Abstract

A polygonal holographic scanner that combines a reflection volume hologram on dichromated gelatin with a computer-generated hologram (CGH) is described. Such a scanning system allows for a compact folded version and highly efficient Bragg diffraction into a single order. A design of the scanner with a nonspherical wave front based on ray tracing and the damped least-squares optimization technique allows a flat-field linearized scan to be used. A suitable trade-off between field flatness and position linearity of scan is adopted. The optimized wave front designated by polynomials is encoded into a CGH. Experiments demonstrating the feasibility of this scannner are presented. Additional data on the diffraction efficiency and the spectrally diffracted intensity of the reflection volume gratings are also shown.

© 1984 Optical Society of America

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References

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  1. O. Bryngdahl, W-H. Lee, “Laser Beam Scanning Using Computer-Generated Holograms,” Appl. Opt. 15, 183 (1976).
    [CrossRef] [PubMed]
  2. C. J. Kramer, “Holographic Laser Scanners for Nonimpact Printing,” Laser Focus 17, 70 (1981).
  3. L. Beiser, “Holographic Scan Aberration Correction: a Clarification,” Appl. Opt. 16, 2361 (1977).
    [CrossRef] [PubMed]
  4. R. V. Pole, H. W. Werlich, R. J. Krusche, “Holographic Light Deflection,” Appl. Opt. 17, 3294 (1978).
    [CrossRef] [PubMed]
  5. H. Funato, “Holographic Scanner for Laser Printer,” Proc. Soc. Photo-Opt. Instrum. Eng. 390, 174 (1983).
  6. Y. Ono, N. Nishida, “Holographic Disk Scanners for Bow-Free Scanning,” Appl. Opt. 22, 2132 (1983).
    [CrossRef] [PubMed]
  7. Y. Ishii, “Reflection Volume Holographic Scanners with Field-Curvature Corrections,” Appl. Opt. 22, 3491 (1983).
    [CrossRef] [PubMed]
  8. A. K. Rigler, R. J. Pegis, “Optimization Methods in Optics,” in The Computer in Optical Research, B. R. Frieden, Ed. (Springer, Berlin, 1980).
    [CrossRef]
  9. D. W. Marquardt, “An Algorithm for Least-Squares Estimation of Nonlinear Parameters,” J. Soc. Ind. Appl. Math. 11, 431 (1963).
    [CrossRef]
  10. W-H. Lee, “Computer-Generated Holograms: Techniques and Applications,” Prog. Opt. 16, 121 (1978).
  11. D. Meyerhofer, “Dichromated Gelatin,” in Holographic Recording Materials, H. M. Smith, Ed. (Springer, Berlin, 1980).
  12. B. J. Chang, “Dichromated Gelatin Holograms and Their Applications,” Opt. Eng. 19, 642 (1980).
    [CrossRef]
  13. T. Kubota, T. Ose, “Lippmann Color Holograms Recorded in Methylene-Blue-Sensitized Dichromated Gelatin,” Opt. Lett. 4, 289 (1979).
    [CrossRef] [PubMed]
  14. R. C. Fairchild, J. R. Fienup, “Computer-Originated Aspheric Optical Elements,” Opt. Eng. 21, 133 (1982).
    [CrossRef]
  15. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), Chap.3.
  16. C. B. Burckhardt, “Diffraction by Stratified Dielectric Grating,” J. Opt. Soc. Am. 56, 1502 (1966).
    [CrossRef]
  17. S. K. Case, W. J. Dallas, “Volume Holograms Constructed from Computer-Generated Masks,” Appl. Opt. 15, 2537 (1978).

1983 (3)

1982 (1)

R. C. Fairchild, J. R. Fienup, “Computer-Originated Aspheric Optical Elements,” Opt. Eng. 21, 133 (1982).
[CrossRef]

1981 (1)

C. J. Kramer, “Holographic Laser Scanners for Nonimpact Printing,” Laser Focus 17, 70 (1981).

1980 (1)

B. J. Chang, “Dichromated Gelatin Holograms and Their Applications,” Opt. Eng. 19, 642 (1980).
[CrossRef]

1979 (1)

1978 (3)

W-H. Lee, “Computer-Generated Holograms: Techniques and Applications,” Prog. Opt. 16, 121 (1978).

S. K. Case, W. J. Dallas, “Volume Holograms Constructed from Computer-Generated Masks,” Appl. Opt. 15, 2537 (1978).

R. V. Pole, H. W. Werlich, R. J. Krusche, “Holographic Light Deflection,” Appl. Opt. 17, 3294 (1978).
[CrossRef] [PubMed]

1977 (1)

1976 (1)

1966 (1)

1963 (1)

D. W. Marquardt, “An Algorithm for Least-Squares Estimation of Nonlinear Parameters,” J. Soc. Ind. Appl. Math. 11, 431 (1963).
[CrossRef]

Beiser, L.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), Chap.3.

Bryngdahl, O.

Burckhardt, C. B.

Case, S. K.

S. K. Case, W. J. Dallas, “Volume Holograms Constructed from Computer-Generated Masks,” Appl. Opt. 15, 2537 (1978).

Chang, B. J.

B. J. Chang, “Dichromated Gelatin Holograms and Their Applications,” Opt. Eng. 19, 642 (1980).
[CrossRef]

Dallas, W. J.

S. K. Case, W. J. Dallas, “Volume Holograms Constructed from Computer-Generated Masks,” Appl. Opt. 15, 2537 (1978).

Fairchild, R. C.

R. C. Fairchild, J. R. Fienup, “Computer-Originated Aspheric Optical Elements,” Opt. Eng. 21, 133 (1982).
[CrossRef]

Fienup, J. R.

R. C. Fairchild, J. R. Fienup, “Computer-Originated Aspheric Optical Elements,” Opt. Eng. 21, 133 (1982).
[CrossRef]

Funato, H.

H. Funato, “Holographic Scanner for Laser Printer,” Proc. Soc. Photo-Opt. Instrum. Eng. 390, 174 (1983).

Ishii, Y.

Kramer, C. J.

C. J. Kramer, “Holographic Laser Scanners for Nonimpact Printing,” Laser Focus 17, 70 (1981).

Krusche, R. J.

Kubota, T.

Lee, W-H.

W-H. Lee, “Computer-Generated Holograms: Techniques and Applications,” Prog. Opt. 16, 121 (1978).

O. Bryngdahl, W-H. Lee, “Laser Beam Scanning Using Computer-Generated Holograms,” Appl. Opt. 15, 183 (1976).
[CrossRef] [PubMed]

Marquardt, D. W.

D. W. Marquardt, “An Algorithm for Least-Squares Estimation of Nonlinear Parameters,” J. Soc. Ind. Appl. Math. 11, 431 (1963).
[CrossRef]

Meyerhofer, D.

D. Meyerhofer, “Dichromated Gelatin,” in Holographic Recording Materials, H. M. Smith, Ed. (Springer, Berlin, 1980).

Nishida, N.

Ono, Y.

Ose, T.

Pegis, R. J.

A. K. Rigler, R. J. Pegis, “Optimization Methods in Optics,” in The Computer in Optical Research, B. R. Frieden, Ed. (Springer, Berlin, 1980).
[CrossRef]

Pole, R. V.

Rigler, A. K.

A. K. Rigler, R. J. Pegis, “Optimization Methods in Optics,” in The Computer in Optical Research, B. R. Frieden, Ed. (Springer, Berlin, 1980).
[CrossRef]

Werlich, H. W.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), Chap.3.

Appl. Opt. (6)

J. Opt. Soc. Am. (1)

J. Soc. Ind. Appl. Math. (1)

D. W. Marquardt, “An Algorithm for Least-Squares Estimation of Nonlinear Parameters,” J. Soc. Ind. Appl. Math. 11, 431 (1963).
[CrossRef]

Laser Focus (1)

C. J. Kramer, “Holographic Laser Scanners for Nonimpact Printing,” Laser Focus 17, 70 (1981).

Opt. Eng. (2)

B. J. Chang, “Dichromated Gelatin Holograms and Their Applications,” Opt. Eng. 19, 642 (1980).
[CrossRef]

R. C. Fairchild, J. R. Fienup, “Computer-Originated Aspheric Optical Elements,” Opt. Eng. 21, 133 (1982).
[CrossRef]

Opt. Lett. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

H. Funato, “Holographic Scanner for Laser Printer,” Proc. Soc. Photo-Opt. Instrum. Eng. 390, 174 (1983).

Prog. Opt. (1)

W-H. Lee, “Computer-Generated Holograms: Techniques and Applications,” Prog. Opt. 16, 121 (1978).

Other (3)

D. Meyerhofer, “Dichromated Gelatin,” in Holographic Recording Materials, H. M. Smith, Ed. (Springer, Berlin, 1980).

A. K. Rigler, R. J. Pegis, “Optimization Methods in Optics,” in The Computer in Optical Research, B. R. Frieden, Ed. (Springer, Berlin, 1980).
[CrossRef]

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), Chap.3.

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Figures (14)

Fig. 1
Fig. 1

Diffraction efficiency of reflection dichromated gelatin holographic gratings as a function of exposure at 488.0-nm wavelength. The dashed line indicates baking the developed gelatin layer.

Fig. 2
Fig. 2

Peak reconstructing wavelength of reflection gratings used in Fig. 1 as a function of exposure. The reconstructing wavelength which corresponds to the data for baking the DCG plate (β) is almost the same as the recording wavelength.

Fig. 3
Fig. 3

Thickness variation of the exposed developed gelatin layer, which is measured by a surface smoothness instrument, as a function of exposure.

Fig. 4
Fig. 4

Spectrally diffracted intensity of reflection gratings corresponding to the data indicated by arrows in Fig. 2. The reconstructing wavelengths are shown in the figure.

Fig. 5
Fig. 5

Reflection holographic laser scanner for one facet: (a) top view and (b) side view of experimental setup. Recording geometry is shown by solid lines and readout geometry by dashed lines.

Fig. 6
Fig. 6

Reflection holographic scanner attaching four facets.

Fig. 7
Fig. 7

Schematic diagram for computing the spatially variable image distance with flat-field linearized scan.

Fig. 8
Fig. 8

Schematic illustration of ray input in the scanner plane and ray-traced spot in the scanning plane while the input aperture moves along the x direction during optimization.

Fig. 9
Fig. 9

Optimized coefficients of nonspherical wave front at the margin of scanner and 3-D plot of the optimized wavefront.

Fig. 10
Fig. 10

Plots of the square of rms spot radius σ j 2 vs hologram coordinate x. The solid line corresponds to an optimized scanner and the dashed line to a conventional one.

Fig. 11
Fig. 11

(a) CGH used for correction. (b) Holographic interferogram obtained by illuminating the second hologram with both the spherical and plane waves. (c) Computational interferogram which agrees with the interferogram shown in (b).

Fig. 12
Fig. 12

Top view of the geometry for making a corrected scanner. The diffracted wave from the CGH is imaged onto the second hologram plane by the telescope system. The diffracted wave from the second hologram interferes with the reference wave to form the reflection dichromated gelatin scanner shown by dashed lines.

Fig. 13
Fig. 13

Magnified scan spots from (b) the corrected reflection scanner together with those from (a) the conventional scanner. A significant improvement in the scan spots can be seen. The scan spots are displayed on half of the flat scanning plane, for simplicity.

Fig. 14
Fig. 14

(a) Ray-trace sample aperture. Ray aberration plots vs input heights of the moving aperture in the (b) x and (c) y coordinates for θ = 16°, respectively.

Tables (2)

Tables Icon

Table I Processing Procedure of a DCG Plate

Tables Icon

Table II Scan Angles θ, Corresponding Locations (r + F) tanθ for Scan Nonlinearity, Corresponding Locations(r + F)θ for Scan Linearity, and Measured Values

Equations (25)

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( x ( θ ) r + z ( θ ) ) = ( cos θ - sin θ sin θ cos θ ) ( h ( θ ) r + F ) ,
x ( θ ) = B P ¯ = ( r + F ) ( θ cos θ - sin θ ) ,
z ( θ ) = D B ¯ = ( r + F ) ( θ sin θ + cos θ ) - r .
ϕ = ϕ t + ( ϕ o - ϕ r ) ,
ϕ ( x , y ) = 2 π λ ( F 2 + x 2 + y 2 - F + C 20 x 2 + C 40 x 4 + C 60 x 6 + C 80 x 8 + C 02 y 2 + C 04 y 4 + C 06 y 6 + C 08 y 8 + C 22 x 2 y 2 + C 44 x 4 y 4 ) ϕ S + ϕ C ,
( grad ϕ ) 2 = ( 2 π λ ν ) 2 ,
ν s = λ 2 π grad ϕ = λ 2 π ( i ϕ x + j ϕ y + k ϕ z ) ,
l i = λ 2 π ( ϕ x ) z = 0 ,
m i = λ 2 π ( ϕ y ) z = 0 ,
n i = ± 1 - l i 2 - m i 2 ,
X k j = x k j + l i L = x k j + l i n i z ( θ ) ,
Y k = y k + m i L = y k + m i n i z ( θ ) ,
L = ( x k j - X k j ) 2 + ( y k - Y k ) 2 + z 2 .
x k j = x k + 1.25 ( j - 1 ) ,
θ j = tan - 1 [ - 1.25 ( j - 1 ) / r ] .
Γ 1 = 1 20 j = 1 20 W 1 , j σ j 2 ,
σ j 2 = 1 N k = 1 N [ ( X k j - X k j ) 2 + ( Y k - Y k ) 2 ]
Γ j = j = 16 20 W 2 , j [ x ( θ j ) - X k j ] ,
Φ = j = 1 6 Γ j 2 = Γ T ( C ) Γ ( C ) ,
Γ ( C h + Γ C h ) Γ ( C h ) + J ( C h ) Δ C h ,
J ( C h ) = ( Γ 1 C 20 , , Γ 1 C 44 Γ 6 C 20 , , Γ 6 C 44 ) C = C h .
Φ ( C h + Δ C h ) Γ T ( C h ) Γ ( C h ) + 2 Γ T ( C h ) J ( C h ) Δ C h + Δ C h T J T ( C h ) J ( C h ) Δ C h .
J T ( C h ) J ( C h ) Δ C h = - J T ( C h ) Γ ( C h ) .
[ J T ( C h ) J ( C h ) + ρ I ] Δ C h = - J T ( C h ) Γ ( C h ) ,
M 2 y 1.5 × 2 × 1 2 π ( ϕ C y )

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