Abstract

A simple phase-characterization method for spatial light modulators is proposed. The low-cost method permits high-precision measurement and provides data for the setting of the spatial-light-modulator operating point in the phase-modulation mode. The dynamic phase response is used to perform efficient kinoform recording. In order to record the kinoform, we modify the global iterative coding to compute phase holograms. Finally, modified phase–phase correlation is introduced. The phase–phase correlator permits sharper correlation peaks, better energy transmission, and higher discrimination than an amplitude–phase correlation. Optical experimental results are presented.

© 1995 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
  4. K. Chalasinka-Macukow, C. Gorecki, “Optoelectronic implementation of the quasi-phase correlator,” Opt. Commun. 93, 11–18 (1992).
    [CrossRef]
  5. J. C. Kirsch, D. A Gregory, M. W. Thie, B. K. Jones, “Modulation characteristics of the Epson liquid crystal television,” Opt. Eng. 31, 963–970 (1992).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  9. S. S. Coturia, S. E. Monroe, 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, 248–256 (1992).
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    [CrossRef] [PubMed]
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    [CrossRef]
  12. J. L. Horner, “Clarification of Horner efficiency,” Appl. Opt. 31, 4629–4630 (1992).
    [CrossRef] [PubMed]
  13. T. H. Barnes, K. Matsumoto, T. Eiju, K. Matsuda, N. Ooyama, “The application of phase-only filters to optical interconnects and pattern recognition,” J. Mod. Opt. 37, 1849–1863 (1990).
    [CrossRef]
  14. J. L. Horner, J. R. Leger, “Pattern recognition with binary phase-only filters,” Appl. Opt. 24, 609–611 (1985).
    [CrossRef] [PubMed]
  15. G. Paul-Hus, Y. Sheng, “Optical on-axis real-time phase-dominant correlator using liquid crystal television,” Opt. Eng. 32, 2165–2172 (1993).
    [CrossRef]
  16. C. Soutar, S. E. Monroe, J. Knopp, “Complex characterization of the Epson liquid crystal television,” Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1959, 269–283 (1993).
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    [CrossRef]

1993 (2)

A. Bergeron, H. H. Arsenault, J. Gauvin, D. Gingras, “Computer-generated holograms improved by a global iterative coding,” Opt. Eng. 32, 2216–2226 (1993).
[CrossRef]

G. Paul-Hus, Y. Sheng, “Optical on-axis real-time phase-dominant correlator using liquid crystal television,” Opt. Eng. 32, 2165–2172 (1993).
[CrossRef]

1992 (4)

K. Chalasinka-Macukow, C. Gorecki, “Optoelectronic implementation of the quasi-phase correlator,” Opt. Commun. 93, 11–18 (1992).
[CrossRef]

J. C. Kirsch, D. A Gregory, M. W. Thie, B. K. Jones, “Modulation characteristics of the Epson liquid crystal television,” Opt. Eng. 31, 963–970 (1992).
[CrossRef]

D. A. Gregory, J. C. Kirsch, E. C. Tam, “Full complex modulation using liquid-crystal televisions,” Appl. Opt. 31, 163–165 (1992).
[CrossRef] [PubMed]

J. L. Horner, “Clarification of Horner efficiency,” Appl. Opt. 31, 4629–4630 (1992).
[CrossRef] [PubMed]

1991 (1)

1990 (2)

O. K. Ersoy, Y. Yoon, N. Keshava, D. Zimmerman, “Nonlinear matched filtering II,” Opt. Eng. 29, 1002–1012 (1990).
[CrossRef]

T. H. Barnes, K. Matsumoto, T. Eiju, K. Matsuda, N. Ooyama, “The application of phase-only filters to optical interconnects and pattern recognition,” J. Mod. Opt. 37, 1849–1863 (1990).
[CrossRef]

1988 (1)

1985 (1)

1984 (1)

1982 (1)

1964 (1)

A. VanderLugt, “Signal detection by complex filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

Amako, J.

Arsenault, H. H.

A. Bergeron, H. H. Arsenault, J. Gauvin, D. Gingras, “Computer-generated holograms improved by a global iterative coding,” Opt. Eng. 32, 2216–2226 (1993).
[CrossRef]

Barnes, T. H.

T. H. Barnes, K. Matsumoto, T. Eiju, K. Matsuda, N. Ooyama, “The application of phase-only filters to optical interconnects and pattern recognition,” J. Mod. Opt. 37, 1849–1863 (1990).
[CrossRef]

Bergeron, A.

A. Bergeron, H. H. Arsenault, J. Gauvin, D. Gingras, “Computer-generated holograms improved by a global iterative coding,” Opt. Eng. 32, 2216–2226 (1993).
[CrossRef]

Chalasinka-Macukow, K.

K. Chalasinka-Macukow, C. Gorecki, “Optoelectronic implementation of the quasi-phase correlator,” Opt. Commun. 93, 11–18 (1992).
[CrossRef]

Coturia, S. S.

S. S. Coturia, S. E. Monroe, 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, 248–256 (1992).

Eiju, T.

T. H. Barnes, K. Matsumoto, T. Eiju, K. Matsuda, N. Ooyama, “The application of phase-only filters to optical interconnects and pattern recognition,” J. Mod. Opt. 37, 1849–1863 (1990).
[CrossRef]

Ersoy, O. K.

O. K. Ersoy, Y. Yoon, N. Keshava, D. Zimmerman, “Nonlinear matched filtering II,” Opt. Eng. 29, 1002–1012 (1990).
[CrossRef]

Gauvin, J.

A. Bergeron, H. H. Arsenault, J. Gauvin, D. Gingras, “Computer-generated holograms improved by a global iterative coding,” Opt. Eng. 32, 2216–2226 (1993).
[CrossRef]

Gianino, P. D.

Gingras, D.

A. Bergeron, H. H. Arsenault, J. Gauvin, D. Gingras, “Computer-generated holograms improved by a global iterative coding,” Opt. Eng. 32, 2216–2226 (1993).
[CrossRef]

Gorecki, C.

K. Chalasinka-Macukow, C. Gorecki, “Optoelectronic implementation of the quasi-phase correlator,” Opt. Commun. 93, 11–18 (1992).
[CrossRef]

Gregory, D. A

J. C. Kirsch, D. A Gregory, M. W. Thie, B. K. Jones, “Modulation characteristics of the Epson liquid crystal television,” Opt. Eng. 31, 963–970 (1992).
[CrossRef]

Gregory, D. A.

D. A. Gregory, J. C. Kirsch, E. C. Tam, “Full complex modulation using liquid-crystal televisions,” Appl. Opt. 31, 163–165 (1992).
[CrossRef] [PubMed]

J. C. Kirsch, J. A. Loudin, D. A. Gregory, “Hybrid modulation properties of the Epson LCTV,” in Wave Propagation and Scattering in Varied Media II, V. R. Varadan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1558, 432–441 (1991).

Horner, J. L.

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, 963–970 (1992).
[CrossRef]

Keshava, N.

O. K. Ersoy, Y. Yoon, N. Keshava, D. Zimmerman, “Nonlinear matched filtering II,” Opt. Eng. 29, 1002–1012 (1990).
[CrossRef]

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, 963–970 (1992).
[CrossRef]

D. A. Gregory, J. C. Kirsch, E. C. Tam, “Full complex modulation using liquid-crystal televisions,” Appl. Opt. 31, 163–165 (1992).
[CrossRef] [PubMed]

J. C. Kirsch, J. A. Loudin, D. A. Gregory, “Hybrid modulation properties of the Epson LCTV,” in Wave Propagation and Scattering in Varied Media II, V. R. Varadan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1558, 432–441 (1991).

Knopp, J.

C. Soutar, S. E. Monroe, J. Knopp, “Complex characterization of the Epson liquid crystal television,” Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1959, 269–283 (1993).

S. S. Coturia, S. E. Monroe, 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, 248–256 (1992).

Konforti, N.

Leger, J. R.

Loudin, J. A.

J. C. Kirsch, J. A. Loudin, D. A. Gregory, “Hybrid modulation properties of the Epson LCTV,” in Wave Propagation and Scattering in Varied Media II, V. R. Varadan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1558, 432–441 (1991).

Marom, E.

Matsuda, K.

T. H. Barnes, K. Matsumoto, T. Eiju, K. Matsuda, N. Ooyama, “The application of phase-only filters to optical interconnects and pattern recognition,” J. Mod. Opt. 37, 1849–1863 (1990).
[CrossRef]

Matsumoto, K.

T. H. Barnes, K. Matsumoto, T. Eiju, K. Matsuda, N. Ooyama, “The application of phase-only filters to optical interconnects and pattern recognition,” J. Mod. Opt. 37, 1849–1863 (1990).
[CrossRef]

Monroe, S. E.

S. S. Coturia, S. E. Monroe, 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, 248–256 (1992).

C. Soutar, S. E. Monroe, J. Knopp, “Complex characterization of the Epson liquid crystal television,” Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1959, 269–283 (1993).

Ooyama, N.

T. H. Barnes, K. Matsumoto, T. Eiju, K. Matsuda, N. Ooyama, “The application of phase-only filters to optical interconnects and pattern recognition,” J. Mod. Opt. 37, 1849–1863 (1990).
[CrossRef]

Paul-Hus, G.

G. Paul-Hus, Y. Sheng, “Optical on-axis real-time phase-dominant correlator using liquid crystal television,” Opt. Eng. 32, 2165–2172 (1993).
[CrossRef]

Sheng, Y.

G. Paul-Hus, Y. Sheng, “Optical on-axis real-time phase-dominant correlator using liquid crystal television,” Opt. Eng. 32, 2165–2172 (1993).
[CrossRef]

Sonehara, T.

Soutar, C.

C. Soutar, S. E. Monroe, J. Knopp, “Complex characterization of the Epson liquid crystal television,” Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1959, 269–283 (1993).

Tam, E. C.

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, 963–970 (1992).
[CrossRef]

VanderLugt, A.

A. VanderLugt, “Signal detection by complex filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

Wu, S. T.

Yoon, Y.

O. K. Ersoy, Y. Yoon, N. Keshava, D. Zimmerman, “Nonlinear matched filtering II,” Opt. Eng. 29, 1002–1012 (1990).
[CrossRef]

Zimmerman, D.

O. K. Ersoy, Y. Yoon, N. Keshava, D. Zimmerman, “Nonlinear matched filtering II,” Opt. Eng. 29, 1002–1012 (1990).
[CrossRef]

Appl. Opt. (6)

IEEE Trans. Inf. Theory (1)

A. VanderLugt, “Signal detection by complex filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

J. Mod. Opt. (1)

T. H. Barnes, K. Matsumoto, T. Eiju, K. Matsuda, N. Ooyama, “The application of phase-only filters to optical interconnects and pattern recognition,” J. Mod. Opt. 37, 1849–1863 (1990).
[CrossRef]

Opt. Commun. (1)

K. Chalasinka-Macukow, C. Gorecki, “Optoelectronic implementation of the quasi-phase correlator,” Opt. Commun. 93, 11–18 (1992).
[CrossRef]

Opt. Eng. (4)

J. C. Kirsch, D. A Gregory, M. W. Thie, B. K. Jones, “Modulation characteristics of the Epson liquid crystal television,” Opt. Eng. 31, 963–970 (1992).
[CrossRef]

G. Paul-Hus, Y. Sheng, “Optical on-axis real-time phase-dominant correlator using liquid crystal television,” Opt. Eng. 32, 2165–2172 (1993).
[CrossRef]

O. K. Ersoy, Y. Yoon, N. Keshava, D. Zimmerman, “Nonlinear matched filtering II,” Opt. Eng. 29, 1002–1012 (1990).
[CrossRef]

A. Bergeron, H. H. Arsenault, J. Gauvin, D. Gingras, “Computer-generated holograms improved by a global iterative coding,” Opt. Eng. 32, 2216–2226 (1993).
[CrossRef]

Opt. Lett. (1)

Other (3)

C. Soutar, S. E. Monroe, J. Knopp, “Complex characterization of the Epson liquid crystal television,” Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1959, 269–283 (1993).

J. C. Kirsch, J. A. Loudin, D. A. Gregory, “Hybrid modulation properties of the Epson LCTV,” in Wave Propagation and Scattering in Varied Media II, V. R. Varadan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1558, 432–441 (1991).

S. S. Coturia, S. E. Monroe, 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, 248–256 (1992).

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Figures (10)

Fig. 1
Fig. 1

Interferometric setup for phase measurement: LCTV, liquid-crystal television; FT, Fourier transform.

Fig. 2
Fig. 2

Fringe patterns for gray levels (a) 0, (b) 10, (c) 20, and (d) 31.

Fig. 3
Fig. 3

Dynamic phase response of the LCTV.

Fig. 4
Fig. 4

Amplitude response for a phase-operation mode.

Fig. 5
Fig. 5

Global iterative coding algorithm: CGH, computer-generated hologram.

Fig. 6
Fig. 6

Original input (left) and optical reconstruction (right) of a kinoform: (a) fire symbol, 128 × 128 points; (b) space shuttle, 64 × 64 points.

Fig. 7
Fig. 7

Gray-level airplane images for the correlation experiments.

Fig. 8
Fig. 8

Correlation (a) simulations and (b) experiments: amplitude–phase (shaded) and phase–phase (white).

Fig. 9
Fig. 9

Three-dimensional plot of the theoretical amplitude–phase Space Shuttle correlation.

Fig. 10
Fig. 10

Three-dimensional plot of the theoretical phase–phase Space Shuttle correlation.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

f ( x , y ) = { 1 2 a [ ( x - Δ x 2 ) 2 + y 2 ] 1 / 2 } + ( 1 2 a { [ ( x + Δ x 2 ) 2 + x 2 ] 1 / 2 } ) .
r = ( x 2 + y 2 ) 1 / 2 ,
( r / 2 a ) = 1 , r < a ,
( r / 2 a ) = 0 , r > a .
f m ( x , y ) = A exp ( - j ϕ 2 ) { 1 2 a [ ( x - Δ x 2 ) 2 + y 2 ] 1 / 2 } + ( A + δ A ) exp ( j ϕ 2 ) ( 1 2 a { [ ( x + Δ x 2 ) 2 ] 1 / 2 } ) ,
F ( υ x , υ y ) 2 = ( a r ) 2 [ J 1 ( 2 π υ r a ) ] 2 × [ ( δ A ) 2 + ( 4 A 2 + 4 A δ A ) × cos 2 ( π υ x Δ x + ϕ 2 ) ] ,
υ x = x ν / λ f .
w p ( x , y ) = exp { j [ 2 π w o ( x , y ) A max ] } ,
W p ( u , v ) = A p ( u , v ) exp [ j ϕ p ( u , v ) ] = FT [ w p ( x , y ) ] .
W c ( u , v ) = exp [ j ϕ p ( u , v ) ] .
PCR = C ( 0 , 0 ) 2 - - C ( x , y ) 2 d x d y .

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