Abstract

Conventional phase-shifting interferometry (PSI) needs at least three interferograms. A novel algorithm of two-step PSI, with an arbitrary known phase step, by which a complex object field can be reconstructed with only two interferograms is proposed. This algorithm is then applied to an information security system based on double random-phase encoding in the Fresnel domain. The feasibility of this method and its robustness against occlusion and additional noise attacks are verified by computer simulations. This approach can considerably improve the efficiency of data transmission and is very suitable for Internet use.

© 2006 Optical Society of America

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X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, J. Opt. A, Pure Appl. Opt. 7, 624 (2005).
[CrossRef]

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2004 (4)

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2001 (1)

2000 (5)

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He, M. Z.

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[CrossRef]

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[CrossRef]

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L. Z. Cai, M. Z. He, Q. Liu, and X. L. Yang, Appl. Opt. 43, 3078 (2004).
[CrossRef] [PubMed]

Hennelly, B.

Ide, M.

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Kim, D. H.

Kim, H.

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M. Z. He, L. Z. Cai, Q. Liu, W. C. Wang, and X. F. Meng, Opt. Commun. 247, 29 (2005).
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T. Nomura, K. Uota, and Y. Morimoto, Opt. Eng. 43, 2228 (2004).
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S. Lai, B. King, and M. A. Neifeld, Opt. Commun. 173, 155 (2000).
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T. Nomura, K. Uota, and Y. Morimoto, Opt. Eng. 43, 2228 (2004).
[CrossRef]

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[CrossRef]

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Páez, G.

Réfrégier, P.

Rosen, J.

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X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, J. Opt. A, Pure Appl. Opt. 7, 624 (2005).
[CrossRef]

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Singh, K.

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Appl. Opt. (7)

J. Opt. A, Pure Appl. Opt. (1)

X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, J. Opt. A, Pure Appl. Opt. 7, 624 (2005).
[CrossRef]

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

Opt. Commun. (2)

S. Lai, B. King, and M. A. Neifeld, Opt. Commun. 173, 155 (2000).
[CrossRef]

M. Z. He, L. Z. Cai, Q. Liu, W. C. Wang, and X. F. Meng, Opt. Commun. 247, 29 (2005).
[CrossRef]

Opt. Eng. (1)

T. Nomura, K. Uota, and Y. Morimoto, Opt. Eng. 43, 2228 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (8)

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Figures (3)

Fig. 1
Fig. 1

Optical setup for the realization of the proposed security system.

Fig. 2
Fig. 2

Results of this information security system for an amplitude grayscale image. (a) The image to be encrypted, (b) one of the RPMs, (c) one of the interferograms, and (d) correctly retrieved image.

Fig. 3
Fig. 3

Robustness of this method against occlusion and noise attack for an amplitude grayscale image. (a) One of the interferograms with 25% occlusion; (b) retrieved image from (a); (c) one of the interferograms with Gaussian noise of standard deviation 0.1; and (d) retrieved image from (c).

Equations (13)

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I 1 ( x , y ) = A 0 2 ( x , y ) + A r 2 + 2 A 0 ( x , y ) A r cos φ ( x , y ) ,
I 2 ( x , y ) = A 0 2 ( x , y ) + A r 2 + 2 A 0 ( x , y ) A r cos [ φ ( x , y ) δ ] = A 0 2 ( x , y ) + A r 2 + 2 A 0 ( x , y ) A r [ cos φ ( x , y ) cos δ + sin φ ( x , y ) sin δ ] .
A 0 ( x , y ) cos φ ( x , y ) = I 1 a 2 A r ,
A 0 ( x , y ) sin φ ( x , y ) = I 2 I 1 cos δ ( 1 cos δ ) a 2 A r sin δ .
( I 1 a ) 2 sin 2 δ + [ I 2 I 1 cos δ ( 1 cos δ ) a ] 2 = 4 A r 2 ( a A r 2 ) sin 2 δ .
a = v v 2 4 u w 2 u ,
u = 2 ( 1 cos δ ) ,
v = 2 ( 1 cos δ ) ( I 1 + I 2 ) 4 A r 2 sin 2 δ ,
w = I 1 2 + I 2 2 2 I 1 I 2 cos δ + 4 A r 4 sin 2 δ = ( I 1 I 2 cos δ ) 2 + I 2 2 sin 2 δ + 4 A r 4 sin 2 δ .
v 2 4 u w = 64 sin 2 δ sin 2 ( δ 2 ) A r 2 [ cos ( φ δ 2 ) A 0 + cos ( δ 2 ) A r ] 2 0 ;
U ( x , y ) = A 0 ( x , y ) exp [ i φ ( x , y ) ] = A 0 ( x , y ) cos φ ( x , y ) + i A 0 ( x , y ) sin φ ( x , y ) = I 1 a 2 A r + i I 2 I 1 cos δ ( 1 cos δ ) a 2 A r sin δ .
U ( x , y ) = FR z 2 { FR z 1 { U 0 ( x 0 , y 0 ) exp [ i 2 π p ( x 0 , y 0 ) ] } exp [ i 2 π q ( x 1 , y 1 ) ] } ,
O ( x 0 , y 0 ) = IFR z 1 { IFR z 2 [ U ( x , y ) ] × exp [ i 2 π q ( x 1 , y 1 ) ] } exp [ i 2 π p ( x 0 , y 0 ) ] ,

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