Abstract

Commercial twisted nematic liquid-crystal television provides coupled phase and amplitude modulation. We propose a simple wedged shear plate interferometer for in situ measurement of its phase modulation and operating curve. For a given operating curve, the coupled-mode modulation holograms are designed with an iterative method. We adjust the operating curve by rotating the polarizer and analyzer to obtain the optimal operating curve. The phase-mostly holograms yield good-quality reconstructed images with the zero-order spot reduced to a minimum. Experimental results are shown.

© 1995 Optical Society of America

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References

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  1. N. Konforti, E. Maron, S. T. Wu, “Phase-only modulation with twisted nematic liquid-crystal spatial light modulator,” Opt. Lett. 13, 251–253 (1988).
    [CrossRef] [PubMed]
  2. Y. Sheng, G. Paul-Hus, “Optical on-axis imperfect phase-only correlator using liquid-crystal television,” Appl. Opt. 32, 5782–5785 (1993).
    [CrossRef] [PubMed]
  3. S. S. Cotariu, S. E. Monoroe, J. Knopp, “A live input, live filter, liquid crystal correlator,” in Advances in Optical Information Processing V, D. R. Pape, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1704, 248–253 (1992).
  4. Y. Sheng, D. Roberge, H. Szu, T. Lu, “Optical wavelet matched filters for shift-invariant pattern recognition,” Opt. Lett. 18, 299–301 (1993).
    [CrossRef] [PubMed]
  5. D. Roberge, Y. Sheng, “Optical implementation of the phase-only composite filter using liquid crystal television,” in Optical Pattern Recognition V, D. P. Casasent, Tien-Hsin Chao, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2237, 196–203 (1994).
  6. R. Juday, “Correlation with a spatial light modulator having phase and amplitude cross coupling,” Appl. Opt. 28, 4865–4869 (1989).
    [CrossRef] [PubMed]
  7. J. L. Pezzaniti, R. A. Chipman, “Phase-only modulation of a twisted nematic liquid-crystal TV by use of the eigenpolarization states,” Opt. Lett. 18, 1567–1569 (1993).
    [CrossRef] [PubMed]
  8. E. Tam, F. T. S. Yu, A. Tanone, S. Wu, D. Gregory, “Implementation of kinoforms using a continuous-phase spatial light modulator,” in OSA Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 259.
  9. A. Tanone, Z. Zhang, C. M. Uang, F. T. S. Yu, D. A. Gregory, “Phase modulation depth for a real-time kinoform using a liquid crystal television,” Opt. Eng. 32, 517–521 (1993).
    [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. C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
    [CrossRef]
  12. J. C. Kirsch, D. A. Gregory, M. W. Thie, B. K. Jones, “Modulation characteristics of the Epson liquid crystal television,” Opt. Eng. 31, 963–969 (1992).
    [CrossRef]
  13. K. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial light modulator,” Opt. Eng. 29, 240–245 (1990).
    [CrossRef]
  14. J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).
  15. F. Wyrowski, “Diffractive optical elements: iterative calculation of quantized, blazed phase structures,” J. Opt. Soc. Am. A. 7, 961–969 (1990).
    [CrossRef]

1994

C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
[CrossRef]

1993

1992

J. C. Kirsch, D. A. Gregory, M. W. Thie, B. K. Jones, “Modulation characteristics of the Epson liquid crystal television,” Opt. Eng. 31, 963–969 (1992).
[CrossRef]

1991

1990

F. Wyrowski, “Diffractive optical elements: iterative calculation of quantized, blazed phase structures,” J. Opt. Soc. Am. A. 7, 961–969 (1990).
[CrossRef]

K. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial light modulator,” Opt. Eng. 29, 240–245 (1990).
[CrossRef]

1989

1988

1980

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

Amako, J.

Chipman, R. A.

Cotariu, S. S.

S. S. Cotariu, S. E. Monoroe, J. Knopp, “A live input, live filter, liquid crystal correlator,” in Advances in Optical Information Processing V, D. R. Pape, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1704, 248–253 (1992).

Fienup, J. R.

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

Gregory, D.

E. Tam, F. T. S. Yu, A. Tanone, S. Wu, D. Gregory, “Implementation of kinoforms using a continuous-phase spatial light modulator,” in OSA Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 259.

Gregory, D. A.

A. Tanone, Z. Zhang, C. M. Uang, F. T. S. Yu, D. A. Gregory, “Phase modulation depth for a real-time kinoform using a liquid crystal television,” Opt. Eng. 32, 517–521 (1993).
[CrossRef]

J. C. Kirsch, D. A. Gregory, M. W. Thie, B. K. Jones, “Modulation characteristics of the Epson liquid crystal television,” Opt. Eng. 31, 963–969 (1992).
[CrossRef]

Jones, B. K.

J. C. Kirsch, D. A. Gregory, M. W. Thie, B. K. Jones, “Modulation characteristics of the Epson liquid crystal television,” Opt. Eng. 31, 963–969 (1992).
[CrossRef]

Juday, R.

Kirsch, J. C.

J. C. Kirsch, D. A. Gregory, M. W. Thie, B. K. Jones, “Modulation characteristics of the Epson liquid crystal television,” Opt. Eng. 31, 963–969 (1992).
[CrossRef]

Knopp, J.

S. S. Cotariu, S. E. Monoroe, J. Knopp, “A live input, live filter, liquid crystal correlator,” in Advances in Optical Information Processing V, D. R. Pape, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1704, 248–253 (1992).

Konforti, N.

Lu, K.

C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
[CrossRef]

K. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial light modulator,” Opt. Eng. 29, 240–245 (1990).
[CrossRef]

Lu, T.

Maron, E.

Monoroe, S. E.

S. S. Cotariu, S. E. Monoroe, J. Knopp, “A live input, live filter, liquid crystal correlator,” in Advances in Optical Information Processing V, D. R. Pape, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1704, 248–253 (1992).

Paul-Hus, G.

Pezzaniti, J. L.

Roberge, D.

Y. Sheng, D. Roberge, H. Szu, T. Lu, “Optical wavelet matched filters for shift-invariant pattern recognition,” Opt. Lett. 18, 299–301 (1993).
[CrossRef] [PubMed]

D. Roberge, Y. Sheng, “Optical implementation of the phase-only composite filter using liquid crystal television,” in Optical Pattern Recognition V, D. P. Casasent, Tien-Hsin Chao, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2237, 196–203 (1994).

Saleh, B. E. A.

K. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial light modulator,” Opt. Eng. 29, 240–245 (1990).
[CrossRef]

Sheng, Y.

Y. Sheng, G. Paul-Hus, “Optical on-axis imperfect phase-only correlator using liquid-crystal television,” Appl. Opt. 32, 5782–5785 (1993).
[CrossRef] [PubMed]

Y. Sheng, D. Roberge, H. Szu, T. Lu, “Optical wavelet matched filters for shift-invariant pattern recognition,” Opt. Lett. 18, 299–301 (1993).
[CrossRef] [PubMed]

D. Roberge, Y. Sheng, “Optical implementation of the phase-only composite filter using liquid crystal television,” in Optical Pattern Recognition V, D. P. Casasent, Tien-Hsin Chao, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2237, 196–203 (1994).

Sonehara, T.

Soutar, C.

C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
[CrossRef]

Szu, H.

Tam, E.

E. Tam, F. T. S. Yu, A. Tanone, S. Wu, D. Gregory, “Implementation of kinoforms using a continuous-phase spatial light modulator,” in OSA Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 259.

Tanone, A.

A. Tanone, Z. Zhang, C. M. Uang, F. T. S. Yu, D. A. Gregory, “Phase modulation depth for a real-time kinoform using a liquid crystal television,” Opt. Eng. 32, 517–521 (1993).
[CrossRef]

E. Tam, F. T. S. Yu, A. Tanone, S. Wu, D. Gregory, “Implementation of kinoforms using a continuous-phase spatial light modulator,” in OSA Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 259.

Thie, M. W.

J. C. Kirsch, D. A. Gregory, M. W. Thie, B. K. Jones, “Modulation characteristics of the Epson liquid crystal television,” Opt. Eng. 31, 963–969 (1992).
[CrossRef]

Uang, C. M.

A. Tanone, Z. Zhang, C. M. Uang, F. T. S. Yu, D. A. Gregory, “Phase modulation depth for a real-time kinoform using a liquid crystal television,” Opt. Eng. 32, 517–521 (1993).
[CrossRef]

Wu, S.

E. Tam, F. T. S. Yu, A. Tanone, S. Wu, D. Gregory, “Implementation of kinoforms using a continuous-phase spatial light modulator,” in OSA Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 259.

Wu, S. T.

Wyrowski, F.

F. Wyrowski, “Diffractive optical elements: iterative calculation of quantized, blazed phase structures,” J. Opt. Soc. Am. A. 7, 961–969 (1990).
[CrossRef]

Yu, F. T. S.

A. Tanone, Z. Zhang, C. M. Uang, F. T. S. Yu, D. A. Gregory, “Phase modulation depth for a real-time kinoform using a liquid crystal television,” Opt. Eng. 32, 517–521 (1993).
[CrossRef]

E. Tam, F. T. S. Yu, A. Tanone, S. Wu, D. Gregory, “Implementation of kinoforms using a continuous-phase spatial light modulator,” in OSA Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 259.

Zhang, Z.

A. Tanone, Z. Zhang, C. M. Uang, F. T. S. Yu, D. A. Gregory, “Phase modulation depth for a real-time kinoform using a liquid crystal television,” Opt. Eng. 32, 517–521 (1993).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A.

F. Wyrowski, “Diffractive optical elements: iterative calculation of quantized, blazed phase structures,” J. Opt. Soc. Am. A. 7, 961–969 (1990).
[CrossRef]

Opt. Eng.

A. Tanone, Z. Zhang, C. M. Uang, F. T. S. Yu, D. A. Gregory, “Phase modulation depth for a real-time kinoform using a liquid crystal television,” Opt. Eng. 32, 517–521 (1993).
[CrossRef]

C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
[CrossRef]

J. C. Kirsch, D. A. Gregory, M. W. Thie, B. K. Jones, “Modulation characteristics of the Epson liquid crystal television,” Opt. Eng. 31, 963–969 (1992).
[CrossRef]

K. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial light modulator,” Opt. Eng. 29, 240–245 (1990).
[CrossRef]

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

Opt. Lett.

Other

S. S. Cotariu, S. E. Monoroe, J. Knopp, “A live input, live filter, liquid crystal correlator,” in Advances in Optical Information Processing V, D. R. Pape, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1704, 248–253 (1992).

D. Roberge, Y. Sheng, “Optical implementation of the phase-only composite filter using liquid crystal television,” in Optical Pattern Recognition V, D. P. Casasent, Tien-Hsin Chao, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2237, 196–203 (1994).

E. Tam, F. T. S. Yu, A. Tanone, S. Wu, D. Gregory, “Implementation of kinoforms using a continuous-phase spatial light modulator,” in OSA Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 259.

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Figures (6)

Fig. 1
Fig. 1

Wedged shear plate interferometer that measures the phase modulation of the LCTV.

Fig. 2
Fig. 2

Interference in the wedge shear plate interferometer. Regions a and c show interference of two wave fronts with the same gray levels. Region b shows interference of two wave fronts with different gray levels.

Fig. 3
Fig. 3

Operating curves of the coupled-mode LCTV measured in the system shown in Fig. 1, where g is the gray level.

Fig. 4
Fig. 4

Theoretical complex transmittance of the LCTV obtained from Eqs. (1)(4), modified for twist angle α = 80.9°.

Fig. 5
Fig. 5

Diffraction intensity distribution of a phase-mostly grating on the coupled-mode LCTV with ψ1 = 16° and ψ2 = 76°.

Fig. 6
Fig. 6

Reconstructed images from the coupled-mode LCTV with ψ1 = 16° and ψ2 = 76°. The image of the space shuttle is the impulse response of the phase-mostly filter, and the other images are reconstructed from the kinoforms generated by the iterative method.

Equations (11)

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T = [ π 2 γ sin γ cos ( ψ 1 - ψ 2 ) + cos γ sin ( ψ 1 - ψ 2 ) ] 2 + [ β γ sin γ sin ( ψ 1 + ψ 2 ) ] 2 ,
δ = β - tan - 1 [ β γ sin γ sin ( ψ 1 + ψ 2 ) π 2 γ sin γ cos ( ψ 1 - ψ 2 ) + cos γ sin ( ψ 1 - ψ 2 ) ] ,
β = π d λ [ n e ( θ ) - n o ] ,
γ = [ ( π 2 ) 2 + β 2 ] 1 / 2 ,
δ = β + tan - 1 [ β γ tan ( γ ) ]
t = [ 1 - ( π 2 γ ) 2 sin 2 ( γ ) ] 1 / 2 .
t = ξ cos δ + ( R 2 - ξ 2 sin 2 δ ) 1 / 2 .
e i = [ f ( x ) 2 - λ i h i ( x ) 2 ] d x ,
λ i = f ( x ) h i ( x ) d x h i ( x ) 2 d x .
F ( u ) = m = - α m exp [ j m ϕ ( u ) ] ,
α m = 1 2 π 0 2 π { A ( ϕ ) exp [ j ϕ ( ϕ ) ] } exp ( - j m ϕ ) d ϕ ,

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