Abstract

A novel architecture of the optical multiple-image encryption based on the modified Gerchberg-Saxton algorithm (MGSA) by using cascading phase only functions (POFs) in the Fresnel transform (FrT) domain is presented. This proposed method can greatly increase the capacity of the system by avoiding the crosstalk, completely, between the encrypted target images. Each present stage encrypted target image is encoded as to a complex function by using the MGSA with constraining the encrypted target image of the previous stage. Not only the wavelength and position parameters in the FrT domain can be keys to increase system security, the created POFs are also served mutually as the encryption keys to decrypt target image from present stage into next stage in the cascaded scheme. Compared with a prior method [Appl. Opt. 48, 2686–2692 (2009)], the main advantages of this proposed encryption system is that it does not need any transformative lenses and this makes it very efficient and easy to implement optically. Simulation results show that this proposed encryption system can successfully achieve the multiple-image encryption via fewer POFs, which is more advantageous in simpler implementation and efficiency than a prior method where each decryption stage requires two POFs to accomplish this task.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2011

2009

2008

2007

2006

G. Situ and J. Zhang, “Position multiplexing for multiple-image encryption,” J. Opt. A 8, 391–397 (2006).
[CrossRef]

H. E. Hwang and P. Han, “Fast algorithm of phase masks for image encryption in the Fresnel domain,” J. Opt. Soc. Am. A 23, 1870–1874 (2006).
[CrossRef]

2005

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29–37 (2005).
[CrossRef]

G. Situ and J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30, 1306–1308 (2005).
[CrossRef]

2004

G. Situ and J. Zhang, “A lensless optical security system based on computer-generated phase only masks,” Opt. Commun. 232, 115–122 (2004).
[CrossRef]

G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29, 1584–1586 (2004).
[CrossRef]

Y. C. Chang, H. T. Chang, and C. J. Kuo, “Hybrid image cryptosystem based on dyadic phase displacement in the Fourier domain,” Opt. Commun. 236, 245–257 (2004).
[CrossRef]

2003

G. H. Lin, H. T. Chang, W. N. Lai, and C. H. Chuang, “Public-key-based optical image cryptosystem with data embedding techniques,” Opt. Eng. 42, 2331–2339 (2003).
[CrossRef]

G. Situ and J. Zhang, “A cascaded iterative Fourier transform algorithm for optical security applications,” Optik 114, 473–477 (2003).
[CrossRef]

2002

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285 (2002).
[CrossRef]

H. T. Chang, W. C. Lu, and C. J. Kuo, “Multiple-Phase Retrieval for Optical Security Systems by Use of Random-Phase Encoding,” Appl. Opt. 41, 4815–4834 (2002).
[CrossRef]

C. H. Yeh, H. T. Chang, H. C. Chien, and C. J. Kuo, “Design of cascaded phase keys for hierarchical security system,” Appl. Opt. 41, 6128–6134 (2002).
[CrossRef]

2001

H. T. Chang, “Image encryption using separate amplitude-based virtual image and iteratively-retrieved phase information,” Opt. Eng. 40, 2165–2171 (2001).
[CrossRef]

S. T. Liu, Q. L. Mi, and B. H. Zhu, “Optical image encryption with multistage and multichannel fractional Fourier-domain filtering,” Opt. Lett. 26, 1242–1244 (2001).
[CrossRef]

2000

1996

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

1995

1972

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

1971

R. W. Gerchberg and W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik 34, 275–284 (1971).

Amaya, D.

Bolognini, N.

Cai, L. Z.

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29–37 (2005).
[CrossRef]

Chang, H. T.

H. E. Hwang, H. T. Chang, and W. N. Lie, “Lensless optical data embedding system using concealogram and cascaded digital Fresnel hologram,” J. Opt. Soc. Am. A 28, 1453–1461, (2011).
[CrossRef]

H. E. Hwang, H. T. Chang, and W. N. Lie, “Multiple-image encryption and multiplexing using modified Gerchberg-Saxton algorithm and phase modulation in Fresnel transform domain,” Opt. Lett. 34, 3917–3919 (2009).
[CrossRef]

H. E. Hwang, H. T. Chang, and W. N. Lie, “Fast double-phase retrieval in Fresnel domain using modified Gerchberg-Saxton algorithm for lensless optical security systems,” Opt. Express 17, 13700–13710 (2009).
[CrossRef]

Y. C. Chang, H. T. Chang, and C. J. Kuo, “Hybrid image cryptosystem based on dyadic phase displacement in the Fourier domain,” Opt. Commun. 236, 245–257 (2004).
[CrossRef]

G. H. Lin, H. T. Chang, W. N. Lai, and C. H. Chuang, “Public-key-based optical image cryptosystem with data embedding techniques,” Opt. Eng. 42, 2331–2339 (2003).
[CrossRef]

C. H. Yeh, H. T. Chang, H. C. Chien, and C. J. Kuo, “Design of cascaded phase keys for hierarchical security system,” Appl. Opt. 41, 6128–6134 (2002).
[CrossRef]

H. T. Chang, W. C. Lu, and C. J. Kuo, “Multiple-Phase Retrieval for Optical Security Systems by Use of Random-Phase Encoding,” Appl. Opt. 41, 4815–4834 (2002).
[CrossRef]

H. T. Chang, “Image encryption using separate amplitude-based virtual image and iteratively-retrieved phase information,” Opt. Eng. 40, 2165–2171 (2001).
[CrossRef]

Chang, Y. C.

Y. C. Chang, H. T. Chang, and C. J. Kuo, “Hybrid image cryptosystem based on dyadic phase displacement in the Fourier domain,” Opt. Commun. 236, 245–257 (2004).
[CrossRef]

Chatwin, C.

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

Chien, H. C.

Chuang, C. H.

G. H. Lin, H. T. Chang, W. N. Lai, and C. H. Chuang, “Public-key-based optical image cryptosystem with data embedding techniques,” Opt. Eng. 42, 2331–2339 (2003).
[CrossRef]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

R. W. Gerchberg and W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik 34, 275–284 (1971).

Han, P.

He, M. Z.

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29–37 (2005).
[CrossRef]

Hennelly, B. M.

Hwang, H. E.

Javidi, B.

Joseph, J.

Kelly, D. P.

Kreske, K.

Kuo, C. J.

Y. C. Chang, H. T. Chang, and C. J. Kuo, “Hybrid image cryptosystem based on dyadic phase displacement in the Fourier domain,” Opt. Commun. 236, 245–257 (2004).
[CrossRef]

C. H. Yeh, H. T. Chang, H. C. Chien, and C. J. Kuo, “Design of cascaded phase keys for hierarchical security system,” Appl. Opt. 41, 6128–6134 (2002).
[CrossRef]

H. T. Chang, W. C. Lu, and C. J. Kuo, “Multiple-Phase Retrieval for Optical Security Systems by Use of Random-Phase Encoding,” Appl. Opt. 41, 4815–4834 (2002).
[CrossRef]

Lai, W. N.

G. H. Lin, H. T. Chang, W. N. Lai, and C. H. Chuang, “Public-key-based optical image cryptosystem with data embedding techniques,” Opt. Eng. 42, 2331–2339 (2003).
[CrossRef]

Li, Y.

Li, Y. C.

Lie, W. N.

Lin, G. H.

G. H. Lin, H. T. Chang, W. N. Lai, and C. H. Chuang, “Public-key-based optical image cryptosystem with data embedding techniques,” Opt. Eng. 42, 2331–2339 (2003).
[CrossRef]

Liu, Q.

Y. L. Xiao, X. Zhou, S. Yuan, Q. Liu, and Y. C. Li, “Multiple-image optical encryption: an improved encoding approach,” Appl. Opt. 48, 2686–2692 (2009).
[CrossRef]

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29–37 (2005).
[CrossRef]

Liu, S. T.

Lu, W. C.

H. T. Chang, W. C. Lu, and C. J. Kuo, “Multiple-Phase Retrieval for Optical Security Systems by Use of Random-Phase Encoding,” Appl. Opt. 41, 4815–4834 (2002).
[CrossRef]

McDonald, J.

Meng, X. F.

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29–37 (2005).
[CrossRef]

Mi, Q. L.

Naughton, T. J.

Refregier, P.

Rosen, J.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

R. W. Gerchberg and W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik 34, 275–284 (1971).

Sheridan, J. T.

Singh, K.

Situ, G.

G. Situ and J. Zhang, “Position multiplexing for multiple-image encryption,” J. Opt. A 8, 391–397 (2006).
[CrossRef]

G. Situ and J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30, 1306–1308 (2005).
[CrossRef]

G. Situ and J. Zhang, “A lensless optical security system based on computer-generated phase only masks,” Opt. Commun. 232, 115–122 (2004).
[CrossRef]

G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29, 1584–1586 (2004).
[CrossRef]

G. Situ and J. Zhang, “A cascaded iterative Fourier transform algorithm for optical security applications,” Optik 114, 473–477 (2003).
[CrossRef]

Tanno, N.

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285 (2002).
[CrossRef]

Tebaldi, M.

Torroba, R.

Unnikrishnan, G.

Wang, R. K.

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

Wang, X. C.

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29–37 (2005).
[CrossRef]

Watson, I. A.

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

Xiao, Y. L.

Yeh, C. H.

Yuan, S.

Zhang, J.

G. Situ and J. Zhang, “Position multiplexing for multiple-image encryption,” J. Opt. A 8, 391–397 (2006).
[CrossRef]

G. Situ and J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30, 1306–1308 (2005).
[CrossRef]

G. Situ and J. Zhang, “A lensless optical security system based on computer-generated phase only masks,” Opt. Commun. 232, 115–122 (2004).
[CrossRef]

G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29, 1584–1586 (2004).
[CrossRef]

G. Situ and J. Zhang, “A cascaded iterative Fourier transform algorithm for optical security applications,” Optik 114, 473–477 (2003).
[CrossRef]

Zhang, Y.

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285 (2002).
[CrossRef]

Zheng, C. H.

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285 (2002).
[CrossRef]

Zhou, X.

Zhu, B. H.

Appl. Opt.

J. Opt. A

G. Situ and J. Zhang, “Position multiplexing for multiple-image encryption,” J. Opt. A 8, 391–397 (2006).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285 (2002).
[CrossRef]

Y. C. Chang, H. T. Chang, and C. J. Kuo, “Hybrid image cryptosystem based on dyadic phase displacement in the Fourier domain,” Opt. Commun. 236, 245–257 (2004).
[CrossRef]

G. Situ and J. Zhang, “A lensless optical security system based on computer-generated phase only masks,” Opt. Commun. 232, 115–122 (2004).
[CrossRef]

M. Z. He, L. Z. Cai, Q. Liu, X. C. Wang, and X. F. Meng, “Multiple image encryption and watermarking by random phase matching,” Opt. Commun. 247, 29–37 (2005).
[CrossRef]

Opt. Eng.

H. T. Chang, “Image encryption using separate amplitude-based virtual image and iteratively-retrieved phase information,” Opt. Eng. 40, 2165–2171 (2001).
[CrossRef]

G. H. Lin, H. T. Chang, W. N. Lai, and C. H. Chuang, “Public-key-based optical image cryptosystem with data embedding techniques,” Opt. Eng. 42, 2331–2339 (2003).
[CrossRef]

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

Opt. Express

Opt. Lett.

Optik

G. Situ and J. Zhang, “A cascaded iterative Fourier transform algorithm for optical security applications,” Optik 114, 473–477 (2003).
[CrossRef]

R. W. Gerchberg and W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik 34, 275–284 (1971).

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

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Figures (10)

Fig. 1.
Fig. 1.

Flow chart of modified Gerchberg-Saxton algorithm.

Fig. 2.
Fig. 2.

Single-image optical decryption architecture of the lensless Fresnel diffraction based on MGSA.

Fig. 3.
Fig. 3.

Block diagram of the proposed multiple-image encryption based on MGSA.

Fig. 4.
Fig. 4.

The proposed optical architecture of the multiple-image decryption based on MGSA by cascading POFs in the FrT domain.

Fig. 5.
Fig. 5.

Four encrypted target images: (a) g2(x2,y2), (b) g3(x3,y3), (c) g4(x4,y4), and (d) g5(x5,y5).

Fig. 6.
Fig. 6.

Noise-like POFs recorded in (POM1)(POM4), respectively, (a) POM1; (b) POM2; (c) POM3, and (d) POM4.

Fig. 7.
Fig. 7.

Decrypted four images compared to the original four images shown in Fig. 5, the CC values are all greater than 0.99.

Fig. 8.
Fig. 8.

Second decryption stage with a wrong parameter z2=65mm (correct z2=62mm), which cause the successive decrypted images: (a) g^2(x2,y2), (b) g^3(x3,y3), and (c) g^4(x4,y4) to be seriously degraded even all the POMs are correct.

Fig. 9.
Fig. 9.

(a) CC between g2(x2,y2) and g^2(x2,y2) as a function of the position shift Δz; (b) CC between g3(x3,y3) and g^3(x3,y3) as a function of the position shift Δz; (c) CC between g4(x4,y4) and g^4(x4,y4) as a function of the position shift Δz.

Fig. 10.
Fig. 10.

Variation of CC of the decrypted image with a function of a number of target images (N=100) for the keys are all correct.

Equations (8)

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

ρ=E{[gE[g]][|grec|E[|grec|]]}{E{[gE[g]]2}E{[|grec|E[|grec|]]2}}1/2,
FT{g1(x1,y1)exp[jψ1(x1,y1)];λ;z}=g1(x1,y1)exp[jψ1(x1,y1)]·exp{j2π(x1x2+y1y2)λz}dx1dy1=g^2(x2,y2)exp[jθ1(x2,y2)],
FrT{g1(x1,y1)exp[jψ1(x1,y1)];λ;z}=exp(j2πzλ)jλzg1(x1,y1)exp[jψ1(x1,y1)]exp{jπλz[(x2x1)2+(y2y1)2]}dx1dy1=g^2(x2,y2)exp[jθ1(x2,y2)],
FrT{gn(xn,yn)exp[jψn(xn,yn)];λ;zn}=gn+1(xn+1,yn+1)exp[jθn(xn+1,yn+1)],
FrT{exp[jψ1(x1,y1)];λ;z1}=g^2(x2,y2)exp[jθ1(x2,y2)].
FrT{g^2(x2,y2)exp[jθ1(x2,y2)]exp[jψ2(x2,y2)jθ1(x2,y2)];λ;z2}=FrT{g^2(x2,y2)exp[jψ2(x2,y2)];λ;z2}=g^3(x3,y3)exp[jθ2(x3,y3)].
FrT{g^n(xn,yn)exp[jθn1(xn,yn)]exp[jψn(xn,yn)jθn1(xn,yn)];λ;zn}=FrT{g^n(xn,yn)exp[jψn(xn,yn)];λ;zn}=g^n+1(xn+1,yn+1)exp[jθn(xn+1,yn+1)].
POMn=exp[j(ψnθn1)],1nNandθ0=0.

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