Abstract

A new laser grating scanner concept with attractive capabilities is described. The grating used in this scanner is a computer-generated hologram. The constructional parameters of this type of computer-generated hologram are discussed. In addition to achieving a laser beam deflection, the computer-generated hologram can correct the curvature of the scanning beam. Experiments demonstrating the feasibility of this type of scanner in a drum and disk configuration are presented. Realization of two-dimensional scan patterns using computer-generated holograms is illustrated by experimental results.

© 1976 Optical Society of America

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References

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  1. L. Beiser, Laser Applications, Monte Ross, Ed. (Academic, New York, 1974), Vol. 2, p. 53.
  2. I. Cindrich, Appl. Opt. 6, 1531 (1967).
    [CrossRef] [PubMed]
  3. D. H. McMahon, A. R. Franklin, J. B. Thaxter, Appl. Opt. 8, 399 (1969).
    [CrossRef] [PubMed]
  4. L. Beiser, U.S. Patent3,614,193 (1971);Electro-Opt. Syst. Des. 33 (October1973).
  5. A. Bramley, Appl. Opt. 12, 2780 (1973),U.S. Patent3,721,486 (1973).
  6. G. Pieuchard, J. Flamand, A. Labeyrie, U.S. Patent3,721,487 (1973).
  7. R. V. Pole, H. W. Wollenmann, Appl. Opt. 14, 976 (1975).
    [CrossRef] [PubMed]
  8. O. Bryngdahl, Opt. Commun. 10, 164 (1974).
    [CrossRef]
  9. W-H. Lee, O. Bryngdahl, Opt. Commun. 12, 382 (1974).
    [CrossRef]
  10. J. C. Wyant, Appl. Opt. 14, 1057 (1975).
    [CrossRef] [PubMed]
  11. G. M. Stamps, U.S. Patent2,976,362 (1961).
  12. R. L. Fowler, U.S. Patent3,818,132 (1974).
  13. T. S. Huang, Proc. IEEE 59, 1335 (1971).
    [CrossRef]
  14. W-H. Lee, Appl. Opt. 13, 1677 (1974).
    [CrossRef] [PubMed]
  15. W-H. Lee, J. Opt. Soc. Am. 65, 518 (1975).
    [CrossRef]

1975 (3)

1974 (3)

W-H. Lee, Appl. Opt. 13, 1677 (1974).
[CrossRef] [PubMed]

O. Bryngdahl, Opt. Commun. 10, 164 (1974).
[CrossRef]

W-H. Lee, O. Bryngdahl, Opt. Commun. 12, 382 (1974).
[CrossRef]

1973 (1)

A. Bramley, Appl. Opt. 12, 2780 (1973),U.S. Patent3,721,486 (1973).

1971 (1)

T. S. Huang, Proc. IEEE 59, 1335 (1971).
[CrossRef]

1969 (1)

1967 (1)

Beiser, L.

L. Beiser, Laser Applications, Monte Ross, Ed. (Academic, New York, 1974), Vol. 2, p. 53.

L. Beiser, U.S. Patent3,614,193 (1971);Electro-Opt. Syst. Des. 33 (October1973).

Bramley, A.

A. Bramley, Appl. Opt. 12, 2780 (1973),U.S. Patent3,721,486 (1973).

Bryngdahl, O.

O. Bryngdahl, Opt. Commun. 10, 164 (1974).
[CrossRef]

W-H. Lee, O. Bryngdahl, Opt. Commun. 12, 382 (1974).
[CrossRef]

Cindrich, I.

Flamand, J.

G. Pieuchard, J. Flamand, A. Labeyrie, U.S. Patent3,721,487 (1973).

Fowler, R. L.

R. L. Fowler, U.S. Patent3,818,132 (1974).

Franklin, A. R.

Huang, T. S.

T. S. Huang, Proc. IEEE 59, 1335 (1971).
[CrossRef]

Labeyrie, A.

G. Pieuchard, J. Flamand, A. Labeyrie, U.S. Patent3,721,487 (1973).

Lee, W-H.

McMahon, D. H.

Pieuchard, G.

G. Pieuchard, J. Flamand, A. Labeyrie, U.S. Patent3,721,487 (1973).

Pole, R. V.

Stamps, G. M.

G. M. Stamps, U.S. Patent2,976,362 (1961).

Thaxter, J. B.

Wollenmann, H. W.

Wyant, J. C.

Appl. Opt. (6)

J. Opt. Soc. Am. (1)

Opt. Commun. (2)

O. Bryngdahl, Opt. Commun. 10, 164 (1974).
[CrossRef]

W-H. Lee, O. Bryngdahl, Opt. Commun. 12, 382 (1974).
[CrossRef]

Proc. IEEE (1)

T. S. Huang, Proc. IEEE 59, 1335 (1971).
[CrossRef]

Other (5)

L. Beiser, Laser Applications, Monte Ross, Ed. (Academic, New York, 1974), Vol. 2, p. 53.

G. M. Stamps, U.S. Patent2,976,362 (1961).

R. L. Fowler, U.S. Patent3,818,132 (1974).

G. Pieuchard, J. Flamand, A. Labeyrie, U.S. Patent3,721,487 (1973).

L. Beiser, U.S. Patent3,614,193 (1971);Electro-Opt. Syst. Des. 33 (October1973).

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Figures (13)

Fig. 1
Fig. 1

Rotating grating scanner. As the grating rotates, the spots focused on the back focal plane of the lens L produce circular scan lines.

Fig. 2
Fig. 2

Space-variant grating scanner. The scan line on the back focal plane of the lens L is produced by moving different parts of the CGH across the laser beam.

Fig. 3
Fig. 3

CGH for drum configuration scanner: (a) off-axis Fresnel zone plate type with focusing power along both axes; (b) off-axis cylinder zone plate type with focusing power only along x. For clearness these plots were simplified and contain much fewer lines than those used in the experiments.

Fig. 4
Fig. 4

CGH for disk configuration scanner: (a) polar transformation of the CGH in Fig. 3(a); (b) polar transformation of the CGH in Fig. 3(b). For clearness these plots were simplified and contain much fewer lines than those used in the experiments.

Fig. 5
Fig. 5

Optical system illustrating the curved field problem in scanning. The CGH can be constructed to correct the curvature of the scan beam so that a flat scan on the surface A′ is produced.

Fig. 6
Fig. 6

Schematics of the experimental CGH scanner: (a) configuration with a rotating drum; (b) configuration with a rotating disk. M, modulator; l, focusing lens; CGH, computer-generated hologram.

Fig. 7
Fig. 7

Recording made with the rotating drum configuration scanner using the CGH of Fig. 3(b). (a) Fraunhofer diffraction pattern of the CGH when it is illuminated in the area marked a in Fig. 3(b). (b) This picture is taken at a short distance from the back focal plane of the lens. It shows the astigmatic focus of the diffracted wave from the CGH. The center disk is due to the undiffracted laser beam. (c) The correction of the astigmatism in the CGH with a cylinder lens inserted just behind the CGH.

Fig. 8
Fig. 8

Recording made with the rotating drum configuration scanner using the CGH of Fig. 3(b): (a) to (c) show the positions of the scan spots when the areas marked a, b, and c of the CGH in Fig. 3(b) are illuminated; (d) shows the complete scan line when the drum rotates.

Fig. 9
Fig. 9

Show resolution of a feasibility scanner. Recording made with the rotating drum configuration scanner using the CGH of Fig. 3(b): (a) 100 spots/scan; (b) 200 spots/scan; (c) 300 spots/ scan.

Fig. 10
Fig. 10

Recording made with the rotating disk configuration scanner using the hologram of Fig. 4(b): (a) to (c) shows the scan spots corresponding to the illumination of the areas marked a, b, and c of the CGH in Fig. 4(b); (d) shows the complete scan line when the disk rotates.

Fig. 11
Fig. 11

Formation of two-dimensional scan patterns with the rotating drum scanner configuration. (a) CGH producing the top horizontal line in the scan pattern in (c). The vertical scan line in (c) is produced by the CGH in (b). For clearness the CGH plots were simplified to contain fewer lines than those used in the experiment.

Fig. 12
Fig. 12

Formation of two-dimensional scan patterns with the rotating drum scanner configuration. (a) CGH with spatial frequency variation taken from a section of a triangular waveform. For clearness, the number of lines in this plot were fewer than that used in the experiment. (b) Scan pattern produced by the CGH in (a). (c) Scan pattern produced by combining three CGH's similar to the one shown in (a).

Fig. 13
Fig. 13

Formation of a spiral scan pattern using the drum scanner configuration: (a) simplified version of the CGH used in the experiment; (b) recording of the spiral scan pattern.

Tables (1)

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Table I Mechanical Scanner Configurations

Equations (38)

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u = ± R cos φ , υ = ± R sin φ ,
u = ± υ .
N = R θ D / λ F = θ ( D / d ) .
t ( x , y ) = ½ [ 1 + cos ϕ ( x , y ) ] .
ϕ ( x , y ) / 2 π = n .
ϕ ( x , y ) = 2 π y / d + ψ ( x , y ) .
ν x ( x , y ) = ( 2 π ) 1 ψ ( x , y ) / x .
θ = sin 1 [ λ ν x ( x , y ) ] .
ψ ( x , y ) / x = 2 π x / w Δ x .
ψ ( x , y ) = π x 2 / w Δ x + g ( y ) .
g ( y ) = π y 2 / w Δ x .
ϕ ( x , y ) = 2 π y / d + π ( x 2 + y 2 ) / w Δ x .
y = w Δ x / d ± [ ( w Δ x / d ) 2 ( x 2 2 nw Δ x ) ] 1 / 2 .
ϕ ( x , y ) = π [ ( x x ) 2 + y 2 ] / w Δ x + 2 π y / d = π ( x 2 + y 2 ) / w Δ x + 2 π y / d 2 π x x / w Δ x + π x 2 / w Δ x .
θ = sin 1 λ x / w Δ x .
N = L / Δ x .
L / 2 w Δ x = Q / d ,
N = 2 Qw / d = 2 Q N f ,
ν y = 1 / d + y / w Δ x for 0 y w .
Δ x > d .
w < L / 2 Q .
ϕ ( r , φ ) = 2 π r / d + π ( r 2 + r a 2 φ 2 ) / w Δ x ,
ϕ ( x , y ) = 2 π y / d + π r 2 / w Δ x + π r 2 ( 1 cos θ ) / h ,
sin θ = λ ν ; ν = x / w Δ x .
ϕ ( x , y ) 2 π y / d + π r 2 / w Δ x + π λ r 2 x 2 / 2 w 2 Δ x 2 h .
ν ( x ) = x / w Δ x + λ x 3 / w 2 Δ x 2 h = Q / d [ x + λ ( Q / d ) ( Q / f n ) x 3 ] = Q / d [ x + sin θ 0 ( Q / f n ) x 3 ] ,
y = nd x 2 d / 2 w Δ x .
r = n r 0 + r 0 φ 2 / φ 0 2 .
ν φ = 2 r 0 φ / r φ 0 2 ,
Q r = 2 π ( r 0 / r i ) φ 0 2 ,
ϕ ( x , y ) = 2 π x / d + 2 π y / b + π ( x 2 + y 2 ) / T 2 .
ϕ ( x , y ) = 2 π x / d + 2 π x y / T 1 2 .
ϕ ( x , y ) = 2 π y / d + 2 π f ( x ) y / b + π ( x 2 + y 2 ) / T 2 .
f ( x ) = { x + P / 2 for P / 2 x < 0 , x P / 2 for 0 < x P / 2 ,
ϕ ( x , y ) = 2 π x / d + Bx ( 1 + 2 π y / L 1 ) sin 2 π x / L 1 .
ν x = Bx / L 1 cos 2 π x / L 1
ν y = Bx / L 1 sin 2 π x / L 1 .
ν = ( ν x 2 + ν y 2 ) 1 / 2 = Bx / L 1 .

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