Abstract

In this Letter, we present a three-dimensional (3D) photon counting double-random-phase encryption (DRPE) technique using passive integral imaging. A 3D photon counting DRPE can encrypt a 3D scene and provides more security and authentications due to photon counting Poisson nonlinear transformation on the encrypted image. In addition, 3D imaging allows verification of the 3D object at different depths. Preliminary results and performance evaluation have been presented.

© 2013 Optical Society of America

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References

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2013 (1)

2012 (1)

A. Stern and B. Javidi, IEEE Photon. J. 4, 1188 (2012).
[CrossRef]

2011 (2)

2010 (1)

2009 (3)

M. Daneshpanah and B. Javidi, Opt. Lett. 34, 1105 (2009).
[CrossRef]

O. Matoba, T. Nomura, E. Perez-Cabre, M. S. Millan, and B. Javidi, Proc. IEEE 97, 1128 (2009).
[CrossRef]

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, Proc. IEEE 97, 1067 (2009).
[CrossRef]

2008 (1)

2007 (1)

2006 (1)

2005 (2)

2001 (2)

2000 (2)

1999 (1)

1998 (2)

1995 (1)

1994 (1)

B. Javidi and J. L. Horner, Opt. Eng. 33, 1752 (1994).
[CrossRef]

1989 (1)

Aggoun, A.

Aloni, D.

Arai, J.

Arcos, S.

Bollaro, F.

Carnicer, A.

Cho, M.

Clemente, P.

Daneshpanah, M.

Davies, N.

Duran, V.

Gluckstad, J.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 1985).

Goudail, F.

Guillanume, M.

Horner, J. L.

B. Javidi and J. L. Horner, Opt. Eng. 33, 1752 (1994).
[CrossRef]

Ide, M.

Javidi, B.

Juvells, I.

Kawakita, M.

Kung, S. Y.

Kuroda, K.

Lancis, J.

Manolache, S.

Martinez-Corral, M.

X. Xiao, B. Javidi, M. Martinez-Corral, and A. Stern, Appl. Opt. 52, 546 (2013).
[CrossRef]

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, Proc. IEEE 97, 1067 (2009).
[CrossRef]

Martinez-Cuenca, R.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, Proc. IEEE 97, 1067 (2009).
[CrossRef]

Matoba, O.

McCormick, M.

Melon, P.

Millan, M. S.

O. Matoba, T. Nomura, E. Perez-Cabre, M. S. Millan, and B. Javidi, Proc. IEEE 97, 1128 (2009).
[CrossRef]

Mogensen, P. C.

Montes-Usategui, M.

Nomura, T.

O. Matoba, T. Nomura, E. Perez-Cabre, M. S. Millan, and B. Javidi, Proc. IEEE 97, 1128 (2009).
[CrossRef]

B. Javidi and T. Nomura, Opt. Lett. 25, 28 (2000).
[CrossRef]

Okada-Shudo, Y.

Okano, F.

Okui, M.

Perez-Cabre, E.

E. Perez-Cabre, M. Cho, and B. Javidi, Opt. Lett. 36, 22 (2011).
[CrossRef]

O. Matoba, T. Nomura, E. Perez-Cabre, M. S. Millan, and B. Javidi, Proc. IEEE 97, 1128 (2009).
[CrossRef]

Refregier, P.

Refregieran, P.

Saavedra, G.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, Proc. IEEE 97, 1067 (2009).
[CrossRef]

Shimura, T.

Stern, A.

Tajahuerce, E.

Tan, X.

Tavakoli, B.

Torres-Company, V.

Watson, E.

Xiao, X.

Yeom, S.

Appl. Opt. (3)

IEEE Photon. J. (1)

A. Stern and B. Javidi, IEEE Photon. J. 4, 1188 (2012).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Eng. (1)

B. Javidi and J. L. Horner, Opt. Eng. 33, 1752 (1994).
[CrossRef]

Opt. Express (3)

Opt. Lett. (10)

Proc. IEEE (2)

O. Matoba, T. Nomura, E. Perez-Cabre, M. S. Millan, and B. Javidi, Proc. IEEE 97, 1128 (2009).
[CrossRef]

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, Proc. IEEE 97, 1067 (2009).
[CrossRef]

Other (1)

J. W. Goodman, Statistical Optics (Wiley, 1985).

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Figures (6)

Fig. 1.
Fig. 1.

(a) Primary image, (b) encrypted image, (c) photon-limited encrypted image with Np=1000, and (d) photon-limited decrypted image with Np=1000.

Fig. 2.
Fig. 2.

Pickup stage for 3D photon counting double-random-phase encryption.

Fig. 3.
Fig. 3.

(a) Primary images, (b) conventional encrypted 2D images, and (c) photon-limited encrypted 2D images with Np=1000.

Fig. 4.
Fig. 4.

(a) Regular decrypted 2D images, (b) photon-limited decrypted 2D images with Np=1000, and (c) 3D photon-limited decrypted images at z=300mm using 10×10 photon-limited decrypted images with Np=1000.

Fig. 5.
Fig. 5.

Peak to correlation energy (PCE) results of decrypted 3D images and decrypted 2D images for true and false classes.

Fig. 6.
Fig. 6.

Correlation results using kth law (k=0.3) nonlinear filter for true and false classes for 2D and 3D photon counting images.

Equations (8)

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IE(x)=I1{I[f(x)exp{i2πns(x)}]exp[i2πnf(μ)]},
λE(x)=IE(x)x=1NxIE(x),
CE(x)|λE(x)Poisson[NpλE(x)],
fphm(x)=|I1{I[CEm(x)]exp[i2πnf(μ)]}|,
I˜z(x)=1NPMm=1Mfphm(x+Δx{m1}),
Δx=(Nxpf)/(cxz),
r(x)=I1{|I[I˜z(x)]F(μ)|kexp[i(ϕI˜z(μ)ϕF(μ))]},
PCE=max[|r(x)|2]/i=1N|r(xi)|2.

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