Abstract

An analytical model is developed to predict the structures of the scan fields generated by two-mirror–two-axis beam scanning systems of different architectures, including (1) two oscillating galvanometric scanners, (2) the paddle scanner two-mirror system, and (3) the golf club two-mirror system. It is found that the scan field generated by these systems can be divided into two regions, and scan patterns on the plane of observation depend strongly on the system configuration only in the near-field region. This finding leads to a unified approach to evaluate the structure of scan fields in the far-field region, which paves the way for an investigation of the optical distortions in the scan patterns generated by two-mirror–two-axis beam scanning systems of different architectures.

© 2008 Optical Society of America

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References

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  1. Y. Li, “Laser beam scanning by rotary mirrors. II. Conic-section scan patterns,” Appl. Opt. 34, 6417-6430 (1995).
    [CrossRef] [PubMed]
  2. Y. Li and J. Katz, “Laser beam scanning by rotary mirrors. I. Modeling mirror scanning devices,” Appl. Opt. 34, 6403-6416 (1995).
    [CrossRef] [PubMed]
  3. Y. Li, “Single-mirror beam steering system: analysis and synthesis of high order conic-section scan patterns,” Appl. Opt. 47, 386-398 (2008).
    [CrossRef] [PubMed]
  4. Y. Li and J. Katz, “Asymmetric distribution of the scanned field of a rotating reflective polygon,” Appl. Opt. 36, 342-352 (1997).
    [CrossRef] [PubMed]
  5. G. F. G. Marshall, “Scanning devices and systems,” in Applied Optics and Optical Engineering, R. Kingslake and B. J. Thompson, eds. (Academic, 1980), Vol. 6, pp. 203-262.
  6. J. I. Montagu, “Galvanometric and resonant scanners,” in Handbook of Optical and Laser Scanning, G. F. Marshall, ed. (Marcel Dekker, 2004), pp. 417-476.
    [CrossRef]
  7. G. Tsoukantas, K. Salonitis, A. Stournaras, P. Stavropoulos, and G. Chryssolouris, “On optical design limitations of generalized two-mirror remote beam delivery laser systems: the case of remote welding,” Int. J. Adv. Manuf. Technol. 32, 932-941 (2007).
    [CrossRef]
  8. T. Smith, “On systems of plane reflecting surfaces,” Trans. Opt. Soc. 30, 68-78 (1928).
    [CrossRef]
  9. R. E. Hopkins, “Mirror and prism systems,” in Applied Optics and Optical Engineering, R. Kingslake, ed. (Academic, 1965), Vol. 2, pp. 269-308.
  10. L. Beiser, Unified Optical Scanning Technology (Wiley, 2003).
    [CrossRef]
  11. A. P. Hildebrand, “Generating multidimensional scan using a single rotating component,” in Selected Papers on Laser Scanning and Focusing, L. Beiser, ed., Vol. 378 of SPIE Milstone Series (SPIE, 1985), pp. 328-333 [reprinted from Proc. SPIE. 84, 85-90 (1976)].
  12. L. J. Hornbeck, “Active yoke hidden hinge digital micromirror device,” U.S. patent 5,535,047 (9 July 1996).
  13. G. C. Holst, CCD Arrays, Cameras, and Displays (SPIE, 1996), Sec. 5.2.
  14. J. M. Eastman and A. M. Quinn, “Advanced technology in laser-based hand-held bar code scanners,” Opt. Photon. News 3(9), 25-31 (1992).
    [CrossRef]
  15. L. Beiser, Laser Scanning Notebook (SPIE, 1992), p. 3.
  16. E. Miesak, E. Rogstad, and S. Yang, “Image resolution in a scanning laser display system,” Proc. SPIE 4294, 56-59 (2001).
    [CrossRef]

2008 (1)

2007 (1)

G. Tsoukantas, K. Salonitis, A. Stournaras, P. Stavropoulos, and G. Chryssolouris, “On optical design limitations of generalized two-mirror remote beam delivery laser systems: the case of remote welding,” Int. J. Adv. Manuf. Technol. 32, 932-941 (2007).
[CrossRef]

2001 (1)

E. Miesak, E. Rogstad, and S. Yang, “Image resolution in a scanning laser display system,” Proc. SPIE 4294, 56-59 (2001).
[CrossRef]

1997 (1)

1995 (2)

1992 (1)

J. M. Eastman and A. M. Quinn, “Advanced technology in laser-based hand-held bar code scanners,” Opt. Photon. News 3(9), 25-31 (1992).
[CrossRef]

1928 (1)

T. Smith, “On systems of plane reflecting surfaces,” Trans. Opt. Soc. 30, 68-78 (1928).
[CrossRef]

Beiser, L.

L. Beiser, Unified Optical Scanning Technology (Wiley, 2003).
[CrossRef]

L. Beiser, Laser Scanning Notebook (SPIE, 1992), p. 3.

Chryssolouris, G.

G. Tsoukantas, K. Salonitis, A. Stournaras, P. Stavropoulos, and G. Chryssolouris, “On optical design limitations of generalized two-mirror remote beam delivery laser systems: the case of remote welding,” Int. J. Adv. Manuf. Technol. 32, 932-941 (2007).
[CrossRef]

Eastman, J. M.

J. M. Eastman and A. M. Quinn, “Advanced technology in laser-based hand-held bar code scanners,” Opt. Photon. News 3(9), 25-31 (1992).
[CrossRef]

Hildebrand, A. P.

A. P. Hildebrand, “Generating multidimensional scan using a single rotating component,” in Selected Papers on Laser Scanning and Focusing, L. Beiser, ed., Vol. 378 of SPIE Milstone Series (SPIE, 1985), pp. 328-333 [reprinted from Proc. SPIE. 84, 85-90 (1976)].

Holst, G. C.

G. C. Holst, CCD Arrays, Cameras, and Displays (SPIE, 1996), Sec. 5.2.

Hopkins, R. E.

R. E. Hopkins, “Mirror and prism systems,” in Applied Optics and Optical Engineering, R. Kingslake, ed. (Academic, 1965), Vol. 2, pp. 269-308.

Hornbeck, L. J.

L. J. Hornbeck, “Active yoke hidden hinge digital micromirror device,” U.S. patent 5,535,047 (9 July 1996).

Katz, J.

Li, Y.

Marshall, G. F. G.

G. F. G. Marshall, “Scanning devices and systems,” in Applied Optics and Optical Engineering, R. Kingslake and B. J. Thompson, eds. (Academic, 1980), Vol. 6, pp. 203-262.

Miesak, E.

E. Miesak, E. Rogstad, and S. Yang, “Image resolution in a scanning laser display system,” Proc. SPIE 4294, 56-59 (2001).
[CrossRef]

Montagu, J. I.

J. I. Montagu, “Galvanometric and resonant scanners,” in Handbook of Optical and Laser Scanning, G. F. Marshall, ed. (Marcel Dekker, 2004), pp. 417-476.
[CrossRef]

Quinn, A. M.

J. M. Eastman and A. M. Quinn, “Advanced technology in laser-based hand-held bar code scanners,” Opt. Photon. News 3(9), 25-31 (1992).
[CrossRef]

Rogstad, E.

E. Miesak, E. Rogstad, and S. Yang, “Image resolution in a scanning laser display system,” Proc. SPIE 4294, 56-59 (2001).
[CrossRef]

Salonitis, K.

G. Tsoukantas, K. Salonitis, A. Stournaras, P. Stavropoulos, and G. Chryssolouris, “On optical design limitations of generalized two-mirror remote beam delivery laser systems: the case of remote welding,” Int. J. Adv. Manuf. Technol. 32, 932-941 (2007).
[CrossRef]

Smith, T.

T. Smith, “On systems of plane reflecting surfaces,” Trans. Opt. Soc. 30, 68-78 (1928).
[CrossRef]

Stavropoulos, P.

G. Tsoukantas, K. Salonitis, A. Stournaras, P. Stavropoulos, and G. Chryssolouris, “On optical design limitations of generalized two-mirror remote beam delivery laser systems: the case of remote welding,” Int. J. Adv. Manuf. Technol. 32, 932-941 (2007).
[CrossRef]

Stournaras, A.

G. Tsoukantas, K. Salonitis, A. Stournaras, P. Stavropoulos, and G. Chryssolouris, “On optical design limitations of generalized two-mirror remote beam delivery laser systems: the case of remote welding,” Int. J. Adv. Manuf. Technol. 32, 932-941 (2007).
[CrossRef]

Tsoukantas, G.

G. Tsoukantas, K. Salonitis, A. Stournaras, P. Stavropoulos, and G. Chryssolouris, “On optical design limitations of generalized two-mirror remote beam delivery laser systems: the case of remote welding,” Int. J. Adv. Manuf. Technol. 32, 932-941 (2007).
[CrossRef]

Yang, S.

E. Miesak, E. Rogstad, and S. Yang, “Image resolution in a scanning laser display system,” Proc. SPIE 4294, 56-59 (2001).
[CrossRef]

Appl. Opt. (4)

Int. J. Adv. Manuf. Technol. (1)

G. Tsoukantas, K. Salonitis, A. Stournaras, P. Stavropoulos, and G. Chryssolouris, “On optical design limitations of generalized two-mirror remote beam delivery laser systems: the case of remote welding,” Int. J. Adv. Manuf. Technol. 32, 932-941 (2007).
[CrossRef]

Opt. Photon. News (1)

J. M. Eastman and A. M. Quinn, “Advanced technology in laser-based hand-held bar code scanners,” Opt. Photon. News 3(9), 25-31 (1992).
[CrossRef]

Proc. SPIE (1)

E. Miesak, E. Rogstad, and S. Yang, “Image resolution in a scanning laser display system,” Proc. SPIE 4294, 56-59 (2001).
[CrossRef]

Trans. Opt. Soc. (1)

T. Smith, “On systems of plane reflecting surfaces,” Trans. Opt. Soc. 30, 68-78 (1928).
[CrossRef]

Other (8)

R. E. Hopkins, “Mirror and prism systems,” in Applied Optics and Optical Engineering, R. Kingslake, ed. (Academic, 1965), Vol. 2, pp. 269-308.

L. Beiser, Unified Optical Scanning Technology (Wiley, 2003).
[CrossRef]

A. P. Hildebrand, “Generating multidimensional scan using a single rotating component,” in Selected Papers on Laser Scanning and Focusing, L. Beiser, ed., Vol. 378 of SPIE Milstone Series (SPIE, 1985), pp. 328-333 [reprinted from Proc. SPIE. 84, 85-90 (1976)].

L. J. Hornbeck, “Active yoke hidden hinge digital micromirror device,” U.S. patent 5,535,047 (9 July 1996).

G. C. Holst, CCD Arrays, Cameras, and Displays (SPIE, 1996), Sec. 5.2.

G. F. G. Marshall, “Scanning devices and systems,” in Applied Optics and Optical Engineering, R. Kingslake and B. J. Thompson, eds. (Academic, 1980), Vol. 6, pp. 203-262.

J. I. Montagu, “Galvanometric and resonant scanners,” in Handbook of Optical and Laser Scanning, G. F. Marshall, ed. (Marcel Dekker, 2004), pp. 417-476.
[CrossRef]

L. Beiser, Laser Scanning Notebook (SPIE, 1992), p. 3.

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Figures (7)

Fig. 1
Fig. 1

Schematic diagrams of the most common architectures of 2D scanning systems: (a) Two-galvo 2D scanner (the G-G system), (b) combination of a paddle scanner and a galvo (P-G system) and (c) the golf club scanner (the G-C system).

Fig. 2
Fig. 2

Cross-section view of the model scanner proposed for a unified treatment of the three most common architectures of two-mirror–two-axis beam scanning systems.

Fig. 3
Fig. 3

Diagram illustrating the waist, WA, of the scan field between the two mirrors and location of the second mirror in the G-C system at the waist position to simulate point source scanning and also to reduce the size of the second mirror.

Fig. 4
Fig. 4

Curves for the factor κ in Eqs. (4.3, 4.4, 4.5). Comparison of the scan patterns before and after pincushion distortion correction.

Fig. 5
Fig. 5

Scan linearity (LIN) of raster pattern scanning on screens of different formats.

Fig. 6
Fig. 6

Changes of size and orientation of a laser spot with an elliptical cross section. (a) Diagram illustrating notation and the coordinate system in calculations of changes of spot size and orientation across a curved scan path; (b) deformation of an elliptical spot in raster scanning over the 5 4 format screen.

Fig. 7
Fig. 7

Deformation of rectangular pixels: (a) illustration of the use of four degenerated ellipses to describe a rectangular pixel, (b) parameters for specification of a deformed pixel, (c) deformation of the 1.8 1 rectangular pixels in a laser projection image on the 16 9 HDTV screen.

Tables (1)

Tables Icon

Table 1 Scan Patterns in Near- and Far-Field Regions Generated by Three Different Two-Mirror–two-Axis Beam Scanning Systems a

Equations (43)

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θ 1 = θ 10 + Δ θ 1 , θ 2 = θ 20 + Δ θ 2 ,
X = ( P cos 2 Δ θ 2 h + d tan Δ θ 1 ) tan 2 Δ θ 1 + 2 q sin θ 10 sin ( θ 10 Δ θ 1 ) cos 2 Δ θ 1 ,
Y = P tan 2 Δ θ 2 .
q = d = 0 , h h .
X = ( P cos 2 Δ θ 2 + h ) tan 2 Δ θ 1 , Y = P tan 2 Δ θ 2 .
h = q = 0.
X = ( P cos 2 Δ θ 2 + d tan Δ θ 1 ) tan 2 Δ θ 1 , Y = P tan 2 Δ θ 2 .
d = 0.
h = q cos θ 10 cos Θ 1 m ,
X = P cos 2 Δ θ 2 tan 2 Δ θ 1 + 2 q ( sin θ 10 sin ( θ 10 Δ θ 1 ) cos 2 Δ θ 1 cos θ 10 2 cos Θ 1 m tan 2 Δ θ 1 ) ,
Y = P tan 2 Δ θ 2 .
X = P cos 2 Δ θ 2 tan 2 Δ θ 1 + 2 q ( 1 cos Δ θ 1 + sin Δ θ 1 cos 2 Δ θ 1 tan 2 Δ θ 1 2 cos Θ 1 m ) .
Δ ( AR ) = 100 | X | Δ θ 1 = Θ 1 m , Δ θ 2 = 0 , | h | 0 | X | Δ θ 1 = Θ 1 m , Δ θ 2 = 0 , | h | = 0 | Y | Δ θ 1 = 0 , Δ θ 2 = Θ 2 m ( % ) = 100 | h | P tan 2 Θ 1 m tan 2 Θ 2 m ( % ) .
( 0 C ¯ ) P-G = 2 d P 1 cos 2 Θ 1 m cos 2 Θ 1 m .
( 0 C ¯ ) G-C = 2 q P 1 cos Θ 1 m cos 2 Θ 1 m .
X = P cos 2 Δ θ 2 tan 2 Δ θ 1 and Y = P tan 2 Δ θ 2 .
AR = | X | Δ θ 1 = Θ 1 m , Δ θ 2 = 0 | Y | Δ θ 1 = 0 , Δ θ 2 = Θ 2 m = tan 2 Θ 1 m tan 2 Θ 2 m .
SLB = Δ W H = AR 2 1 cos 2 Θ 2 m cos 2 Θ 2 m ,
X = P cos 2 Δ θ 2 tan ( 2 h ( t ) Δ θ 1 ) , Y = P tan 2 Δ θ 2 ,
h ( t ) = cos κ 2 Δ θ 2 .
SLB = AR 2 ( K cos 2 Θ 2 m cos 2 Θ 2 m ) with     K = tan ( 2 Θ 1 m cos κ 2 Θ 2 m ) tan 2 Θ 1 m .
κ = ln { arctan [ tan 2 Θ 1 m cos 2 Θ 2 m ] } ln ( 2 Θ 1 m ) ln ( cos 2 Θ 2 m ) .
LIN = 100 V min V ¯ ( % ) ( V ¯ = V max + V min 2 ) ,
v = ( X ˙ ) 2 + ( Y ˙ ) 2 ,
v = 2 θ ˙ 1 P cos 2 Δ θ 2 × ( 1 cos 2 2 Δ θ 1 + m tan 2 Δ θ 1 tan 2 Δ θ 2 ) 2 + m 2 cos 2 2 Δ θ 2 ,
m = θ ˙ 2 / θ ˙ 1 .
v = 2 θ ˙ 1 P cos 2 2 Δ θ 1 cos 2 Δ θ 2 .
V max = v | Δ θ 1 = Δ θ 2 = 0 = 2 θ ˙ 1 P , V min = v | Δ θ 1 = Θ 1 m , Δ θ 2 = Θ 2 m = 2 θ ˙ 1 P cos 2 2 Θ 1 m cos 2 Θ 2 m .
LIN = 100 2 cos 2 2 Θ 1 m cos 2 Θ 2 m 1 + cos 2 2 Θ 1 m cos 2 Θ 2 m ( % ) .
ξ = w ξ cos φ + a , η = w η sin φ + b ,
X = P cos 2 Δ θ 2 tan 2 Δ θ 1 ξ cos 2 Δ θ 1 η tan 2 Δ θ 1 tan 2 Δ θ 2 ,
Y = P tan 2 Δ θ 2 + η cos 2 Δ θ 2 .
χ = 1 2 arctan [ ( sin 4 Δ θ 1 sin 2 Δ θ 2 ) / F ] , F = sin 2 2 Δ θ 1 sin 2 2 Δ θ 2 cos 2 2 Δ θ 1 + ε 2 cos 2 2 Δ θ 2 ,
D X = ( w ξ cos 2 Δ θ 1 ) 2 + ( w η tan 2 Δ θ 1 tan 2 Δ θ 2 ) 2 ,
D Y = w η cos 2 Δ θ 2 .
ξ = w 1 , η = w 2 sin φ .
ξ = w 1 cos φ , η = w 2 .
X = P cos 2 Δ θ 2 tan 2 Δ θ 1 ± w 1 cos 2 Δ θ 1 ( w 2 sin φ ) tan 2 Δ θ 1 tan 2 Δ θ 2 ,
Y = P tan 2 Δ θ 2 + w 2 sin φ cos 2 Δ θ 2 .
X = P cos 2 Δ θ 2 tan 2 Δ θ 1 w 1 cos φ cos 2 Δ θ 1 ± w 2 tan 2 Δ θ 1 tan 2 Δ θ 2 ,
Y = P tan 2 Δ θ 2 w 2 cos 2 Δ θ 2 .
v X = w 1 cos 2 Δ θ 1 + w 2 tan 2 Δ θ 1 tan 2 Δ θ 2 , v Y = w 2 cos 2 Δ θ 2 .
u = arctan ( tan 2 Δ θ 1 sin 2 Δ θ 2 ) .

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