Abstract

An improved optical security system based on two phase-only computer-generated masks is proposed. The two transparencies are placed together in a 4f correlator so that a known output image is received. In addition to simple verification, our security system is capable of identifying the type of input mask according to the corresponding output image it generates. The two phase masks are designed with an iterative optimization algorithm with constraints in the input and the output domains. A simulation is presented with the resultant images formed by the two phase-only elements. Various mask combinations are compared to show that a combination is unique and cannot be duplicated. This uniqueness is an advantage in security systems.

© 2000 Optical Society of America

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References

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  1. B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
    [CrossRef]
  2. B. Javidi, G. S. Zhang, J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
    [CrossRef]
  3. B. Javidi, E. Ahouzi, “Optical security system with Fourier plane encoding,” Appl. Opt. 37, 6247–6255 (1998).
    [CrossRef]
  4. R. K. Wang, I. A. Watson, C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
    [CrossRef]
  5. J. Rosen, “Learning in correlators based on projections onto constraint sets,” Opt. Lett. 18, 1183–1185 (1993).
    [CrossRef] [PubMed]
  6. H. Stark, ed., Image Recovery Theory and Application, 1st ed. (Academic, New York, 1987).
  7. P. Refregier, B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
    [CrossRef] [PubMed]
  8. B. Javidi, L. Bernard, N. Towghi, “Noise performance of double-phase encryption compared to XOR encryption,” Opt. Eng. 38, 9–19 (1999).
    [CrossRef]
  9. B. K. Jennison, J. P. Allebach, D. W. Sweeney, “Iterative approaches to computer-generated holography,” Opt. Eng. 28, 629–637 (1989).
    [CrossRef]

1999 (1)

B. Javidi, L. Bernard, N. Towghi, “Noise performance of double-phase encryption compared to XOR encryption,” Opt. Eng. 38, 9–19 (1999).
[CrossRef]

1998 (1)

1996 (2)

B. Javidi, G. S. Zhang, J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
[CrossRef]

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

1995 (1)

1994 (1)

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

1993 (1)

1989 (1)

B. K. Jennison, J. P. Allebach, D. W. Sweeney, “Iterative approaches to computer-generated holography,” Opt. Eng. 28, 629–637 (1989).
[CrossRef]

Ahouzi, E.

Allebach, J. P.

B. K. Jennison, J. P. Allebach, D. W. Sweeney, “Iterative approaches to computer-generated holography,” Opt. Eng. 28, 629–637 (1989).
[CrossRef]

Bernard, L.

B. Javidi, L. Bernard, N. Towghi, “Noise performance of double-phase encryption compared to XOR encryption,” Opt. Eng. 38, 9–19 (1999).
[CrossRef]

Chatwin, C.

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

Horner, J. L.

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

Javidi, B.

B. Javidi, L. Bernard, N. Towghi, “Noise performance of double-phase encryption compared to XOR encryption,” Opt. Eng. 38, 9–19 (1999).
[CrossRef]

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

B. Javidi, G. S. Zhang, J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
[CrossRef]

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

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

Jennison, B. K.

B. K. Jennison, J. P. Allebach, D. W. Sweeney, “Iterative approaches to computer-generated holography,” Opt. Eng. 28, 629–637 (1989).
[CrossRef]

Li, J.

B. Javidi, G. S. Zhang, J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
[CrossRef]

Refregier, P.

Rosen, J.

Sweeney, D. W.

B. K. Jennison, J. P. Allebach, D. W. Sweeney, “Iterative approaches to computer-generated holography,” Opt. Eng. 28, 629–637 (1989).
[CrossRef]

Towghi, N.

B. Javidi, L. Bernard, N. Towghi, “Noise performance of double-phase encryption compared to XOR encryption,” Opt. Eng. 38, 9–19 (1999).
[CrossRef]

Wang, R. K.

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

Watson, I. A.

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

Zhang, G. S.

B. Javidi, G. S. Zhang, J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
[CrossRef]

Appl. Opt. (1)

Opt. Eng. (5)

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

B. Javidi, G. S. Zhang, J. Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification,” Opt. Eng. 35, 2506–2512 (1996).
[CrossRef]

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

B. Javidi, L. Bernard, N. Towghi, “Noise performance of double-phase encryption compared to XOR encryption,” Opt. Eng. 38, 9–19 (1999).
[CrossRef]

B. K. Jennison, J. P. Allebach, D. W. Sweeney, “Iterative approaches to computer-generated holography,” Opt. Eng. 28, 629–637 (1989).
[CrossRef]

Opt. Lett. (2)

Other (1)

H. Stark, ed., Image Recovery Theory and Application, 1st ed. (Academic, New York, 1987).

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Figures (9)

Fig. 1
Fig. 1

4f correlator used for optical security verification.

Fig. 2
Fig. 2

Block diagram of the main POCS algorithm used to compute the phase-only mask h 1(ξ, η).

Fig. 3
Fig. 3

Two expected output images of the correlator used in the computer simulation.

Fig. 4
Fig. 4

Block diagram of the mini POCS algorithm used to compute the phase-only mask H 2(u, ν).

Fig. 5
Fig. 5

Phase function of the mask H 2(u, ν).

Fig. 6
Fig. 6

Average mean-square error (MSE) versus the iterations number for the POCS algorithm in the case of the scale (solid curve) and the duck (dashed curve).

Fig. 7
Fig. 7

Phase distributions of h 1(ξ, η) for the output images of (a) the duck and (b) the scale.

Fig. 8
Fig. 8

Resultant images of |c(x, y)|2 for (a) the duck and (b) the scale.

Fig. 9
Fig. 9

Table of all cross correlations between functions h 1 and the inverse FT of functions H 2. The second index of each function denotes the number of the process used to design the functions. Only the pairs that were designed together at the same process yield the image of the scale.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

cx, y=-1h1ξ, ηH2u, ν=-1h1ξ, ηexpjΦu, ν,
cx, y=Ax, yexpjψx, y,
h1ξ, η=-1cx, yH2u, ν=-1cx, yexp-jΦu, ν.
P1cx, y=Ax, yexpjψx, y,
P2h1ξ, η=expjϕξ, ηifξ, ηW0otherwise,
en=1M P1cx, y2-γn|cnx, y|22 dxdy,
P1H2u, ν=expjΦu, ν,
P2h2ξ, η=h2ξ, ηifξ, ηW0otherwise,
en=1BB |h2,nξ, η|2dξdη,
EIR=minimum value of the image intensity-maximum value of the background intensityminimum value of the image intensity+maximum value of the background intensity.

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