Abstract

In this Letter, low-frequency photorefractive holographic moiré fringe patterns are proposed as secure numerical code generators that could be useful for storage or data transmission. These dynamic moiré patterns are holographically obtained by the superposition of two or more sinusoidal gratings with slightly different pitches. The Bi12TiO20 photorefractive crystal sample is used as holographic medium. An optical numerical base was defined with patterns representing the 0, 1 and 1 digits as bits. Then, the complete set of these optical bits is combined to form bytes, where a numerical sequence is represented. The results show that the proposed numerical code is simple, robust and extremely secure, then could be used efficiently as standard numerical identification in robotic vision or eventually in storage or transmission of secure numerical data.

© 2013 Optical Society of America

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References

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2006 (2)

S. K. Kaura, D. P. Chhachhia, and A. K. Aggarwal, J. Opt. A 8, 67 (2006).

A. K. Aggarwal, S. K. Kaura, D. P. Chhachhia, and A. K. Sharma, Opt. Laser Technol. 38, 117 (2006).
[CrossRef]

2005 (1)

P. A. M. dos Santos and G. N. de Oliveira, Opt. Eng. 44, 12 (2005).

2004 (1)

J. A. Munõz-Rodrigues and R. Rodrigues-Vera, Opt. Commun. 236, 295 (2004).
[CrossRef]

2003 (1)

2002 (1)

P. A. M. dos Santos, Opt. Commun. 212, 211 (2002).
[CrossRef]

1997 (1)

1995 (1)

1979 (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Aggarwal, A. K.

A. K. Aggarwal, S. K. Kaura, D. P. Chhachhia, and A. K. Sharma, Opt. Laser Technol. 38, 117 (2006).
[CrossRef]

S. K. Kaura, D. P. Chhachhia, and A. K. Aggarwal, J. Opt. A 8, 67 (2006).

Chen, J.

Chhachhia, D. P.

A. K. Aggarwal, S. K. Kaura, D. P. Chhachhia, and A. K. Sharma, Opt. Laser Technol. 38, 117 (2006).
[CrossRef]

S. K. Kaura, D. P. Chhachhia, and A. K. Aggarwal, J. Opt. A 8, 67 (2006).

Dalsgaard, E.

de Oliveira, G. N.

P. A. M. dos Santos and G. N. de Oliveira, Opt. Eng. 44, 12 (2005).

dos Santos, P. A. M.

P. A. M. dos Santos and G. N. de Oliveira, Opt. Eng. 44, 12 (2005).

P. A. M. dos Santos, Opt. Commun. 212, 211 (2002).
[CrossRef]

Eddins, S. L.

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB (Pearson Prentice Hall, 2004), p. 14.

Gonzalez, R. C.

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB (Pearson Prentice Hall, 2004), p. 14.

Kaura, S. K.

S. K. Kaura, D. P. Chhachhia, and A. K. Aggarwal, J. Opt. A 8, 67 (2006).

A. K. Aggarwal, S. K. Kaura, D. P. Chhachhia, and A. K. Sharma, Opt. Laser Technol. 38, 117 (2006).
[CrossRef]

Kim, S.-J.

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Lai, H.

Liu, H.

Liu, S.

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Munõz-Rodrigues, J. A.

J. A. Munõz-Rodrigues and R. Rodrigues-Vera, Opt. Commun. 236, 295 (2004).
[CrossRef]

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Rodrigues-Vera, R.

J. A. Munõz-Rodrigues and R. Rodrigues-Vera, Opt. Commun. 236, 295 (2004).
[CrossRef]

Seo, D.-H.

Sharma, A. K.

A. K. Aggarwal, S. K. Kaura, D. P. Chhachhia, and A. K. Sharma, Opt. Laser Technol. 38, 117 (2006).
[CrossRef]

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Woods, R. E.

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB (Pearson Prentice Hall, 2004), p. 14.

Yeh, P.

P. Yeh, Introduction of Photorefractive Nonlinear Optics (Wiley, 1993).

Zang, X.

Appl. Opt. (2)

Ferroelectrics (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

J. Opt. A (1)

S. K. Kaura, D. P. Chhachhia, and A. K. Aggarwal, J. Opt. A 8, 67 (2006).

Opt. Commun. (2)

P. A. M. dos Santos, Opt. Commun. 212, 211 (2002).
[CrossRef]

J. A. Munõz-Rodrigues and R. Rodrigues-Vera, Opt. Commun. 236, 295 (2004).
[CrossRef]

Opt. Eng. (1)

P. A. M. dos Santos and G. N. de Oliveira, Opt. Eng. 44, 12 (2005).

Opt. Laser Technol. (1)

A. K. Aggarwal, S. K. Kaura, D. P. Chhachhia, and A. K. Sharma, Opt. Laser Technol. 38, 117 (2006).
[CrossRef]

Opt. Lett. (1)

Other (2)

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB (Pearson Prentice Hall, 2004), p. 14.

P. Yeh, Introduction of Photorefractive Nonlinear Optics (Wiley, 1993).

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Figures (6)

Fig. 1.
Fig. 1.

Crystal sample and axis configuration.

Fig. 2.
Fig. 2.

Moiré-like fringe pattern and its profile.

Fig. 3.
Fig. 3.

Experimental setup.

Fig. 4.
Fig. 4.

Moiré pattern images used as bits in the proposed optical numerical base.

Fig. 5.
Fig. 5.

Code generator algorithm, where H means fringes in the horizontal direction, V in the vertical direction, and D in a diagonal direction. I1, I2, and I3 are the sequences of images (bits) in the entrance of the system to form bytes in the process.

Fig. 6.
Fig. 6.

Equivalence diagram for the word FRINGE.

Equations (7)

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

I(r)=I0(1+Mcoskg·r),
ESC(r)=Dkμmsin(kg·r)1+mcos(kg·r),
Δn(r)=12r41n03ESC(r)=Δn0sin(kg·r)
η=[πΔn(r)λcos(θB)msin(ρl)ρ]2,
Δn(r)=2Δn0cos(kgm·r)sin(k¯g·r)
Δn(x)=2Δn0cos(kgmx)sin(k¯gx)
Δn(y)=2Δn0cos(kgmy)sin(k¯gy)

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