Abstract

A fully-phase optical asymmetric-image verification system based on a joint transform correlator (JTC) is proposed in this study. Conventional joint power spectra in JTCs are used as the amplitude information for reconstructing only the symmetric target images at the output plane. A previous method, in which an additional phase mask is used at the frequency domain as the phase information, proposed by Chang and Chen [9] was proposed to enable the reconstruction of asymmetric images at the output plane. However, the dominating effect arose from the additional phase makes the wrongly reconstructed image recognizable when the phase key at the input plane is incorrect. In the proposed method, the joint power spectra is nonlinearly transformed into the phase information for reconstructing both symmetric and asymmetric images at the output plane, while the dominating effect in the previous method can be released as well. Simulation results of using two different nonlinear transformations with different parameters are provided to verify the proposed method.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
  8. H.T. Chang and C.T. Chen, "Enhanced optical image verification based on joint transform correlator adopting Fourier hologram," Opt. Rev. 11, 165-169 (2004).
    [CrossRef]
  9. H.T. Chang and ChingT. Chen, "Asymmetric-image verification for security optical systems based on joint transform correlator architecture," Opt. Commun. 239, 43-54 (2004).
    [CrossRef]
  10. H.T. Chang, W. C. Lu, and C. J. Kuo, "Multiple-phase retrieval for optical security systems using random phase encoding," Appl. Opt. 41, 4825-4834 (2002).
    [CrossRef] [PubMed]

2004

H.T. Chang and C.T. Chen, "Enhanced optical image verification based on joint transform correlator adopting Fourier hologram," Opt. Rev. 11, 165-169 (2004).
[CrossRef]

H.T. Chang and ChingT. Chen, "Asymmetric-image verification for security optical systems based on joint transform correlator architecture," Opt. Commun. 239, 43-54 (2004).
[CrossRef]

H.T. Chang and ChingT. Chen, "Asymmetric-image verification for security optical systems based on joint transform correlator architecture," Opt. Commun. 239, 43-54 (2004).
[CrossRef]

2002

2001

D. Abookasis, O. Arazi, J. Rosen, and B. Javidi, "Security optical systems based on a joint transform correlator with significant output images," Opt. Eng. 40, 1584-1589 (2001).
[CrossRef]

2000

B. Javidi and T. Nomura, "Polarization encoding for optical security systems," Opt. Eng. 39, 2439-2443 (2000).
[CrossRef]

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

1994

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

1993

1982

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

1966

Abookasis, D.

D. Abookasis, O. Arazi, J. Rosen, and B. Javidi, "Security optical systems based on a joint transform correlator with significant output images," Opt. Eng. 40, 1584-1589 (2001).
[CrossRef]

Arazi, O.

D. Abookasis, O. Arazi, J. Rosen, and B. Javidi, "Security optical systems based on a joint transform correlator with significant output images," Opt. Eng. 40, 1584-1589 (2001).
[CrossRef]

Chang, H.T.

H.T. Chang and ChingT. Chen, "Asymmetric-image verification for security optical systems based on joint transform correlator architecture," Opt. Commun. 239, 43-54 (2004).
[CrossRef]

H.T. Chang and C.T. Chen, "Enhanced optical image verification based on joint transform correlator adopting Fourier hologram," Opt. Rev. 11, 165-169 (2004).
[CrossRef]

H.T. Chang, W. C. Lu, and C. J. Kuo, "Multiple-phase retrieval for optical security systems using random phase encoding," Appl. Opt. 41, 4825-4834 (2002).
[CrossRef] [PubMed]

Chen, C.T.

H.T. Chang and C.T. Chen, "Enhanced optical image verification based on joint transform correlator adopting Fourier hologram," Opt. Rev. 11, 165-169 (2004).
[CrossRef]

Ching, H.T.

H.T. Chang and ChingT. Chen, "Asymmetric-image verification for security optical systems based on joint transform correlator architecture," Opt. Commun. 239, 43-54 (2004).
[CrossRef]

Fienup, J.R.

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

Goodman, J.W.

Horner, J.L.

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

Javidi, B.

D. Abookasis, O. Arazi, J. Rosen, and B. Javidi, "Security optical systems based on a joint transform correlator with significant output images," Opt. Eng. 40, 1584-1589 (2001).
[CrossRef]

B. Javidi and T. Nomura, "Polarization encoding for optical security systems," Opt. Eng. 39, 2439-2443 (2000).
[CrossRef]

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

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

Kuo, C. J.

Lu, W. C.

Nomura, T.

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

B. Javidi and T. Nomura, "Polarization encoding for optical security systems," Opt. Eng. 39, 2439-2443 (2000).
[CrossRef]

Rosen, J.

D. Abookasis, O. Arazi, J. Rosen, and B. Javidi, "Security optical systems based on a joint transform correlator with significant output images," Opt. Eng. 40, 1584-1589 (2001).
[CrossRef]

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

Weaver, C.J.

Appl. Opt.

Opt. Commun.

H.T. Chang and ChingT. Chen, "Asymmetric-image verification for security optical systems based on joint transform correlator architecture," Opt. Commun. 239, 43-54 (2004).
[CrossRef]

Opt. Eng.

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

B. Javidi and T. Nomura, "Polarization encoding for optical security systems," Opt. Eng. 39, 2439-2443 (2000).
[CrossRef]

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

D. Abookasis, O. Arazi, J. Rosen, and B. Javidi, "Security optical systems based on a joint transform correlator with significant output images," Opt. Eng. 40, 1584-1589 (2001).
[CrossRef]

Opt. Lett.

Opt. Rev.

H.T. Chang and C.T. Chen, "Enhanced optical image verification based on joint transform correlator adopting Fourier hologram," Opt. Rev. 11, 165-169 (2004).
[CrossRef]

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Figures (10)

Fig. 1.
Fig. 1.

Optical setup of the original JTC architecture for symmetric image verification.

Fig. 2.
Fig. 2.

The schematic diagram of the proposed architecture.

Fig. 3.
Fig. 3.

The block diagram of the proposed method.

Fig. 4.
Fig. 4.

Two representative nonlinear functions: (a) power law: η = ξb ; (b) Log-sigmoid η = 1 1 + e a ξ .

Fig. 5.
Fig. 5.

(a) The symmetric and (b) asymmetric test imgaes.

Fig. 6.
Fig. 6.

(a) Two phase keys at the input plane; (b) The joint power spectrum at the Fourier plane. (c) The power spectrum transformed by the power-law function with the parameter b = 0.3, (d) The power spectrum transformed by the log-sigmoid function with the parameter a = 9.

Fig. 7.
Fig. 7.

(a) The histogram of original joint power spectrum; (b) The histogram of the spectrum after using the power-law transformation; (c) The histogram of the spectrum after using the transform of log-sigmoid function.

Fig. 8.
Fig. 8.

Reconstructed results of the verification system based on the previous optical architecture: (a) symmetric image with the correct phase key h 1(x, y); (b) asymmetric image with the correct phase key h 1(x, y); (c) symmetric image with a wrong phase key h 1(x, y); (d) asymmetric image with a wrong phase key h 1(x, y).

Fig. 9.
Fig. 9.

Reconstructed results of the proposed verification system using the power-law function for converting the joint power spectrum to phase information: (a) symmetric image with the correct phase key h 1(x, y); (b) asymmetric image with the correct phase key h 1(x, y); (c) symmetric image with a wrong phase key h 1(x, y); (d) asymmetric image with a wrong phase key h 1(x, y).

Fig. 10.
Fig. 10.

Reconstructed results of the proposed verification system using the log-sigmoid function for converting the joint power spectrum to phase information: (a) symmetric image with the correct phase keys h 1(x, y) and H 3(u, v); (b) asymmetric image with the correct phase key h 1(x, y) and H 3(u, v); (c) symmetric image with a wrong phase key h 1(x, y) and correct H 3(u, v); (d) asymmetric image with a wrong phase key h 1(x, y) and correct H 3(u, v).

Tables (2)

Tables Icon

Table 1. MSE results under different values of the parameter b in the power-law function in reconstructing symmetric and asymmetric images with correct and wrong phase keys h 1(x, y) and H 3(u, v).

Tables Icon

Table 2. MSE results under different values of the parameter a in the log-sigmoid function in reconstructing the image with correct phase keys h 1(x, y) and H 3(u, v).

Equations (6)

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

S P ( u , v ) = FT { h 1 ( x , y ) + h 2 ( x , y ) } 2 .
η = g ( ξ ) = ξ b ,
η = g ( ξ ) = 1 1 + e a ξ ,
e i H 3 ( u , v ) = e i O k ( u , v ) e i S I ( u , v ) = e i [ O k ( u , v ) S I ( u , v ) ] ,
H 3 ( u , v ) = { O k ( u , v ) S I ( u , v ) , if O k ( u , v ) S I ( u , v ) O k ( u , v ) S I ( u , v ) + 2 π , if O k ( u , v ) < S I ( u , v ) .
MSE [ o ( x , y ) , o k ( x , y ) ] = 1 B 2 x = 0 B 1 y = 0 B 1 [ o ( x , y ) o k ( x , y ) ] 2 .

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