Abstract

The focus path of a laser beam deflected by a prismatic polygon mirror was calculated. It is shown that the larger the focal distance of the objective or the polygon radius, the closer the focus path approaches a straight scanning line. Especially in the case of small pattern scanning, a remarkably small deviation between actual focus path and straight scanning line can be achieved by suitable sizing and arrangement of the optical elements.

© 1976 Optical Society of America

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References

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  1. L. Beiser, in Technical Program, Electro-Optics Systems Design Conference (1972), p. 255.
  2. L. Beiser, “Laser Scanning Systems,” in Laser Applications, M. Ross, Ed. (Academic, New York, 1974), Vol. 2, pp. 53–159.

1972

L. Beiser, in Technical Program, Electro-Optics Systems Design Conference (1972), p. 255.

Beiser, L.

L. Beiser, in Technical Program, Electro-Optics Systems Design Conference (1972), p. 255.

L. Beiser, “Laser Scanning Systems,” in Laser Applications, M. Ross, Ed. (Academic, New York, 1974), Vol. 2, pp. 53–159.

Electro-Optics Systems Design Conference

L. Beiser, in Technical Program, Electro-Optics Systems Design Conference (1972), p. 255.

Other

L. Beiser, “Laser Scanning Systems,” in Laser Applications, M. Ross, Ed. (Academic, New York, 1974), Vol. 2, pp. 53–159.

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Figures (9)

Fig. 1
Fig. 1

Scan device with prismatic polygon mirror (postobjective setup).

Fig. 2
Fig. 2

Definition of φ, P(xF,yF,zF), ro, xmax, Yo, f, ψ, and δ.

Fig. 3
Fig. 3

Geometrical relationship between P′ and P.

Fig. 4
Fig. 4

Path of the laser beam focus in the scanning plane, δ = 0°, f = 450 mm, ψ = 45°, ro = 60 mm, Yo = 68.056 mm, xmax = 80 mm.

Fig. 5
Fig. 5

Geometrical relationship between Dy,max, ρ, and xmax.

Fig. 6
Fig. 6

Different curve types of the path of the laser beam focus.

Fig. 7
Fig. 7

Significance of A/B.

Fig. 8
Fig. 8

Relative deviation DEV/xmax from a straight scanning line as a function of A/B; parameter: xmax/B.

Fig. 9
Fig. 9

Path of the laser beam focus in the scanning plane, δ = 0°, f = 50 mm, ψ = 45°, ro = 35.65 mm, Yo = 53.36 mm, xmax = 7 mm.

Equations (24)

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z F = P z = E z + R z = E z + R z = - f sin ψ cos δ .
x F = P x = - A * sin ( 2 φ + α ) + 2 r o sin φ ,
y F = P y = - A * cos ( 2 φ + α ) + 2 r o cos φ ,
A * = - P x y
B = 2 r o .
x F = - A sin 2 φ + B sin φ ,
y F = - A cos 2 φ + B cos φ .
D y ( φ ) = y F ( φ ) - y F ( φ = 0 ) = A ( 1 - cos 2 φ ) - B ( 1 - cos φ ) .
D y , max - [ ρ - ( ρ 2 - x max 2 ) 1 / 2 ] , ( ρ = f · sin ψ > x max ) .
A B = Y o - f sin ψ 2 r o > 0.25.
A B = Y o - f sin ψ 2 r o < 0.25.
lim φ 0 A B = lim φ 0 1 - cos φ 1 - cos 2 φ = 0.25.
DEV ( A , B ) = D y ( A , B , φ max , I ) = A ( 1 - cos 2 φ max , I ) - B ( 1 - cos φ max , I ) ,
DEV ( A , B ) = D y ( A , B , φ ex , II ) = A ( 1 - cos 2 φ ex , II ) - B ( 1 - cos φ ex , II ) ,
DEV ( A , B ) = D y ( A , B , φ ex , III ) - D y ( A , B , φ max , III ) = A ( 1 - cos 2 φ ex , III ) - B ( 1 - cos φ ex , III ) - A ( 1 - cos 2 φ max , III ) + B ( 1 - cos φ max , III ) ,
DEV ( A , B ) = - D y ( A , B , φ max , IV ) = A ( 1 - cos 2 φ max , IV ) + B ( 1 - cos φ max , IV ) ,
x max = - A · sin 2 φ max + B sin φ max
[ d D y ( φ ) d φ ] φ e x = 0.
DEV x max = 1 x max B [ A B ( 1 - cos 2 φ max , I ) - 1 + cos φ max , I ] for type I ,
DEV x max = 1 x max B [ A B ( 1 - cos 2 φ ex , II ) - 1 + cos φ ex , II ] for type II ,
DEV x max = 1 x max B [ A B ( 1 - cos 2 φ ex , III ) + cos φ ex , III - A B ( 1 - cos 2 φ max , III ) - cos φ max , III ] for type III ,
DEV x max = 1 x max B [ - A B ( 1 - cos 2 φ max , IV ) + 1 - cos φ max , IV ] for type IV ,
x max B = 80 120 = 0.667 , A B = 68.056 - 450 · sin 45 ° 120 = - 2.0845 , DEV = 9.453 mm , DEV x max = 9.453 80 = 0.118.
x max B = 7 71.3 = 0.09818 , A B = 53.36 - 50.1 · sin 45 ° 71.3 = 0.25153 , DEV = 0.00596 mm , DEV x max = 0.00596 7 = 0.00085.

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