Abstract

We report on complete wave-front control with amplitude- and phase-modulation liquid-crystal devices (LCD’s). A twisted nematic device is used for amplitude modulation, and an electrically controlled birefringent device is used for phase modulation. Because the LCD’s are optically coupled with afocal optics and are driven by individual LCD driver circuits, the amplitude and the phase can be controlled two dimensionally and independently. Complex amplitude data are calculated, and on-axis computer-generated holograms are directly recorded. Furthermore, we discuss LCD performance requirements for high-quality reconstruction.

© 1993 Optical Society of America

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  2. H. Bartlet, “Computer-generated holographic component with optimum light efficiency,” Appl. Opt. 23, 1499–1502 (1984).
    [CrossRef]
  3. U. Efron, S. T. Wu, T. D. Bates, “Nematic liquid crystals for spatial light modulators: recent studies,” J. Opt. Soc. Am. B 3, 247–252 (1986).
    [CrossRef]
  4. T. Sonehara, O. Okumura, “A new twisted nematic ECB (TN-ECB) mode for a reflective light valve,” in Japan Display ’89 Digest (Society for Information Display, Playa del Rey, Calif., 1989), pp. 192–195.
  5. K. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
    [CrossRef]
  6. 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]
  7. J. Amako, T. Sonehara, “Kinoform using an electrically controlled liquid-crystal spatial light modulator,” Appl. Opt. 30, 4622–4628 (1991).
    [CrossRef] [PubMed]
  8. H. M. Kim, J. W. Jeong, M. H. Kang, S. I. Jeong, “Phase correction of a spatial light modulator displaying a binary phase-only filter,” Appl. Opt. 27, 4167–4168 (1988).
    [CrossRef] [PubMed]
  9. T. H. Barns, K. Matsuda, T. Eiju, K. Matsumoto, F. Johnson, “Joint transform correlator using a phase only spatial light modulator,” Jpn. J. Appl. Phys. 29, L1293–L1296 (1990).
    [CrossRef]
  10. S. Morozumi, K. Oguchi, H. Ohshima, “Liquid crystal television displays: latest developments,” Opt. Eng. 23, 241–246(1984).
  11. J. P. Allebach, N. C. Gallagher, B. Liu, “Aliasing error in digital holography,” Appl. Opt. 15, 2183–2188 (1976).
    [CrossRef] [PubMed]
  12. D. M. Cottrell, J. A. Davis, T. R. Hedman, R. A. Lilly, “Multiple imaging phase-encoded optical elements written as programmable spatial light modulator,” Appl. Opt. 29, 2505–2509 (1990).
    [CrossRef] [PubMed]
  13. D. M. Cottrell, R. A. Lilly, L. A. Davis, T. Day, “Optical correlator performance of binary phase-only filters using Fourier and Hartley transforms,” Appl. Opt. 26, 3755–3761 (1987).
    [CrossRef] [PubMed]
  14. A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
    [CrossRef]
  15. L. B. Lesem, P. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
    [CrossRef]

1991 (1)

1990 (4)

T. H. Barns, K. Matsuda, T. Eiju, K. Matsumoto, F. Johnson, “Joint transform correlator using a phase only spatial light modulator,” Jpn. J. Appl. Phys. 29, L1293–L1296 (1990).
[CrossRef]

K. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

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]

D. M. Cottrell, J. A. Davis, T. R. Hedman, R. A. Lilly, “Multiple imaging phase-encoded optical elements written as programmable spatial light modulator,” Appl. Opt. 29, 2505–2509 (1990).
[CrossRef] [PubMed]

1988 (1)

1987 (1)

1986 (1)

1984 (2)

H. Bartlet, “Computer-generated holographic component with optimum light efficiency,” Appl. Opt. 23, 1499–1502 (1984).
[CrossRef]

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

1981 (1)

A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

1976 (1)

1969 (1)

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

Allebach, J. P.

Amako, J.

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

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]

Barns, T. H.

T. H. Barns, K. Matsuda, T. Eiju, K. Matsumoto, F. Johnson, “Joint transform correlator using a phase only spatial light modulator,” Jpn. J. Appl. Phys. 29, L1293–L1296 (1990).
[CrossRef]

Bartlet, H.

Bates, T. D.

Cottrell, D. M.

Davis, J. A.

Davis, L. A.

Day, T.

Efron, U.

Eiju, T.

T. H. Barns, K. Matsuda, T. Eiju, K. Matsumoto, F. Johnson, “Joint transform correlator using a phase only spatial light modulator,” Jpn. J. Appl. Phys. 29, L1293–L1296 (1990).
[CrossRef]

Gallagher, N. C.

Hedman, T. R.

Hirsch, P.

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

Jeong, J. W.

Jeong, S. I.

Johnson, F.

T. H. Barns, K. Matsuda, T. Eiju, K. Matsumoto, F. Johnson, “Joint transform correlator using a phase only spatial light modulator,” Jpn. J. Appl. Phys. 29, L1293–L1296 (1990).
[CrossRef]

Jordan, J. A.

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

Kang, M. H.

Kim, H. M.

Lesem, L. B.

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

Lilly, R. A.

Lim, J. S.

A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

Liu, B.

Lu, K.

K. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

Matsuda, K.

T. H. Barns, K. Matsuda, T. Eiju, K. Matsumoto, F. Johnson, “Joint transform correlator using a phase only spatial light modulator,” Jpn. J. Appl. Phys. 29, L1293–L1296 (1990).
[CrossRef]

Matsumoto, K.

T. H. Barns, K. Matsuda, T. Eiju, K. Matsumoto, F. Johnson, “Joint transform correlator using a phase only spatial light modulator,” Jpn. J. Appl. Phys. 29, L1293–L1296 (1990).
[CrossRef]

Morozumi, S.

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

Oguchi, K.

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

Ohshima, H.

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

Okumura, O.

T. Sonehara, O. Okumura, “A new twisted nematic ECB (TN-ECB) mode for a reflective light valve,” in Japan Display ’89 Digest (Society for Information Display, Playa del Rey, Calif., 1989), pp. 192–195.

Oppenheim, A. V.

A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

Saleh, B. E. A.

K. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

Sonehara, T.

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

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]

T. Sonehara, O. Okumura, “A new twisted nematic ECB (TN-ECB) mode for a reflective light valve,” in Japan Display ’89 Digest (Society for Information Display, Playa del Rey, Calif., 1989), pp. 192–195.

Takeda, Y.

Y. Takeda, “Complex light spatial modulator,” U.S. patent3,890,035 (17June1975).

Wu, S. T.

Appl. Opt. (6)

IBM J. Res. Dev. (1)

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

J. Opt. Soc. Am. B (1)

Jpn. J. Appl. Phys. (2)

T. H. Barns, K. Matsuda, T. Eiju, K. Matsumoto, F. Johnson, “Joint transform correlator using a phase only spatial light modulator,” Jpn. J. Appl. Phys. 29, L1293–L1296 (1990).
[CrossRef]

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. (2)

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

K. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

Proc. IEEE (1)

A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

Other (2)

Y. Takeda, “Complex light spatial modulator,” U.S. patent3,890,035 (17June1975).

T. Sonehara, O. Okumura, “A new twisted nematic ECB (TN-ECB) mode for a reflective light valve,” in Japan Display ’89 Digest (Society for Information Display, Playa del Rey, Calif., 1989), pp. 192–195.

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Figures (11)

Fig. 1
Fig. 1

(a) LC molecular configuration on the TN LCD and (b) phase shift and amplitude transmittance versus applied voltage. ●, ■, amplitude transmittance; ○, □, phase shift. Condition 1 (●, ○): parallel polarizer system; condition 2 (■, □): crossed polarizer system. The TN LCD has an off-state twist angle of 80°.

Fig. 2
Fig. 2

(a) LC molecular configuration on the ECB LCD and (b) phase shift and amplitude transmittance versus applied voltage. ●, amplitude transmittance; ○, phase shift. The ECB LCD has an off-state molecular orientation aligned parallel to the panel faces.

Fig. 3
Fig. 3

Optical setup for the experiment. The incoherent light source used for LCD alignment is not illustrated.

Fig. 4
Fig. 4

Picture in focus on the second LCD’s screen after two LCD’s are successfully aligned. Two identical patterns are viewed, are recorded on two LCD’s separately, and are used for data registration.

Fig. 5
Fig. 5

(a) Original image (a PANDA). Optical reconstruction for contrast ratios of(b) 26:1, (c)5:1, and(d) 1:1 (phase only). A 256 × 220 pixel field on each LCD was used for recording the CGH. The number of quantizing levels was 16.

Fig. 6
Fig. 6

Optical reconstruction with quantizing levels of (a) 16, (b) 8, (c) 4, and (d) 2. A 256 × 220 pixel field on each LCD was used for recording the CGH. The contrast ratio was 26:1.

Fig. 7
Fig. 7

Reconstructed image of a three-dimensional object (a chair). Complex amplitude modulation: (a) the front slice and (b) the back slice in focus, phase-only modulation; (c) the front slice and (d) the back slice in focus. A 256 × 220 pixel field on each LCD was used for recording the CGH. Quantizing levels were 16, and the contrast ratio was 26:1.

Fig. 8
Fig. 8

Dependence of amplitude transmittance T and phase shift ϕ on the normalized applied voltage V. The functions were defined for computer simulation.

Fig. 9
Fig. 9

Relation between the function F and the contrast ratio of the TN LCD for several values of quantizing levels Q (computer simulation). The image [Fig. 4(a)] was sampled in a 64 × 64 grid. The function F provides the difference in amplitude distribution between the computed image and the original.

Fig. 10
Fig. 10

Relation between the function F and the number of quantizing levels for several values of the contrast ratio C (computer simulation). Other conditions are the same as in Fig. 9.

Fig. 11
Fig. 11

Optical reconstruction with misregistration of(a) 0, (b) 2, (c) 4, and (d) 8 pixels between the amplitude and phase data. Quantizing levels of 16 were assigned both for amplitude and phase data and contrast ratio of 26:1 was fixed. A 256 × 220 pixel field on each LCD was used for recording the CGH.

Equations (12)

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C = T max / T min ,
N / ( N + 1 ) < f 2 / f 1 < N / ( N - 1 ) ,
Z = N p 2 / λ .
A ( u ) = L ( u ) F T [ a ( x ) L ( x ) ] = A ( u ) exp [ i ϕ ( u ) ] ,
W TN = A ( u ) exp [ i Δ ϕ ( u ) ] .
W ECB = exp [ i ϕ ( u ) - i Δ ϕ ( u ) ] .
W = Σ A m ( u ) = Σ L m ( u ) FT [ a m ( x ) L m ( x ) ] ,
F = Σ a i j - a i j ,
M = f 1 f 2 / [ f 1 2 + g ( f 1 - s ) ] .
P = M p / M - 1 ,
T = 1 - sin 4 [ π ( 1 - V ) / 2 ] ( 1 - 1 / C ) ,
ϕ = π ( V + 0.01 ) 1 / 2 ,

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