Abstract

The technique of the multiple phase encoding for optical security and verification systems is presented in this paper. This technique is based on a 4-f optical correlator that is a common architecture for optical image encryption and verification systems. However, two or more phase masks are iteratively retrieved by use of the proposed multiple phases retrieval algorithm (MPRA) to obtain the target image. The convergent speed of the iteration process in the MPRA is significantly increased and the recovered image is much more similar to the target image than those in previous approaches. In addition, the quantization effects due to the finite resolution of the phase levels in practical implementation are discussed. The relationships between the number of phase masks and the quantized phase levels are also investigated. According to the simulation results, two and three phase masks are enough to design an efficient security verification system with 64 and 32 phase levels, respectively.

© 2002 Optical Society of America

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2001

2000

1999

J. Horner, B. Javidi, Opt. Eng. 38, Special issue on Optical Security1999.

J.-W. Han, C.-S. Park, D.-H. Ryu, E.-S. Kim, “Optical image encryption based on XOR operations,” Opt. Eng. 37, 47–54 (1999).
[CrossRef]

N. Towghi, B. Javidi, Z. Luo, “Fully phase encrypted image processor,” J. Opt. Soc. Am. A 16, 1915–1927 (1999).
[CrossRef]

1998

1997

1996

L. G. Neto, Y. Sheng, “Optical implementation of image encryption using random phase encoding,” Opt. Eng. 35, 2459–2463 (1996).
[CrossRef]

R. K. Wan, I. A. Watson, C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
[CrossRef]

J. Horner, B. Javidi, Opt. Eng. 35, Special issue on Optical Security1996.

1995

1994

B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

1993

J.-S. R. Jang, “ANFIS: Adaptive-network-based fuzzy inference system,” IEEE Trans. Syst. Man. Cybern. 23, 665–685 (1993).
[CrossRef]

J. Rosen, “Learning in correlators based on projection onto constraint sets,” Opt. Lett. 18, 1183–1185 (1993).
[CrossRef]

1992

1987

J.-H. Chen, A. Gersho, “Gain-adaptive vector quantization with application to speech coding,” IEEE Trans. Commun. COM-35, 918–930 (1987).
[CrossRef]

1982

J. R. Fienup, “Phase retrieval algorithm: a comparison,” Appl. Opt. 22, 2758–2769 (1982).
[CrossRef]

1955

Ahouzi, E.

B. Javidi, A. Sergent, E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

B. Javidi, E. Ahouzi, “Optical security with Fourier plane encoding,” Appl. Opt. 37, 6247–6255 (1998).
[CrossRef]

Broomfield, S. E.

Brown, T. A.

Chang, N.

Chatwin, C.

R. K. Wan, I. A. Watson, C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
[CrossRef]

Chen, J.-H.

J.-H. Chen, A. Gersho, “Gain-adaptive vector quantization with application to speech coding,” IEEE Trans. Commun. COM-35, 918–930 (1987).
[CrossRef]

Chen, R.

Chien, H.

de Bougrenet de la Tocnaye, J.-L.

Deng, X.

Fienup, J. R.

J. R. Fienup, “Phase retrieval algorithm: a comparison,” Appl. Opt. 22, 2758–2769 (1982).
[CrossRef]

Freeman, M. O.

Fukuzaki, I.

Gersho, A.

J.-H. Chen, A. Gersho, “Gain-adaptive vector quantization with application to speech coding,” IEEE Trans. Commun. COM-35, 918–930 (1987).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, Second Edition, (McGraw-Hill, Singapore, 1996), pp. 243–246.

Hamam, H.

Han, J.-W.

J.-W. Han, C.-S. Park, D.-H. Ryu, E.-S. Kim, “Optical image encryption based on XOR operations,” Opt. Eng. 37, 47–54 (1999).
[CrossRef]

Horner, J.

J. Horner, B. Javidi, Opt. Eng. 38, Special issue on Optical Security1999.

J. Horner, B. Javidi, Opt. Eng. 35, Special issue on Optical Security1996.

Horner, J. L.

B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

Jang, J.-S. R.

J.-S. R. Jang, “ANFIS: Adaptive-network-based fuzzy inference system,” IEEE Trans. Syst. Man. Cybern. 23, 665–685 (1993).
[CrossRef]

Javidi, B.

T. Nomura, B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39, 2031–2035 (2000).
[CrossRef]

J. Horner, B. Javidi, Opt. Eng. 38, Special issue on Optical Security1999.

N. Towghi, B. Javidi, Z. Luo, “Fully phase encrypted image processor,” J. Opt. Soc. Am. A 16, 1915–1927 (1999).
[CrossRef]

B. Javidi, E. Ahouzi, “Optical security with Fourier plane encoding,” Appl. Opt. 37, 6247–6255 (1998).
[CrossRef]

B. Javidi, A. Sergent, E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

J. Horner, B. Javidi, Opt. Eng. 35, Special issue on Optical Security1996.

P. Réfrégier, B. Javidi, “Optical image encryption using input plane and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
[CrossRef]

B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

Kamijoh, T.

Katsuki, Y.

Keryer, G.

Kim, E.-S.

J.-W. Han, C.-S. Park, D.-H. Ryu, E.-S. Kim, “Optical image encryption based on XOR operations,” Opt. Eng. 37, 47–54 (1999).
[CrossRef]

Kreske, K.

Kuo, C. J.

Li, Y.

Luo, Z.

Neil, M. A. A.

Neto, L. G.

L. G. Neto, Y. Sheng, “Optical implementation of image encryption using random phase encoding,” Opt. Eng. 35, 2459–2463 (1996).
[CrossRef]

Nomura, T.

T. Nomura, B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39, 2031–2035 (2000).
[CrossRef]

Paige, E. G. S.

Park, C.-S.

J.-W. Han, C.-S. Park, D.-H. Ryu, E.-S. Kim, “Optical image encryption based on XOR operations,” Opt. Eng. 37, 47–54 (1999).
[CrossRef]

Que’mener, E.

Réfrégier, P.

Rosen, J.

Ryu, D.-H.

J.-W. Han, C.-S. Park, D.-H. Ryu, E.-S. Kim, “Optical image encryption based on XOR operations,” Opt. Eng. 37, 47–54 (1999).
[CrossRef]

Sasaki, H.

Sergent, A.

B. Javidi, A. Sergent, E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

Sheng, Y.

L. G. Neto, Y. Sheng, “Optical implementation of image encryption using random phase encoding,” Opt. Eng. 35, 2459–2463 (1996).
[CrossRef]

Towghi, N.

Walba, D. M.

Wan, R. K.

R. K. Wan, I. A. Watson, C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
[CrossRef]

Watson, I. A.

R. K. Wan, I. A. Watson, C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
[CrossRef]

Yeh, C. H.

Appl. Opt.

IEEE Trans. Commun.

J.-H. Chen, A. Gersho, “Gain-adaptive vector quantization with application to speech coding,” IEEE Trans. Commun. COM-35, 918–930 (1987).
[CrossRef]

IEEE Trans. Syst. Man. Cybern.

J.-S. R. Jang, “ANFIS: Adaptive-network-based fuzzy inference system,” IEEE Trans. Syst. Man. Cybern. 23, 665–685 (1993).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

J. Horner, B. Javidi, Opt. Eng. 35, Special issue on Optical Security1996.

J. Horner, B. Javidi, Opt. Eng. 38, Special issue on Optical Security1999.

J.-W. Han, C.-S. Park, D.-H. Ryu, E.-S. Kim, “Optical image encryption based on XOR operations,” Opt. Eng. 37, 47–54 (1999).
[CrossRef]

L. G. Neto, Y. Sheng, “Optical implementation of image encryption using random phase encoding,” Opt. Eng. 35, 2459–2463 (1996).
[CrossRef]

T. Nomura, B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39, 2031–2035 (2000).
[CrossRef]

R. K. Wan, I. A. Watson, C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
[CrossRef]

B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

B. Javidi, A. Sergent, E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).
[CrossRef]

Opt. Lett.

Other

J. W. Goodman, Introduction to Fourier Optics, Second Edition, (McGraw-Hill, Singapore, 1996), pp. 243–246.

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Figures (13)

Fig. 1
Fig. 1

Optical setup of the 4-f correlator for optical security verification.

Fig. 2
Fig. 2

Optical setup of the multiple-phase masks for optical verification systems: (a) The number of phase masks m is even, (b) the number of phase masks n is odd.

Fig. 3
Fig. 3

Block diagram of the double phases retrieval by use of the iteration algorithm.

Fig. 4
Fig. 4

Block diagram of the multiple phases retrieval by use of the iteration algorithm.

Fig. 5
Fig. 5

Comparison of the (a) MSE and (b) correlation coefficients between the recovered and the original images.

Fig. 6
Fig. 6

(a) Original image and the iterated images in the output plane after 100 iterations based on (b) Algorithm 1, (c) Algorithm 2, and (d) the proposed MPRA.

Fig. 7
Fig. 7

Error images between the original and the images retrieved from (a) Algorithm 1, (b) Algorithm 2, and (c) the proposed MPRA.

Fig. 8
Fig. 8

Table of all correlation results between five phase pairs, ϕ1,i (x, y), i = 1, … , 5 and ψ2,j (u, v), j = 1, … , 5. Only the phase pairs retrieved together from the same iteration process can recover the target image.

Fig. 9
Fig. 9

Comparison of the correlation coefficients under different phase resolutions (8, 16, 32, and 64 phase levels) for the proposed method with two phase masks.

Fig. 10
Fig. 10

Comparison of the correlation coefficients using two, three, and four phase masks with eight phase levels in the proposed method.

Fig. 11
Fig. 11

Same as Fig. 10 except with 16 phase levels in the proposed method.

Fig. 12
Fig. 12

Same as Fig. 10 except with 32 phase levels in the proposed method.

Fig. 13
Fig. 13

Same as Fig. 10 except with 64 phase levels in the proposed method.

Equations (14)

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gx, y=IFTFTexpi2πϕ1x, y×expi2πψ2u, v,
Gu, vP1u, v,
P¯2ku, v=FTgk-1x, yFTexpi2πϕ1k-1x, y
ψ2ku, v=P¯2ku, v,
g¯kx, y=IFTFTexpi2πϕ1k-1x, y×expi2πψ2ku, v.
MSE=1M×Nx=1My=1Ngx, y-g¯kx, y2,
C=COVg, g¯kσgσg¯k,
gkx, y=g¯kx, y,if|g¯kx, y-gx, y|γthgx, y,if|g¯kx, y-gx, y|>γth,
p¯1k+1x, y=IFTFTgkx, yexpi2πψ2ku, v,
ϕ1k+1x, y=p¯1k+1x, y,
g¯k+1x, y=IFTFTexpi2πϕ1k+1x, y×expi2πψ2ku, v,
gk+1x, y=g¯k+1x, y,if|g¯k+1x, y-gx, y|γthgx, y,if|g¯k+1x, y-gx, y|>γth.
ϕ11x, y=IFTFTIFTFTIFT×Gu, vPmu, vpm-1x, yPm-2u, vP2u, v
ψ11u, v=FTIFTIFTFTIFT× Gu, vPnu, vpn-1x, yPn-2u, vp2x, y

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