Abstract

Phase distributions to generate holograms for use in laser scanning are investigated to create a multidirectional scanning pattern such as an X, asterisk, and lattice. The scanning direction for elliptic and hyperbolic phase distribution holograms is oblique to the hologram moving direction. A hyperbolic phase-distribution hologram can be used to scan a laser beam in a direction perpendicular to the hologram moving direction. Experimentally, elliptic, and hyperbolic phase distributions were generated using a spherical and a cylindrical lens pair. To converge the scanning beam, a stacked drum configuration holographic scanner has been proposed. Multidirectional scanning is demonstrated using the drum scanner.

© 1983 Optical Society of America

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References

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  1. H. Ikeda, M. Ando, T. Inagaki, Appl. Opt. 18, 2166 (1979).
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  2. L. D. Dickson, G. T. Sincerbox, A. D. Wolfheimer, IBM J. Res. Dev. 26, 228 (1982).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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1982

L. D. Dickson, G. T. Sincerbox, A. D. Wolfheimer, IBM J. Res. Dev. 26, 228 (1982).
[CrossRef]

Y. Ono, N. Nishida, Appl. Opt. 21, 4542 (1982).
[CrossRef] [PubMed]

1979

1976

1975

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Figures (11)

Fig. 1
Fig. 1

Geometry for coordinate systems and for the relationship between the hologram’s moving and scanning directions.

Fig. 2
Fig. 2

Transformation of plane wave using a pair of cylindrical lenses. Their convergent directions are perpendicular to each other, and their focal lengths are different.

Fig. 3
Fig. 3

Phase advanced directions and equal phase line. Arrows show the phase advanced directions.

Fig. 4
Fig. 4

Scanning beam convergence method: (a) Illuminating beam is scanned by scanning hologram movement. The scanned beam is converged by the converging hologram that moves in a direction opposite to the scanning hologram. (b) Geometry for generating scanning and converging holograms. The hologram for scanning is generated by interference between the plane and object waves. The hologram for beam converging is generated by interfering with the same object wave in a different plane and a convergent spherical wave.

Fig. 5
Fig. 5

Stacked drum configuration holographic scanner: (a) top view; (b) side view. Illuminating beam is scanned by the scanning hologram and converged by the opposite side hologram.

Fig. 6
Fig. 6

Interferometer to generate an in-line hologram with hyperbolic phase distribution: (a) side view of object wave; (b) top view of the interferometer.

Fig. 7
Fig. 7

Magnified photograph of the hyperbolic group interference fringe center. Interference fringes due to multiple reflection in a half mirror are superimposed.

Fig. 8
Fig. 8

Interferometer to generate cylindrical wave phase holograms: (a) side view of object wave; (b) top view of the interferometer.

Fig. 9
Fig. 9

Reconstruction geometry for a hologram drum scanner. A collimated laser beam illuminates a hologram in an oblique angle incidence and is scanned with the drum revolution.

Fig. 10
Fig. 10

Multidirectional scanning pattern in a scanning plane. The scan lines are intersected by π/8 rad for each line. Scanning angles are ~12°.

Fig. 11
Fig. 11

Experimental setup for multidirectional scanning with the stacked drum configuration holographic scanner. The bottom intersecting scan lines are the loci of the converged beam. The center intersecting scan lines are the loci of the zero-order diffraction beam from the second hologram. The upper scan lines are the loci of the second-order diffraction beam and so on.

Equations (12)

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ϕ ( X , Y ) = 2 π λ ( X 2 a 2 ± Y 2 b 2 ) ,
X = x cos θ + y sin θ , Y = - x sin θ + y cos θ .
ϕ ( x , y ) = 2 π λ [ ( x cos θ + y sin θ ) 2 a 2 ± ( - x sin θ + y cos θ ) 2 b 2 ] .
ϕ ( x , y ) x = 4 π [ ( b 2 cos 2 θ ± a 2 sin 2 θ ) x + ( b 2 a 2 ) cos θ · sin θ · y ] / [ ( a b ) 2 λ ] ,
ϕ ( x , y ) y = 4 π [ ( b 2 a 2 ) cos θ · sin θ · x + ( b 2 sin 2 θ ± a 2 cos 2 θ ) · y ] / [ ( a b ) 2 λ ] .
ϕ ( x , y ) x ] x = 0 = 4 π ( b 2 a 2 ) cos θ · sin θ · y λ a 2 b 2 ,
ϕ ( x , y ) y ] x = 0 = 4 π ( b 2 sin 2 θ ± a 2 cos 2 θ ) y λ a 2 b 2 .
tan φ = ϕ / y ϕ / x ] x = 0 = b 2 sin 2 θ ± a 2 cos 2 θ ( b 2 a 2 ) cos θ · sin θ .
ϕ c ( x ) = 2 π λ ( f x 2 + x 2 - f x ) .
ϕ d ( y ) = - 2 π λ ( f y 2 + y 2 - f y ) .
ϕ c ( x ) = ( π x 2 ) / ( λ f x ) ,
ϕ d ( y ) = ( π y 2 ) / ( λ f y ) .

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