Abstract

Iron-doped LiNbO3 has been employed to carry out some image processing operations such as sum, difference, or multiplication of two intensity distributions. Contrast enhancement or reversal of a signal can also be obtained. The signals, modulated on low-frequency carriers, are imaged on the ferroelectric crystal, and this disposition permits the use of white light for both writing and reading the information. An advantage of our technique is that the writing of information is accomplished once and for all, and the various image processing operations are carried out by suitable manipulations at the reading stage. A further advantage is that the output information can be displayed in color. The limitations on the source size and its spectral spread imposed by the finite thickness of the recording medium have been analyzed, and some experimental results are given.

© 1980 Optical Society of America

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References

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  1. A. L. Mikaeliane, in US-USSR Science Cooperative Seminar on Optical Information Processing (Plenum, New York, 1976), Vol. 2, p. 217.
  2. L. d'Auria, J. P. Huignard, C. Slezak, E. Spitz, Appl. Opt. 13, 808 (1974).
    [CrossRef]
  3. D. L. Staebler, W. Phillips, Appl. Opt. 13, 789 (1974).
    [CrossRef]
  4. V. Markov, S. Odulov, M. Soskin, Opt. Laser Technol. 11, 95 (Apr.1979).
    [CrossRef]
  5. J. P. Huignard, J. P. Herriau, F. Micheron, Ferroelectrics 11, 393 (1976).
    [CrossRef]
  6. E. N. Leith, J. A. Roth, Appl. Opt. 18, 2803 (1979).
    [CrossRef] [PubMed]
  7. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
  8. J. P. Huignard, F. Micheron, Appl. Phys. Lett. 29, 591 (1976).
    [CrossRef]

1979 (2)

V. Markov, S. Odulov, M. Soskin, Opt. Laser Technol. 11, 95 (Apr.1979).
[CrossRef]

E. N. Leith, J. A. Roth, Appl. Opt. 18, 2803 (1979).
[CrossRef] [PubMed]

1976 (2)

J. P. Huignard, F. Micheron, Appl. Phys. Lett. 29, 591 (1976).
[CrossRef]

J. P. Huignard, J. P. Herriau, F. Micheron, Ferroelectrics 11, 393 (1976).
[CrossRef]

1974 (2)

1969 (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

d'Auria, L.

Herriau, J. P.

J. P. Huignard, J. P. Herriau, F. Micheron, Ferroelectrics 11, 393 (1976).
[CrossRef]

Huignard, J. P.

J. P. Huignard, J. P. Herriau, F. Micheron, Ferroelectrics 11, 393 (1976).
[CrossRef]

J. P. Huignard, F. Micheron, Appl. Phys. Lett. 29, 591 (1976).
[CrossRef]

L. d'Auria, J. P. Huignard, C. Slezak, E. Spitz, Appl. Opt. 13, 808 (1974).
[CrossRef]

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Leith, E. N.

Markov, V.

V. Markov, S. Odulov, M. Soskin, Opt. Laser Technol. 11, 95 (Apr.1979).
[CrossRef]

Micheron, F.

J. P. Huignard, J. P. Herriau, F. Micheron, Ferroelectrics 11, 393 (1976).
[CrossRef]

J. P. Huignard, F. Micheron, Appl. Phys. Lett. 29, 591 (1976).
[CrossRef]

Mikaeliane, A. L.

A. L. Mikaeliane, in US-USSR Science Cooperative Seminar on Optical Information Processing (Plenum, New York, 1976), Vol. 2, p. 217.

Odulov, S.

V. Markov, S. Odulov, M. Soskin, Opt. Laser Technol. 11, 95 (Apr.1979).
[CrossRef]

Phillips, W.

D. L. Staebler, W. Phillips, Appl. Opt. 13, 789 (1974).
[CrossRef]

Roth, J. A.

Slezak, C.

Soskin, M.

V. Markov, S. Odulov, M. Soskin, Opt. Laser Technol. 11, 95 (Apr.1979).
[CrossRef]

Spitz, E.

Staebler, D. L.

D. L. Staebler, W. Phillips, Appl. Opt. 13, 789 (1974).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

J. P. Huignard, F. Micheron, Appl. Phys. Lett. 29, 591 (1976).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Ferroelectrics (1)

J. P. Huignard, J. P. Herriau, F. Micheron, Ferroelectrics 11, 393 (1976).
[CrossRef]

Opt. Laser Technol. (1)

V. Markov, S. Odulov, M. Soskin, Opt. Laser Technol. 11, 95 (Apr.1979).
[CrossRef]

Other (1)

A. L. Mikaeliane, in US-USSR Science Cooperative Seminar on Optical Information Processing (Plenum, New York, 1976), Vol. 2, p. 217.

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of writing and reading arrangement. G represents double grating. Lenses L1 and L2 form an afocal system so that waves incident on the crystal are plane.

Fig. 2
Fig. 2

Geometry used for calculating irradiance distribution inside the crystal.

Fig. 3
Fig. 3

Experimental setup for recording two signals simultaneously. BS is a semireflecting plate.

Fig. 4
Fig. 4

Two reconstructed signals A and B.

Fig. 5
Fig. 5

Sum of A and B.

Fig. 6
Fig. 6

Difference between A and B.

Fig. 7
Fig. 7

Product of A and B.

Equations (28)

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E ( x , y ) = A ( x , y ) [ 1 + m cos 2 π N ( x cos α + y sin α ) ] + B ( x , y ) [ 1 + m cos 2 π N ( x cos α y sin α ] ,
n ( x , y ) = n 0 + γ E ( x , y ) ,
t ( x , y ) = exp { j 2 π λ [ n 0 + γ E ( x , y ) ] d } ,
t ( x , y ) = exp { j 2 π λ d [ n 0 + γ ( A + B ) ] } × [ J 0 ( 2 π λ d γ mA ) + 2 j J 1 ( 2 π λ d γ mA ) × cos 2 π N ( x cos α + y sin α ) + higher-order terms ] × [ J 0 ( 2 π λ d γ mB ) + 2 j J 1 ( 2 π λ d γ mB ) × cos 2 π N ( x cos α y sin α ) + higher-order terms ] ,
exp [ j 2 π N ( x cos α + y sin α ) ] + exp [ j 2 π N ( x cos α y sin α ) ] .
U ( x , y ) = J 0 ( c B ) J 1 ( c A ) exp ( j 2 π N δ y sin α ) + J 0 ( cA ) J 1 ( c B ) exp ( + j 2 π N δ y sin α ) ,
U ( x , y ) = A ( x , y ) + B ( x , y ) exp ( j 4 π N δ y sin α ) .
4 π N δ y sin α = ( 2 n + 1 ) π ,
I ( x , y ) = [ A ( x , y ) B ( x , y ) ] 2 .
U ( x , y ) = exp ( j R · K 1 ) ,
K 1 = 2 π n λ ( sin θ 1 0 cos θ 1 ) ,
U ( x , y ) = exp ( j R · K 1 ) + exp ( j R · K 2 ) = exp ( j R · K 2 ) { 1 + exp ( j R · ( K 1 K 2 ) ] } = exp ( j R · K 2 ) [ 1 + exp ( j R · K ) ] ,
K 1 = K 1 K 2 = 2 π n λ ( sin θ 1 sin θ 2 0 cos θ 1 cos θ 2 ) = 4 π n λ sin ( θ 1 θ 2 2 ) ( cos ( θ 1 + θ 2 2 ) sin ( θ 1 + θ 2 2 ) ) .
θ 1 = β / n , θ 2 = ( β + N λ ) / n ,
I ( x , z ) = 2 + exp ( j 2 π Nx ) · exp [ j z n ( 2 π N β + π N 2 λ ) ] + the complex conjugate .
I ( x , y ) = 1 + sinc ( π N 2 Δ λ z n ) sinc ( 2 π N β 0 z n ) × cos ( 2 π Nx π N 2 λ 0 z n ) .
z = ± 1 mm , 2 Δ λ = 0.1 μ m , N = 50 lines / mm , β 0 = 1 / 200 ( 17 min of arc ) , n = 2.2 .
cos ( ϕ θ ) = ( | K | λ ) / ( 4 π n ) ,
ϕ π / 2 , | K | 2 π N ,
sin θ = ( N λ ) / ( 2 n ) .
Δ θ = N 2 n cos θ Δ λ ,
Δ θ = N n cos θ Δ λ .
η = sin 2 ( ν 2 + ξ 2 ) 1 / 2 [ 1 + ( ξ 2 / ν 2 ) ] ν = ( π Δ nd ) / ( λ cos θ ) ξ = ϑ d / ( 2 cos θ ) ,
ϑ = Δ θ 2 π N Δ λ [ ( π N 2 ) / n ] .
η η 0 = [ sin ( ν 2 + ξ 2 ) 1 / 2 ( ν 2 + ξ 2 ) 1 / 2 ] 2 / ( sin ν ν ) 2 .
ξ = π / 4 = Δ θ · π N d = Δ λ · [ ( π N 2 d ) / 2 n ] .
Δ θ = 1 / 400 ( this corresponds to an angle of n 400 1 200 in air ) ,
Δ λ = 0 . 2 μ m .

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