrared optics,” http://www.optics.arizona.edu/optomech/student%20reports/tutorials/2009/Saayman%20521%20Tutorial.pdf .

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

Schematic diagram illustrating the notation and coordinate systems for a dual-wedge beam steering system. The unit vector for the incident ray is collinear with the z axis, which is also the optical axis of the system.

Fig. 2.
Fig. 2.

Rotating optical wedge scan patterns. The rotational frequency ratio is m; (a) Circular scan pattern produced by system of m=1 and patterns of m=5 and 1/5 on the two sides are identical; (b) Line scan pattern produced by system of m=1 and rose-like scan patterns of m=2 and 1/2 on the two sides are identical; (c) Scan patterns built up by five rotations (i.e., 5π<θ5π) of the two counter-rotating elements having 1% error in their rotational frequency equality; (d) 1% error in rotational frequency equality of the two continuously counter-rotating wedge elements results in a change of the line scan pattern into a rose-like scan pattern of 201 petals.

Fig. 3.
Fig. 3.

Distortions in the line scan patterns produced by a pair of counter-rotating wedge elements; (a) Rotational frequency error has a sinusoidal distribution; (b) Impact of a small difference in the power of ray deflection of the two wedge elements.

Fig. 4.
Fig. 4.

Diagrams illustrating the assembly errors; (a) Wedge prism tilt: the flat surface of W2 not perpendicular to the optical axis of the system; (b) Bearing tilt: a misalignment of a bearing axis with respect to the optical axis of the system.

Fig. 5.
Fig. 5.

Upper limit of the component prism tilt angle versus the planned pointing accuracy δ; (a) (εa)m/δ for wedge prism tilt; (b) (εb)m/δ for bearing tilt.

Fig. 6.
Fig. 6.

Distortions in circle scan and line scan patterns produced by systems with assembly errors; (a) Impact of wedge prism tilt on circle scan pattern; (b) Impact of bearing tilt on circle scan pattern; (c) Impact of wedge prism tilt on line scan pattern; (d) Impact of bearing tilt on line scan pattern.

Equations (41)

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

dq=(nq1)αq(q=1,2),
(KL)=d1[cos(θ1+θ10)sin(θ1+θ10)]+d2[cos(θ2+θ20)sin(θ2+θ20)],
M=±1K2L2.
(xy)=P(KL)=P{d1[cos(θ1+θ10)sin(θ1+θ10)]+d2[cos(θ2+θ20)sin(θ2+θ20)]}.
m=θ2/θ1
p=d2/d1.
(xy)=Pd1{[cos(θ1+θ10)sin(θ1+θ10)]+p[cos(mθ1+θ20)sin(mθ1+θ20)]}.
p=1,ω1=const.,andm=const.
ρ=ρ0cos(kφ+φ0),
(xy)=Pd1[(cosθ1sinθ1)+(cosm(θ1+κcosθ1)sinm(θ1+κcosθ1))],
SLB=100×(ΔH/W)(%),
SLB50tan|Δm|2(%),
X2(1+p)2+Y2(1p)2=1
D1=(n12sin2α1cosα1)sinα1
D2=(F1n22+F2)sinα2,
F=[cosα2n22n12+(sin2α1+cosα1n12sin2α1)2sinα1sinα2(n12sin2α1cosα1)cosΔθ],
s^11(i)=(0,0,1),
n^11=(sinα1cosθ1,sinα1sinθ1,cosα1).
n^12=(0,0,1).
n^21=(sinεacosθ2,sinεasinθ2,cosεa).
n^21=n^210εa(cosθ2,sinθ2,0),
n^22=[sin(α2εa)cosθ2,sin(α2εa)sinθ2,cos(α2εa)]n^220+εa(cosα2cosθ2,cosα2sinθ2,sinα2),
(KL)=D1[cos(θ1+θ10)sin(θ1+θ10)]+D2(1+εaEa)[cos(θ2+θ20)sin(θ2+θ20)]
M=1K2L2.
Ea=1D2[n22n12+(sin2α1+cosα1n12sin2α1)21n12+(sinα1+cosα1n12sin2α1)2(F1n22+F2)cosα2].
cosΦ=M=1K2L2.
D12+D22(1+εaEa)2=sin2Φ.
(D12+D22)Δθ=0=sin2Φm
D12+D22[1+εa(Ea)Δθ=0]2=sin2(Φm+δ).
εa(εa)m=δ[1(D1+D2)2D2|Ea|]Δθ=0,
n^21b=(0,0,1)
n^22b=(sinα2cosθ2,sinα2sinθ2,cosα2).
n^21=(sinεb,0,cosεb)
n^22=(cosεbsinα2cosθ2sinεbcosα2,sinα2sinθ2,sinεbsinα2cosθ2cosεbcosα2).
n^21=n^210+εb(1,0,0)
n^22=n^220+εb(cosα2,0,sinα2cosθ2),
(K+K0L)=D1[cos(θ1+θ10)sin(θ1+θ10)]+D2(1+εbEb)[cos(θ2+θ20)sin(θ2+θ20)]
M=1K2L2.
Eb=1D2[n22n12+(sin2α1+cosα1n12sin2α1)21n12+(sin2α1+cosα1n12sin2α1)2].
K0=εb(F1n22+F2)cosα2=εbD2cotα2.
εb(εb)m=δ[1(D1D2)2D2(|Ea|+cotα2)]Δθ=0,

Metrics