Abstract

A high performance lensless optical security system based on the discrete Fresnel transform is presented. Two phase-only masks are generated with what we believe to be a novel and efficient algorithm. Their position coordinates and the wavelength are used as encoding parameters in the encryption process. Compared with previous studies, the main advantage of this proposed encryption system is that it does not need any iterative algorithms to produce the masks, and that makes it very efficient and easy to implement without losing the encryption security.

© 2006 Optical Society of America

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References

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2004 (2)

G. Situ and J. Zhang, "A cascaded iterative Fourier transform algorithm for optical security applications," Optik (Stuttgart) 114, 473-477 (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]

2003 (1)

2002 (4)

X. Peng, L. Yu, and L. Cai, "Double-lock for image encryption with virtual optical wavelength," Opt. Express 10, 41-45 (2002).
[PubMed]

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, 4825-4834 (2002).
[CrossRef] [PubMed]

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

S. Sinzinger, "Microoptically integrated correlators for security applications," Opt. Commun. 209, 69-74 (2002).
[CrossRef]

2001 (1)

2000 (6)

1999 (3)

1997 (1)

1996 (2)

R. K. Wang, I. A. Watson, and C. Chatwin, "Random phase encoding for optical security," Opt. Eng. (Bellingham) 35, 2464-2460 (1996).
[CrossRef]

L. G. Neto and Y. Sheng, "Optical implementation of image encryption using random phase encoding," Opt. Eng. (Bellingham) 35, 2459-2463 (1996).
[CrossRef]

1995 (1)

Cai, L.

Chang, H. T.

Chatwin, C.

R. K. Wang, I. A. Watson, and C. Chatwin, "Random phase encoding for optical security," Opt. Eng. (Bellingham) 35, 2464-2460 (1996).
[CrossRef]

Chen, N. X.

Cong, W. X.

Glückstad, J.

Gu, B. Y.

Hennelly, B.

Javidi, B.

Joseph, J.

Kreske, K.

Kuo, C. J.

Kuroda, K.

Li, J.

Li, Y.

Liu, S.

Lu, W. C.

Matoba, O.

Mogensen, P. C.

Neto, L. G.

L. G. Neto and Y. Sheng, "Optical implementation of image encryption using random phase encoding," Opt. Eng. (Bellingham) 35, 2459-2463 (1996).
[CrossRef]

Peng, X.

Ran, Q.

Réfrégier, P.

Rosen, J.

Sheng, Y.

L. G. Neto and Y. Sheng, "Optical implementation of image encryption using random phase encoding," Opt. Eng. (Bellingham) 35, 2459-2463 (1996).
[CrossRef]

Sheridan, J. T.

Shimura, T.

Singh, K.

Sinzinger, S.

S. Sinzinger, "Microoptically integrated correlators for security applications," Opt. Commun. 209, 69-74 (2002).
[CrossRef]

Situ, G.

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, "A cascaded iterative Fourier transform algorithm for optical security applications," Optik (Stuttgart) 114, 473-477 (2004).
[CrossRef]

Tajahuerce, E.

Tan, X.

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]

Unnikrishnan, G.

Verrall, S. C.

Wang, R. K.

R. K. Wang, I. A. Watson, and C. Chatwin, "Random phase encoding for optical security," Opt. Eng. (Bellingham) 35, 2464-2460 (1996).
[CrossRef]

Watson, I. A.

R. K. Wang, I. A. Watson, and C. Chatwin, "Random phase encoding for optical security," Opt. Eng. (Bellingham) 35, 2464-2460 (1996).
[CrossRef]

Yu, L.

Zhang, G.

Zhang, J.

G. Situ and J. Zhang, "A cascaded iterative Fourier transform algorithm for optical security applications," Optik (Stuttgart) 114, 473-477 (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]

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]

Zhu, B.

Appl. Opt. (7)

J. Opt. Soc. Am. A (1)

Opt. Commun. (3)

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

S. Sinzinger, "Microoptically integrated correlators for security applications," Opt. Commun. 209, 69-74 (2002).
[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]

Opt. Eng. (Bellingham) (2)

R. K. Wang, I. A. Watson, and C. Chatwin, "Random phase encoding for optical security," Opt. Eng. (Bellingham) 35, 2464-2460 (1996).
[CrossRef]

L. G. Neto and Y. Sheng, "Optical implementation of image encryption using random phase encoding," Opt. Eng. (Bellingham) 35, 2459-2463 (1996).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Optik (Stuttgart) (1)

G. Situ and J. Zhang, "A cascaded iterative Fourier transform algorithm for optical security applications," Optik (Stuttgart) 114, 473-477 (2004).
[CrossRef]

Other (1)

H.P.Herzig, ed., Micro-Optics (Taylor & Francis, 1996).

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Figures (9)

Fig. 1
Fig. 1

Optical setup of the lensless optical security system.

Fig. 2
Fig. 2

Image used as the target image for computer simulation.

Fig. 3
Fig. 3

Phase distribution of ψ 2 ( x 2 , y 2 ) .

Fig. 4
Fig. 4

Phase distribution of ψ 1 ( x 1 , y 1 ) .

Fig. 5
Fig. 5

Decrypted image obtained at the output with correct ψ 1 ( x 1 , y 1 ) , ψ 2 ( x 2 , y 2 ) and the corresponding keys.

Fig. 6
Fig. 6

Correlation coefficient between the target and the recovered image as a function of the wavelength difference between the encryption and decryption beam.

Fig. 7
Fig. 7

Retrieved image when (a) wavelength difference Δ λ = 2.2 × 10 5 nm , ρ = 0.5 , (b) wavelength difference Δ λ = 5.0 × 10 4 nm , ρ = 0.215 .

Fig. 8
Fig. 8

Correlation coefficient between the target and the recovered image as a function of the axial offset of POM 1 from its matched position.

Fig. 9
Fig. 9

Retrieved image when (a) Δ z = 1.08 nm , ρ = 0.5 ; (b) Δ z = 18.0 nm , ρ = 0.282 .

Equations (7)

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u ( x 1 , y 1 ) = exp [ j ψ 2 ( x 2 , y 2 ) ] h ( x 1 , y 1 ; x 2 , y 2 ; z 1 , z 2 ; λ ) d x 2 d y 2 ,
h ( x 1 , y 1 ; x 2 , y 2 ; z 2 ; λ ) = exp ( j 2 π z 2 λ ) j λ z 2 exp { j π λ z 2 [ ( x 1 x 2 ) 2 + ( y 1 y 2 ) 2 ] }
u ( x 1 , y 1 ) = FrT λ { exp [ j ψ 2 ( x 2 , y 2 ) ] ; z 2 } ,
u ( x 1 , y 1 ) = IFrT λ { g ( x 0 , y 0 ) ; z 1 } .
ψ 1 ( x 1 , y 1 ) = arg { u ( x 1 , y 1 ) u ( x 1 , y 1 ) } ,
g ̂ ( x 0 , y 0 ) = FrT λ { u ( x 1 , y 1 ) exp [ j ψ 1 ( x 1 , y 1 ) ] ; z 1 } = FrT λ [ u ( x 1 , y 1 ) u ( x 1 , y 1 ) u ( x 1 , y 1 ) ; z 1 ] = FrT λ [ u ( x 1 , y 1 ) ; z 1 ] = FrT λ { IFrT λ [ g ( x 0 , y 0 ) ; z 1 ] ; z 1 } = g ( x 0 , y 0 ) .
ρ = E { [ g E ( g ) ] [ g ̂ E ( g ̂ ) ] } ( E { [ g E ( g ) ] 2 } E { [ g ̂ E ( g ̂ ) ] 2 } ) 1 2 ,

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