Abstract

A new technique for the optical encoding of images is presented. The method of generalized projections is used to design diffractive optical elements for the phase encryption of biometrics for security applications. The encryption algorithm converges rapidly, and the decryption is seen to be secure and tolerant to additive noise.

© 1996 Optical Society of America

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References

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  1. B. Javidi, J. L. Horner, Opt. Eng. 33, 1752 (1994).
    [CrossRef]
  2. Ph. Réfrégier, B. Javidi, Opt. Lett. 20, 767 (1995).
    [CrossRef] [PubMed]
  3. A. Levi, H. Stark, in Image Recovery: Theory and Application, H. Stark, ed. (Academic, Orlando, Fla., 1987), Chap. 8, p. 277.
  4. R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).
  5. D. C. Youla, in Image Recovery: Theory and Application, H. Stark, ed. (Academic, Orlando, Fla., 1987), Chap. 2, p. 29.
  6. J. R. Fienup, Appl. Opt. 21, 2758 (1982).
    [CrossRef] [PubMed]
  7. D. Zaleta, M. Larsson, W. Daschner, S. H. Lee, Appl. Opt. 34, 2436 (1995).
    [CrossRef] [PubMed]

1995 (2)

1994 (1)

B. Javidi, J. L. Horner, Opt. Eng. 33, 1752 (1994).
[CrossRef]

1982 (1)

1972 (1)

R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).

Daschner, W.

Fienup, J. R.

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).

Horner, J. L.

B. Javidi, J. L. Horner, Opt. Eng. 33, 1752 (1994).
[CrossRef]

Javidi, B.

Larsson, M.

Lee, S. H.

Levi, A.

A. Levi, H. Stark, in Image Recovery: Theory and Application, H. Stark, ed. (Academic, Orlando, Fla., 1987), Chap. 8, p. 277.

Réfrégier, Ph.

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).

Stark, H.

A. Levi, H. Stark, in Image Recovery: Theory and Application, H. Stark, ed. (Academic, Orlando, Fla., 1987), Chap. 8, p. 277.

Youla, D. C.

D. C. Youla, in Image Recovery: Theory and Application, H. Stark, ed. (Academic, Orlando, Fla., 1987), Chap. 2, p. 29.

Zaleta, D.

Appl. Opt. (2)

Opt. Eng. (1)

B. Javidi, J. L. Horner, Opt. Eng. 33, 1752 (1994).
[CrossRef]

Opt. Lett. (1)

Optik (1)

R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).

Other (2)

D. C. Youla, in Image Recovery: Theory and Application, H. Stark, ed. (Academic, Orlando, Fla., 1987), Chap. 2, p. 29.

A. Levi, H. Stark, in Image Recovery: Theory and Application, H. Stark, ed. (Academic, Orlando, Fla., 1987), Chap. 8, p. 277.

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Figures (5)

Fig. 1
Fig. 1

Optical implementation of the encryption algorithm or the decryption system.

Fig. 2
Fig. 2

Mean-squared error (MSE) between the intensity of the input image and the intensity of successive iterates.

Fig. 3
Fig. 3

Biometrie image to be encrypted.

Fig. 4
Fig. 4

(a) First and (b) second phase arrays encrypting the biometric image.

Fig. 5
Fig. 5

(a) Intensity and (b) phase of the decrypted biometric image.

Equations (15)

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f 1 [ m , n ] = w 1 [ m , n ] exp ( j ϕ 1 [ m , n ] ) { C 1 } ,
w 1 [ m , n ] = { 1 if [ m , n ] R 1 0 if [ m , n ] R 1
f 2 [ m , n ] = ( L 1 { f 1 } ) [ m , n ] ,
f 3 [ m , n ] = w 2 [ m , n ] g [ m , n ] exp [ j ( θ [ m , n ] + ϕ 2 [ m , n ] ) ] { C 2 } ,
g [ m , n ] = { | f 2 [ m , n ] | if | f 2 [ m , n ] | M M if | f 2 [ m , n ] | M , w 2 [ m , n ] = { 1 if [ m , n ] R 2 0 if [ m , n ] R 2
f 4 [ m , n ] = ( L 2 { f 3 } ) [ m , n ] ,
f 5 [ m , n ] = { I [ m , n ] exp [ j arctan ( Im { f 4 [ m , n ] } Re { f 4 [ m , n ] } ) ] if [ m , n ] R 3 , f 4 [ m , n ] if [ m , n ] R 3
f 6 [ m , n ] = ( L 2 1 { f 5 } ) [ m , n ] .
ϕ [ m , n ] = arctan ( Im { f 6 [ m , n ] } Re { f 6 [ m , n ] } ) ,
ϕ 2 [ m , n ] = ϕ [ m , n ] θ [ m , n ] ,
f 7 [ m , n ] = w 2 [ m , n ] | f 6 [ m , n ] | exp ( j θ [ m , n ] ) { C 4 } .
f 8 [ m , n ] = ( L 1 1 { f 7 } ) [ m , n ] .
ϕ 1 [ m , n ] = arctan ( Im { f 8 [ m , n ] } Re { f 8 [ m , n ] } ) ,
f 1 [ m , n ] = w 1 [ m , n ] exp ( j ϕ 1 [ m , n ] ) { C 1 } .
ε [ k ] = 1 N 2 n = 0 N 1 m = 0 N 1 ( I [ m , n ] I k [ m , n ] ) 2 .

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