Abstract

Random-phase distributions that are statistically independent individually are used for computing kinoforms. These uncorrelated kinoforms are recorded and read out sequentially by a phase-only liquid-crystal spatial light modulator, and reconstructed images with well-developed speckles are added. The fidelity of the resultant image to an original is improved as the number of additions increases. The dependence of the speckle contrast on the initial random phase and the influence of the liquid-crystal spatial light modulator’s display performance on the image quality are discussed.

© 1995 Optical Society of America

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References

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  1. J. M. Moran, “Laser machining with a holographic lens,” Appl. Opt. 10, 412–415 (1971).
    [CrossRef] [PubMed]
  2. M. Ekberg, M. Larsson, A. Bolle, S. Hard, “Nd:YAG laser machining with multilevel resist kinoforms,” Appl. Opt. 30, 3604–3606 (1991).
    [CrossRef] [PubMed]
  3. W. B. Veldkamp, “Laser beam profile shaping with interlaced binary diffraction gratings,” Appl. Opt. 21, 3209–3212 (1982).
    [CrossRef] [PubMed]
  4. L. B. Lesem, P. Hirsch, J. A. Jordan, “The kinoform: a new wave-front reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
    [CrossRef]
  5. C. Gallagher, B. Liu, “Method for computing kinoforms that reduces image reconstruction error,” Appl. Opt. 12, 2328–2335 (1973).
    [CrossRef] [PubMed]
  6. J. R. Finup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).
  7. F. Wyrowski, R. Hauck, O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 4, 1058–1065 (1988).
    [CrossRef]
  8. J. Amako, H. Miura, T. Sonehara, “Writing and reading kinoform by a phase-only LCSLM,” in Extended Abstracts of Japan Optics ’92 (Optical Society of Japan, Kyoto, 1992), p. 25–26.
  9. J. W. Goodman, “Some fundamental properties of speckles,” J. Opt. Soc. Am. 66, 1145–1150 (1976).
    [CrossRef]
  10. J. Amako, T. Sonehara, “Kinoform using an electrically controlled birefringent liquid-crystal spatial light modulator,” Appl. Opt. 30, 4622–4628 (1991).
    [CrossRef] [PubMed]
  11. A. Kozma, C. R. Christensen, “Effects of speckle on resolution,” J. Opt. Soc. Am. 66, 1257–1260 (1976).
    [CrossRef]
  12. J. W. Goodman, “Dependence of image speckle contrast on surface roughness,” Opt. Commun. 14, 324–327 (1975).
    [CrossRef]
  13. J. Ohtsubo, T. Asakura, “Statistical properties of the sum of partially developed speckle patterns,” Opt. Lett. 1, 98–100 (1977).
    [CrossRef] [PubMed]
  14. M. Bolle, S. Lazare, “Large-scale excimer-laser production of submicron periodic structures on polymer surfaces,” Appl. Surf. Sci. 69, 31–37 (1993).
    [CrossRef]

1993

M. Bolle, S. Lazare, “Large-scale excimer-laser production of submicron periodic structures on polymer surfaces,” Appl. Surf. Sci. 69, 31–37 (1993).
[CrossRef]

1991

1988

F. Wyrowski, R. Hauck, O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 4, 1058–1065 (1988).
[CrossRef]

1982

1980

J. R. Finup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).

1977

1976

1975

J. W. Goodman, “Dependence of image speckle contrast on surface roughness,” Opt. Commun. 14, 324–327 (1975).
[CrossRef]

1973

1971

1969

L. B. Lesem, P. Hirsch, J. A. Jordan, “The kinoform: a new wave-front reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

Amako, J.

J. Amako, T. Sonehara, “Kinoform using an electrically controlled birefringent liquid-crystal spatial light modulator,” Appl. Opt. 30, 4622–4628 (1991).
[CrossRef] [PubMed]

J. Amako, H. Miura, T. Sonehara, “Writing and reading kinoform by a phase-only LCSLM,” in Extended Abstracts of Japan Optics ’92 (Optical Society of Japan, Kyoto, 1992), p. 25–26.

Asakura, T.

Bolle, A.

Bolle, M.

M. Bolle, S. Lazare, “Large-scale excimer-laser production of submicron periodic structures on polymer surfaces,” Appl. Surf. Sci. 69, 31–37 (1993).
[CrossRef]

Bryngdahl, O.

F. Wyrowski, R. Hauck, O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 4, 1058–1065 (1988).
[CrossRef]

Christensen, C. R.

Ekberg, M.

Finup, J. R.

J. R. Finup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).

Gallagher, C.

Goodman, J. W.

J. W. Goodman, “Some fundamental properties of speckles,” J. Opt. Soc. Am. 66, 1145–1150 (1976).
[CrossRef]

J. W. Goodman, “Dependence of image speckle contrast on surface roughness,” Opt. Commun. 14, 324–327 (1975).
[CrossRef]

Hard, S.

Hauck, R.

F. Wyrowski, R. Hauck, O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 4, 1058–1065 (1988).
[CrossRef]

Hirsch, P.

L. B. Lesem, P. Hirsch, J. A. Jordan, “The kinoform: a new wave-front reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

Jordan, J. A.

L. B. Lesem, P. Hirsch, J. A. Jordan, “The kinoform: a new wave-front reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

Kozma, A.

Larsson, M.

Lazare, S.

M. Bolle, S. Lazare, “Large-scale excimer-laser production of submicron periodic structures on polymer surfaces,” Appl. Surf. Sci. 69, 31–37 (1993).
[CrossRef]

Lesem, L. B.

L. B. Lesem, P. Hirsch, J. A. Jordan, “The kinoform: a new wave-front reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

Liu, B.

Miura, H.

J. Amako, H. Miura, T. Sonehara, “Writing and reading kinoform by a phase-only LCSLM,” in Extended Abstracts of Japan Optics ’92 (Optical Society of Japan, Kyoto, 1992), p. 25–26.

Moran, J. M.

Ohtsubo, J.

Sonehara, T.

J. Amako, T. Sonehara, “Kinoform using an electrically controlled birefringent liquid-crystal spatial light modulator,” Appl. Opt. 30, 4622–4628 (1991).
[CrossRef] [PubMed]

J. Amako, H. Miura, T. Sonehara, “Writing and reading kinoform by a phase-only LCSLM,” in Extended Abstracts of Japan Optics ’92 (Optical Society of Japan, Kyoto, 1992), p. 25–26.

Veldkamp, W. B.

Wyrowski, F.

F. Wyrowski, R. Hauck, O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 4, 1058–1065 (1988).
[CrossRef]

Appl. Opt.

Appl. Surf. Sci.

M. Bolle, S. Lazare, “Large-scale excimer-laser production of submicron periodic structures on polymer surfaces,” Appl. Surf. Sci. 69, 31–37 (1993).
[CrossRef]

IBM J. Res. Dev.

L. B. Lesem, P. Hirsch, J. A. Jordan, “The kinoform: a new wave-front reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

F. Wyrowski, R. Hauck, O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 4, 1058–1065 (1988).
[CrossRef]

Opt. Commun.

J. W. Goodman, “Dependence of image speckle contrast on surface roughness,” Opt. Commun. 14, 324–327 (1975).
[CrossRef]

Opt. Eng.

J. R. Finup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).

Opt. Lett.

Other

J. Amako, H. Miura, T. Sonehara, “Writing and reading kinoform by a phase-only LCSLM,” in Extended Abstracts of Japan Optics ’92 (Optical Society of Japan, Kyoto, 1992), p. 25–26.

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Figures (11)

Fig. 1
Fig. 1

Experimental layout.

Fig. 2
Fig. 2

Speckle contrast, C, as a function of the number of speckle additions, N: □ denotes the binary random phase, ■ denotes the continuous random phase, and the solid line represents 1 / N. The original image was a square window.

Fig. 3
Fig. 3

Intensity profiles along the line in the reconstruction plane: the thin profile is for an image of N = 1, and the thick profile is for the average of 50 images added (N = 50).

Fig. 4
Fig. 4

Images recorded on the film: (a) N = 1, (b) N = 50.

Fig. 5
Fig. 5

Images recorded on the film: (a) the original, (b) N = 30, (c) N = 1, and (d) the image from the kinoform computed by the iterative algorithm.

Fig. 6
Fig. 6

Images recorded on the film: (a) η = 0.06 (uniform illumination, (b) η = 0.80, (c) η = 0.90, and (d) η = 0.99. The number of speckle additions was 30.

Fig. 7
Fig. 7

Number of sampling points for each of 16 phase levels (computer simulation): (a) for the binary random phase and (c) for the continuous random phase in the kinoform; (b) for the binary random phase and (d) for the continuous random phase in the reconstructed image.

Fig. 8
Fig. 8

Speckle contrast, C, as a function of the number of speckle additions, N (computer simulation): □ denotes the binary random phase, ■ denotes the continuous random phase, and the solid line represents 1 / N. The original image was the square window in Fig. 2.

Fig. 9
Fig. 9

Images obtained by computer simulation: (a) N = 1, (b) N = 50.

Fig. 10
Fig. 10

Speckle contrast, C, as a function of the number of speckle additions, N (computer simulation): □ denotes Δϕmax = 0, ■ denotes Δϕmax = π, and Δϕmax is the maximum phase error.

Fig. 11
Fig. 11

Signal-to-noise ratio, SNR, as a function of the phase error, Δϕmax (computer simulation). The number of speckle additions was 50.

Equations (8)

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K ( u , v ) = P ( F { a ( x , y ) exp [ j θ ( x , y ) ] } ) ,
D ( x , y ) = F { K m ( u , v ) K n ( u , v ) * } ,
I ( x , y ) = | F { K m ( u , v ) } | 2 .
C = σ / I = 1 / N .
η = exp [ γ ( u 2 + v 2 ) ] d u d v ,
C = [ 2 ( σ r 4 + σ i 4 ) + 4 I s σ r 2 ] 1 / 2 / ( σ r 2 + σ i 2 + I s ) ,
K m ( u , v ) = exp { j [ ϕ m ( u , v ) + Δ ϕ ( u , v ) ] } .
SNR = W / B ,

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