Abstract

We propose a new technique for generating a four-level reconfigurable phase-only hologram, using two binary phase {0, π} ferroelectric liquid-crystal spatial light modulators. The principle is based on the self-imaging properties of periodic structures operating in a Fresnel field double-diffraction system. Fractional Talbot planes are shown to be of particular interest. The problem of hologram bandwidth reduction that results from the holographic pattern replication is addressed. A trade-off between diffraction efficiency and hologram coding capacity is considered.

© 1994 Optical Society of America

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References

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  1. S. E. Broomfield, M. A. A. Neil, E. G. S. Paige, G. G. Yang, Electron. Lett. 28, 26 (1992).
    [CrossRef]
  2. M. O. Freeman, T. A. Brown, D. M. Walba, Appl. Opt. 31, 3917 (1992).
    [CrossRef] [PubMed]
  3. T. D. Wilkinson, D. C. O’Brien, R. J. Mears, Opt. Commun. 109, 222 (1994).
    [CrossRef]
  4. S. E. Broomfield, M. A. A. Neil, E. G. S. Paige, “A four-level, phase-only spatial light modulator,” submitted toElectron. Lett.
  5. A. Lohmann, J. A. Thomas, Appl. Opt. 29, 4337 (1990).
    [CrossRef] [PubMed]
  6. K. Patorski, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol. 27, pp. 1–110.
    [CrossRef]
  7. J. T. Winthrop, C. R. Worthington, J. Opt. Soc. Am. 55, 373 (1965).
    [CrossRef]

1994 (1)

T. D. Wilkinson, D. C. O’Brien, R. J. Mears, Opt. Commun. 109, 222 (1994).
[CrossRef]

1992 (2)

S. E. Broomfield, M. A. A. Neil, E. G. S. Paige, G. G. Yang, Electron. Lett. 28, 26 (1992).
[CrossRef]

M. O. Freeman, T. A. Brown, D. M. Walba, Appl. Opt. 31, 3917 (1992).
[CrossRef] [PubMed]

1990 (1)

1965 (1)

Broomfield, S. E.

S. E. Broomfield, M. A. A. Neil, E. G. S. Paige, G. G. Yang, Electron. Lett. 28, 26 (1992).
[CrossRef]

S. E. Broomfield, M. A. A. Neil, E. G. S. Paige, “A four-level, phase-only spatial light modulator,” submitted toElectron. Lett.

Brown, T. A.

Freeman, M. O.

Lohmann, A.

Mears, R. J.

T. D. Wilkinson, D. C. O’Brien, R. J. Mears, Opt. Commun. 109, 222 (1994).
[CrossRef]

Neil, M. A. A.

S. E. Broomfield, M. A. A. Neil, E. G. S. Paige, G. G. Yang, Electron. Lett. 28, 26 (1992).
[CrossRef]

S. E. Broomfield, M. A. A. Neil, E. G. S. Paige, “A four-level, phase-only spatial light modulator,” submitted toElectron. Lett.

O’Brien, D. C.

T. D. Wilkinson, D. C. O’Brien, R. J. Mears, Opt. Commun. 109, 222 (1994).
[CrossRef]

Paige, E. G. S.

S. E. Broomfield, M. A. A. Neil, E. G. S. Paige, G. G. Yang, Electron. Lett. 28, 26 (1992).
[CrossRef]

S. E. Broomfield, M. A. A. Neil, E. G. S. Paige, “A four-level, phase-only spatial light modulator,” submitted toElectron. Lett.

Patorski, K.

K. Patorski, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol. 27, pp. 1–110.
[CrossRef]

Thomas, J. A.

Walba, D. M.

Wilkinson, T. D.

T. D. Wilkinson, D. C. O’Brien, R. J. Mears, Opt. Commun. 109, 222 (1994).
[CrossRef]

Winthrop, J. T.

Worthington, C. R.

Yang, G. G.

S. E. Broomfield, M. A. A. Neil, E. G. S. Paige, G. G. Yang, Electron. Lett. 28, 26 (1992).
[CrossRef]

Appl. Opt. (2)

Electron. Lett. (1)

S. E. Broomfield, M. A. A. Neil, E. G. S. Paige, G. G. Yang, Electron. Lett. 28, 26 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

T. D. Wilkinson, D. C. O’Brien, R. J. Mears, Opt. Commun. 109, 222 (1994).
[CrossRef]

Other (2)

S. E. Broomfield, M. A. A. Neil, E. G. S. Paige, “A four-level, phase-only spatial light modulator,” submitted toElectron. Lett.

K. Patorski, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol. 27, pp. 1–110.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Quarter-Talbot four-level equivalent hologram.

Fig. 2
Fig. 2

One pixel inversion over one period of Hd. Hd, periodic hologram; H′, constraint-free hologram; Hl, additional distribution resulting from one inversion.

Fig. 3
Fig. 3

(a) Four-level hologram resulting from two {0, π} holograms, (b) pure four-level hologram.

Equations (8)

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U ( u ) = m C m exp ( i 2 π m u / d ) ,
U ( u , z ) = C 0 + m 0 C m , z exp ( i 2 π m u / d ) , C m , z = C m exp ( - 2 π m 2 z Z T ) .
C m , Z T 4 = C m exp ( - i π m 2 / 2 ) .
H d ( u , Z T 4 ) = C 0 + m 0 C 2 m exp ( i 4 π m u / d ) + exp ( - i π 2 ) m C 2 m + 1 exp [ i 2 π ( 2 m + 1 ) u / d ] .
[ exp ( - i π 4 ) + exp ( i π 4 ) ] / 2 = 1 ,
H d ( u , Z T 4 ) = 1 2 [ exp ( - i π 4 ) H d ( u ) + exp ( i π 4 ) H d ( u - d 2 ) ] .
z = Z T 4 = 3 Z T 1 4 = 5 Z T 2 4 = = ( 2 k + 1 ) Z T k 4 .
d > d 1 > d 2 > > d k ,             d k = d 2 k + 1 .

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