Abstract

A programmable kinoform using an electrically controlled birefringent liquid-crystal spatial modulator (ECB-LCSLM) is discussed. The LCSLM is capable of continuous phase modulation from 0 to 2π. For the kinoform generation, the phase distribution is calculated by iterative methods and recorded on the LCSLM with 16 quantizing levels. We discuss the characteristics and the structure of the LCSLM for the implementation of the programmable kinoform while comparing the computed results and optical reconstructions.

© 1991 Optical Society of America

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References

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  1. F. Mok, J. Diep, H. K. Liu, D. Psaltis, “Real-time computer-generated hologram by means of liquid-crystal television spatial light modulator,” Opt. Lett. 11, 748–750 (1986).
    [CrossRef] [PubMed]
  2. J. A. Davis, G. M. Heissenberger, R. A. Lilly, D. M. Cottrell, M. F. Brownell, “High efficiency optical reconstruction of binary phase-only filters using the Hughes liquid crystal light valve,” Appl. Opt. 26, 929–933 (1987).
    [CrossRef] [PubMed]
  3. J. Amako, T. Sonehara, “Computer-generated hologram using TFT active matrix liquid crystal spatial light modulator (TFT-LCSLM),” Jpn. J. Appl. Phys. 29, L1533–L1535 (1990).
    [CrossRef]
  4. N. Konforti, E. Marom, S. T. Wu, “Phase-only modulation with twisted nematic liquid crystal spatial modulators,” Opt. Lett. 13, 251 (1988).
    [CrossRef] [PubMed]
  5. L. B. Lesen, P. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150 (1969).
    [CrossRef]
  6. N. C. Gallagher, B. Liu, “Method for computing kinoforms that reduces image reconstruction error,” Appl. Opt. 12, 232 (1973).
    [CrossRef]
  7. J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).
    [CrossRef]
  8. S. Morozumi, K. Oguchi, H. Ohshima, “Liquid crystal television displays: latest developments,” Opt. Eng. 23, 241–246 (1984).
    [CrossRef]
  9. S. Morozumi, T. Sonehara, H. Kamakura, T. Ono, S. Aruga, “LCD full-color video projector,” in SID'86 Digest (Society for Information Display, Playa del Rey, Calif., 1986), p. 375.

1990

J. Amako, T. Sonehara, “Computer-generated hologram using TFT active matrix liquid crystal spatial light modulator (TFT-LCSLM),” Jpn. J. Appl. Phys. 29, L1533–L1535 (1990).
[CrossRef]

1988

1987

1986

1984

S. Morozumi, K. Oguchi, H. Ohshima, “Liquid crystal television displays: latest developments,” Opt. Eng. 23, 241–246 (1984).
[CrossRef]

1980

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

1973

1969

L. B. Lesen, P. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Amako, J.

J. Amako, T. Sonehara, “Computer-generated hologram using TFT active matrix liquid crystal spatial light modulator (TFT-LCSLM),” Jpn. J. Appl. Phys. 29, L1533–L1535 (1990).
[CrossRef]

Aruga, S.

S. Morozumi, T. Sonehara, H. Kamakura, T. Ono, S. Aruga, “LCD full-color video projector,” in SID'86 Digest (Society for Information Display, Playa del Rey, Calif., 1986), p. 375.

Brownell, M. F.

Cottrell, D. M.

Davis, J. A.

Diep, J.

Fienup, J. R.

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

Gallagher, N. C.

Heissenberger, G. M.

Hirsch, P.

L. B. Lesen, P. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Jordan, J. A.

L. B. Lesen, P. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Kamakura, H.

S. Morozumi, T. Sonehara, H. Kamakura, T. Ono, S. Aruga, “LCD full-color video projector,” in SID'86 Digest (Society for Information Display, Playa del Rey, Calif., 1986), p. 375.

Konforti, N.

Lesen, L. B.

L. B. Lesen, P. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Lilly, R. A.

Liu, B.

Liu, H. K.

Marom, E.

Mok, F.

Morozumi, S.

S. Morozumi, K. Oguchi, H. Ohshima, “Liquid crystal television displays: latest developments,” Opt. Eng. 23, 241–246 (1984).
[CrossRef]

S. Morozumi, T. Sonehara, H. Kamakura, T. Ono, S. Aruga, “LCD full-color video projector,” in SID'86 Digest (Society for Information Display, Playa del Rey, Calif., 1986), p. 375.

Oguchi, K.

S. Morozumi, K. Oguchi, H. Ohshima, “Liquid crystal television displays: latest developments,” Opt. Eng. 23, 241–246 (1984).
[CrossRef]

Ohshima, H.

S. Morozumi, K. Oguchi, H. Ohshima, “Liquid crystal television displays: latest developments,” Opt. Eng. 23, 241–246 (1984).
[CrossRef]

Ono, T.

S. Morozumi, T. Sonehara, H. Kamakura, T. Ono, S. Aruga, “LCD full-color video projector,” in SID'86 Digest (Society for Information Display, Playa del Rey, Calif., 1986), p. 375.

Psaltis, D.

Sonehara, T.

J. Amako, T. Sonehara, “Computer-generated hologram using TFT active matrix liquid crystal spatial light modulator (TFT-LCSLM),” Jpn. J. Appl. Phys. 29, L1533–L1535 (1990).
[CrossRef]

S. Morozumi, T. Sonehara, H. Kamakura, T. Ono, S. Aruga, “LCD full-color video projector,” in SID'86 Digest (Society for Information Display, Playa del Rey, Calif., 1986), p. 375.

Wu, S. T.

Appl. Opt.

IBM J. Res. Dev.

L. B. Lesen, P. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Jpn. J. Appl. Phys.

J. Amako, T. Sonehara, “Computer-generated hologram using TFT active matrix liquid crystal spatial light modulator (TFT-LCSLM),” Jpn. J. Appl. Phys. 29, L1533–L1535 (1990).
[CrossRef]

Opt. Eng.

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

S. Morozumi, K. Oguchi, H. Ohshima, “Liquid crystal television displays: latest developments,” Opt. Eng. 23, 241–246 (1984).
[CrossRef]

Opt. Lett.

Other

S. Morozumi, T. Sonehara, H. Kamakura, T. Ono, S. Aruga, “LCD full-color video projector,” in SID'86 Digest (Society for Information Display, Playa del Rey, Calif., 1986), p. 375.

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Figures (11)

Fig. 1
Fig. 1

(a) Overview of the LCSLM, (b) its pixel structure.

Fig. 2
Fig. 2

Phase shift and transmittance versus applied voltage: ○ phase shift; ●, transmittance. The LCSLM was in the ECB mode with the off-state molecular orientation aligned parallel to the panel faces.

Fig. 3
Fig. 3

Phase distribution and Fraunhofer diffraction pattern of the grating recorded on the LCSLM. The quantizing levels are (a) 2, (b) 4, (c) 8, and (d) 16. One grating period is marked with the letter d. Dead regions between the pixels are omitted in the drawings of the phase functions.

Fig. 4
Fig. 4

Range of the computed image intensity versus the number of iterations. A binary image (a bird) was sampled on a 128 × 128 grid: dashed curves, 2 quantizing levels; solid curves, 16 quantizing levels.

Fig. 5
Fig. 5

(a), (c) Kinoform of the binary image (a bird); (b), (d) its optical reconstruction. A 128 × 128 pixel field was used to record the kinoform on the LCSLM. The quantizing levels were (a), (b) 2 and (c), (d) 16.

Fig. 6
Fig. 6

Range of the computed image intensity versus the number of iterations. A binary image of 1 × 13 spots was sampled on a 128 × 128 grid. The number of quantizing levels was 16.

Fig. 7
Fig. 7

(a) Reconstructed image of 1 × 13 spots, (b) the intensity profile in the output plane. A 128 × 128 pixel field was used to record the kinoform.

Fig. 8
Fig. 8

Range of the computed image intensity versus the number of iterations. A binary image of 13 × 13 spots was used. The other conditions are the same as those in Fig. 6.

Fig. 9
Fig. 9

(a) Reconstructed image of 13 × 13 spots, (b) the intensity profile in the output plane (including the spot of the zero order). The other conditions are the same as in Fig. 7.

Fig. 10
Fig. 10

Reconstructed image from the kinoform with a random phase error (computer simulation). The amplitudes of the phase error are (a) 0, (b) 2π/16, (c) 2π/8, and (d) 2π/4.

Fig. 11
Fig. 11

Range of the computed image intensity versus the number of quantizing levels. The binary image of 13 × 13 spots in Fig. 8 was used and the number of iterations is 50.

Equations (5)

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η m = sinc 2 ( π m / Q ) | k = 1 Q exp [ i ( ϕ 2 π m ) k / Q ] / Q | 2 ,
G k ( u ) = | G k ( u ) | exp [ i ϕ k ( u ) ] ,
G k ( u ) = A k exp [ i ϕ k ( u ) ] .
g k + 1 = | f ( x ) | g k ( x ) / | g k ( x ) | ,
g k + 1 = g k ( x ) + β [ | f ( x ) | g k ( x ) / | g k ( x ) | g k ( x ) ] + β [ | f ( x ) | g k ( x ) / | g k ( x ) | | f ( x ) | g k ( x ) / | g k ( x ) | ] .

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