Abstract

A three-dimensional holographic image is deteriorated due to quantization of the phase in the hologram. As in two-dimensional Fourier holograms, the deterioration is exhibited as a superposition of false images. However, in the three-dimensional case, the false images fall at depth positions other than the plane of the image to which they correspond. If far out of focus, these false images are harmless.

© 1972 Optical Society of America

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References

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  1. B. R. Brown, A. W. Lohmann, Appl. Opt. 5, 967 (1966).
    [CrossRef] [PubMed]
  2. B. R. Brown, A. W. Lohmann, IBM J. Res. Dev. 13, 150 (1969).
    [CrossRef]
  3. A. W. Lohmann, D. P. Paris, Appl. Opt. 6, 1746 (1967).
  4. T. S. Huang, J. Opto-Electron. 1, 49 (1969).
    [CrossRef]
  5. T. S. Huang, G. Anderson, in Proc. 1969 Spring Joint Computer Conference (AFIPS Press, Boston, 1969), Vol. 34, p. 173.
  6. H. Dammann, Phys. Lett. 29A, 301 (1969).
  7. R. A. Gabel, B. Liu, Appl. Opt. 9, 1180 (1970).
    [CrossRef] [PubMed]
  8. H. Dammann, Optik 31, 95 (1970).
  9. J. W. Goodman, A. M. Silvestri, IBM J. Res. Dev. 14, 478 (1970).
    [CrossRef]
  10. Y. Aoki, Proc. IEEE 58, 1856 (1970).
    [CrossRef]
  11. H. Dammann, J. Opt. Soc. Am. 60, 1635 (1970).
    [CrossRef]
  12. W. J. Dallas, Appl. Opt. 10, 674 (1971).
    [CrossRef] [PubMed]
  13. M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1965), pp. 382–386.
  14. W. J. Dallas, Appl. Opt. 10, 673 (1971).
    [CrossRef] [PubMed]
  15. O. Bryngdahl, A. W. Lohmann, J. Opt. Soc. Am. 58, 1325 (1968).
    [CrossRef]

1971 (2)

1970 (5)

R. A. Gabel, B. Liu, Appl. Opt. 9, 1180 (1970).
[CrossRef] [PubMed]

H. Dammann, Optik 31, 95 (1970).

J. W. Goodman, A. M. Silvestri, IBM J. Res. Dev. 14, 478 (1970).
[CrossRef]

Y. Aoki, Proc. IEEE 58, 1856 (1970).
[CrossRef]

H. Dammann, J. Opt. Soc. Am. 60, 1635 (1970).
[CrossRef]

1969 (3)

B. R. Brown, A. W. Lohmann, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

T. S. Huang, J. Opto-Electron. 1, 49 (1969).
[CrossRef]

H. Dammann, Phys. Lett. 29A, 301 (1969).

1968 (1)

1967 (1)

A. W. Lohmann, D. P. Paris, Appl. Opt. 6, 1746 (1967).

1966 (1)

Anderson, G.

T. S. Huang, G. Anderson, in Proc. 1969 Spring Joint Computer Conference (AFIPS Press, Boston, 1969), Vol. 34, p. 173.

Aoki, Y.

Y. Aoki, Proc. IEEE 58, 1856 (1970).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1965), pp. 382–386.

Brown, B. R.

B. R. Brown, A. W. Lohmann, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

B. R. Brown, A. W. Lohmann, Appl. Opt. 5, 967 (1966).
[CrossRef] [PubMed]

Bryngdahl, O.

Dallas, W. J.

Dammann, H.

H. Dammann, J. Opt. Soc. Am. 60, 1635 (1970).
[CrossRef]

H. Dammann, Optik 31, 95 (1970).

H. Dammann, Phys. Lett. 29A, 301 (1969).

Gabel, R. A.

Goodman, J. W.

J. W. Goodman, A. M. Silvestri, IBM J. Res. Dev. 14, 478 (1970).
[CrossRef]

Huang, T. S.

T. S. Huang, J. Opto-Electron. 1, 49 (1969).
[CrossRef]

T. S. Huang, G. Anderson, in Proc. 1969 Spring Joint Computer Conference (AFIPS Press, Boston, 1969), Vol. 34, p. 173.

Liu, B.

Lohmann, A. W.

B. R. Brown, A. W. Lohmann, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

O. Bryngdahl, A. W. Lohmann, J. Opt. Soc. Am. 58, 1325 (1968).
[CrossRef]

A. W. Lohmann, D. P. Paris, Appl. Opt. 6, 1746 (1967).

B. R. Brown, A. W. Lohmann, Appl. Opt. 5, 967 (1966).
[CrossRef] [PubMed]

Paris, D. P.

A. W. Lohmann, D. P. Paris, Appl. Opt. 6, 1746 (1967).

Silvestri, A. M.

J. W. Goodman, A. M. Silvestri, IBM J. Res. Dev. 14, 478 (1970).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1965), pp. 382–386.

Appl. Opt. (5)

IBM J. Res. Dev. (2)

J. W. Goodman, A. M. Silvestri, IBM J. Res. Dev. 14, 478 (1970).
[CrossRef]

B. R. Brown, A. W. Lohmann, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opto-Electron. (1)

T. S. Huang, J. Opto-Electron. 1, 49 (1969).
[CrossRef]

Optik (1)

H. Dammann, Optik 31, 95 (1970).

Phys. Lett. (1)

H. Dammann, Phys. Lett. 29A, 301 (1969).

Proc. IEEE (1)

Y. Aoki, Proc. IEEE 58, 1856 (1970).
[CrossRef]

Other (2)

T. S. Huang, G. Anderson, in Proc. 1969 Spring Joint Computer Conference (AFIPS Press, Boston, 1969), Vol. 34, p. 173.

M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1965), pp. 382–386.

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Figures (4)

Fig. 1
Fig. 1

Reconstruction setup.

Fig. 2
Fig. 2

Two-level phase quantized binary hologram.

Fig. 3
Fig. 3

Two-level quantization: intensity distributions in planes (a) (false image) z = −Δz; (b) z = 0; (c) z = +Δz.

Fig. 4
Fig. 4

Three-level quantization: intensity distributions in planes (a) z = −2Δz; (b) z = +Δz.

Equations (7)

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G F ( μ , ν ) = G F ( μ , ν ) exp [ i ϕ F ( μ , ν ) ] = - g ( x , y ) exp [ - 2 π i ( μ x + ν y ) ] d x d y ,
G ( μ , ν ) = G F ( μ , ν ) exp [ i ϕ ( μ , ν ) ] = G F ( μ , ν ) exp [ i ϕ F ( μ , ν ) ] exp [ i π Δ z λ ( μ 2 + ν 2 ) ] .
G ^ ( μ , ν ) = m = - C m G m ( μ , ν ) , C m = [ ( - 1 ) m / ( m N + 1 ) ] sinc ( 1 / N ) , G m = G F ( μ , ν ) exp [ i ( m N + 1 ) ϕ ( μ , ν ) ] ,
g ^ ( x , y ) = m = - C m g m ( x , y ) .
ϕ M ( μ , ν ) = ( m N + 1 ) ϕ F ( μ , ν ) + ( m N + 1 ) Δ z π λ ( μ 2 + ν 2 ) .
g ^ sinc ( 1 2 ) [ g 0 ( x , y , Δ z ) + g 0 * ( - x , - y , - Δ z ) ] ,
g ^ = sinc ( 1 3 ) [ g 0 ( x , y , Δ z ) + ( 1 2 ) ( g 0 * * g 0 * ) ( - x , - y , - 2 Δ z ) ] .

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