Abstract

Experiments have been performed in which 1000 holograms have been superimposed one upon the other in the same area of photographic emulsion. Each hologram was formed with a uniquely coded reference beam allowing reconstruction of only one of the superimposed holograms while the unaddressed holograms contribute incoherent noise. Signal-to-noise ratios are calculated and measured as a function of the number of superimposed exposures. For the 1000-exposure hologram, the observed signal-to-noise ratio for any one of the individual holograms was 10 dB.

© 1968 Optical Society of America

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References

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  1. G. W. Stroke, F. H. Westervelt, R. G. Zech, Proc. IEEE 55, 109 (1967).
    [CrossRef]
  2. M. Marchant, D. Knight, Opt. Acta 14, 199 (1967). D. Gabor, Nature 208, 422 (1965).
    [CrossRef]
  3. R. J. Collier, K. S. Pennington, Appl. Opt. 6, 1091 (1967).
    [CrossRef] [PubMed]
  4. G. W. Stroke, An Introduction to Coherent Optics and Holography (Academic Press Inc., New York, 1966), p. 107.
  5. M. Born, E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1965), p. 396.
  6. L. H. Enloe, Bell System Tech. J. 46, 1479 (1967).

1967 (4)

G. W. Stroke, F. H. Westervelt, R. G. Zech, Proc. IEEE 55, 109 (1967).
[CrossRef]

M. Marchant, D. Knight, Opt. Acta 14, 199 (1967). D. Gabor, Nature 208, 422 (1965).
[CrossRef]

R. J. Collier, K. S. Pennington, Appl. Opt. 6, 1091 (1967).
[CrossRef] [PubMed]

L. H. Enloe, Bell System Tech. J. 46, 1479 (1967).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1965), p. 396.

Collier, R. J.

Enloe, L. H.

L. H. Enloe, Bell System Tech. J. 46, 1479 (1967).

Knight, D.

M. Marchant, D. Knight, Opt. Acta 14, 199 (1967). D. Gabor, Nature 208, 422 (1965).
[CrossRef]

Marchant, M.

M. Marchant, D. Knight, Opt. Acta 14, 199 (1967). D. Gabor, Nature 208, 422 (1965).
[CrossRef]

Pennington, K. S.

Stroke, G. W.

G. W. Stroke, F. H. Westervelt, R. G. Zech, Proc. IEEE 55, 109 (1967).
[CrossRef]

G. W. Stroke, An Introduction to Coherent Optics and Holography (Academic Press Inc., New York, 1966), p. 107.

Westervelt, F. H.

G. W. Stroke, F. H. Westervelt, R. G. Zech, Proc. IEEE 55, 109 (1967).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1965), p. 396.

Zech, R. G.

G. W. Stroke, F. H. Westervelt, R. G. Zech, Proc. IEEE 55, 109 (1967).
[CrossRef]

Appl. Opt. (1)

Bell System Tech. J. (1)

L. H. Enloe, Bell System Tech. J. 46, 1479 (1967).

Opt. Acta (1)

M. Marchant, D. Knight, Opt. Acta 14, 199 (1967). D. Gabor, Nature 208, 422 (1965).
[CrossRef]

Proc. IEEE (1)

G. W. Stroke, F. H. Westervelt, R. G. Zech, Proc. IEEE 55, 109 (1967).
[CrossRef]

Other (2)

G. W. Stroke, An Introduction to Coherent Optics and Holography (Academic Press Inc., New York, 1966), p. 107.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1965), p. 396.

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of experimental arrangement.

Fig. 2
Fig. 2

Measured noise distribution in the virtual image plane from a single exposure diffuse reference hologram.

Fig. 3
Fig. 3

Photograph (4× enlarged) of one virtual image reconstruction of signal and noise from ten-exposure hologram.

Fig. 4
Fig. 4

Plot of measured S/N corrected for system geometry as a function of the number of multiple exposures.

Equations (14)

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T ( x , y ) = Const . { τ I } - γ / 2 ,
I = i = 1 N I ( i ) , I = i = 1 N f r ( i ) ( x , y ) + f 0 ( i ) ( x , y ) 2 .
T ( x , y ) = Const . { i = 1 N τ ( i ) f 0 ( i ) ( x , y ) + f r ( i ) ( x , y ) 2 } - γ / 2 ,
T ( x , y ) = Const . τ - γ / 2 { i = 1 N f 0 ( i ) ( x , y ) 2 + i = 1 N f r ( i ) ( x , y ) 2 } 1 + γ / 2 × [ i = 1 N f r ( i ) ( x , y ) 2 + i = 1 N f 0 ( i ) ( x , y ) 2 - γ 2 i = 1 N f 0 ( i ) ( x , y ) f r * ( i ) ( x , y ) - γ 2 i = 1 N f 0 * ( i ) ( x , y ) f r ( i ) ( x , y ) ] .
T V ( x , y ) = i = 1 N f 0 ( i ) ( x , y ) f r * ( i ) ( x , y ) .
f V ( x , y ) = f r ( i ) ( x , y ) 2 f 0 ( i ) ( x , y ) + f r ( j ) ( x , y ) i j N f 0 ( i ) ( x , y ) f r * ( i ) ( x , y ) .
f r ( i ) ( x , y ) = m = 1 M A exp i [ k m x ( j ) x + k m y ( j ) y + Φ m ( j ) ] ,
( f V ) A C = M A 2 f 0 ( j ) ( x , y ) + f 0 ( j ) ( x , y ) m n M M A 2 × exp { i [ k m x ( j ) - k n x ( j ) ] x + i [ k m y ( j ) - k n y ( j ) ] y + i [ Φ m ( j ) - Φ n ( j ) ] } .
( f V ) CC = i j N f 0 ( i ) ( x , y ) m M n M A 2 × exp { i [ k m x ( j ) - k n x ( i ) ] x + i [ k m y ( j ) - k n y ( i ) ] } .
f 0 ( j ) ( x , y ) 2 = f 0 2             for all 1 j N
P N = P AC + P CC = 1 2 0 c ( π h 2 ) × { A 4 f 0 2 [ M ( M - 1 ) + M 2 ( N - 1 ) ] } = 1 2 0 c ( π h 2 ) A 4 f 0 2 M 2 N .
I S = 1 2 0 c [ ( π h 2 ) 2 / λ 2 D 2 ] A 4 f 0 2 M 2 ,
I N = P N K N ( π / 4 ) ( 2 θ D ) 2 ,
S / N = I s / I N = π 2 θ 2 h 2 / K N N λ 2 .

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