Abstract

A method for optical encryption of three-dimensional (3D) information by use of digital holography is presented. A phase-shifting interferometer records the phase and amplitude information generated by a 3D object at a plane located in the Fresnel diffraction region with an intensity-recording device. Encryption is performed optically by use of the Fresnel diffraction pattern of a random phase code. Images of the 3D object with different perspectives and focused at different planes can be generated digital or optically after decryption with the proper key. Experimental results are presented.

© 2000 Optical Society of America

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References

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2000 (3)

1999 (4)

1998 (1)

1997 (1)

1995 (2)

1994 (2)

U. Schnars, W. P. O. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
[CrossRef] [PubMed]

B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

1993 (2)

H.-Y. Li, Y. Qiao, D. Psaltis, “Optical network for real-time face recognition,” Appl. Opt. 32, 5026–5035 (1993).
[CrossRef] [PubMed]

H. Lee, S. K. Jin, “Experimental study of volume holographic interconnects using random patterns,” Appl. Phys. Lett. 62, 2191–2193 (1993).
[CrossRef]

1991 (1)

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

1990 (1)

1974 (1)

1965 (1)

J. W. Cooley, J. W. Tukey, “An algorithm for the machine calculation of complex Fourier series,” Math. Comput. 19, 297–301 (1965).
[CrossRef]

Bashaw, M. C.

Bevilacqua, F.

Brangaccio, D. J.

Bruning, J. H.

Cooley, J. W.

J. W. Cooley, J. W. Tukey, “An algorithm for the machine calculation of complex Fourier series,” Math. Comput. 19, 297–301 (1965).
[CrossRef]

Cuche, E.

Denz, C.

C. Denz, K. O. Mueller, F. Visinka, T. T. Tschudi, “Digital volume holographic data storage using phase-coded multiplexing,” Proc. SPIE. 3802, 142–147 (1999).
[CrossRef]

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Depeursinge, C.

Fainman, Y.

Ford, J. E.

Gallagher, J. E.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

Heanue, J. F.

Herriott, D. R.

Hesselink, L.

Horner, J. L.

B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

Itoh, M.

Javidi, B.

Jin, S. K.

H. Lee, S. K. Jin, “Experimental study of volume holographic interconnects using random patterns,” Appl. Phys. Lett. 62, 2191–2193 (1993).
[CrossRef]

Jüptner, W. P. O.

Kawai, H.

Lee, H.

H. Lee, S. K. Jin, “Experimental study of volume holographic interconnects using random patterns,” Appl. Phys. Lett. 62, 2191–2193 (1993).
[CrossRef]

Lee, S. H.

Li, H.-Y.

Matoba, O.

Mueller, K. O.

C. Denz, K. O. Mueller, F. Visinka, T. T. Tschudi, “Digital volume holographic data storage using phase-coded multiplexing,” Proc. SPIE. 3802, 142–147 (1999).
[CrossRef]

Nomura, T.

Ohzu, H.

Ouyang, Y.

C. C. Sun, W. C. Su, B. Wang, Y. Ouyang, “Diffraction selectivity of holograms with random phase encoding,” Opt. Commun. 175, 67–74 (2000).
[CrossRef]

Paek, E. G.

C. L. Wilson, C. I. Watson, E. G. Paek, “Combined optical and neural network fingerprint matching,” in Optical Pattern Recognition VIII, D. P. Casasent, T. Chao, eds., Proc. SPIE3073, 373–382 (1997).
[CrossRef]

Pauliat, G.

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Psaltis, D.

Qiao, Y.

Réfrégier, Ph.

Roosen, G.

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Rosenfeld, D. P.

Schnars, U.

Schwider, J.

J. Schwider, “Advanced evaluation techniques in interferometry,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1990), Vol. XXVIII, pp. 271–359.
[CrossRef]

Su, W. C.

C. C. Sun, W. C. Su, B. Wang, Y. Ouyang, “Diffraction selectivity of holograms with random phase encoding,” Opt. Commun. 175, 67–74 (2000).
[CrossRef]

Sun, C. C.

C. C. Sun, W. C. Su, B. Wang, Y. Ouyang, “Diffraction selectivity of holograms with random phase encoding,” Opt. Commun. 175, 67–74 (2000).
[CrossRef]

Tajahuerce, E.

Takaki, Y.

Tschudi, T.

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Tschudi, T. T.

C. Denz, K. O. Mueller, F. Visinka, T. T. Tschudi, “Digital volume holographic data storage using phase-coded multiplexing,” Proc. SPIE. 3802, 142–147 (1999).
[CrossRef]

Tukey, J. W.

J. W. Cooley, J. W. Tukey, “An algorithm for the machine calculation of complex Fourier series,” Math. Comput. 19, 297–301 (1965).
[CrossRef]

Verrall, S. C.

Visinka, F.

C. Denz, K. O. Mueller, F. Visinka, T. T. Tschudi, “Digital volume holographic data storage using phase-coded multiplexing,” Proc. SPIE. 3802, 142–147 (1999).
[CrossRef]

Wang, B.

C. C. Sun, W. C. Su, B. Wang, Y. Ouyang, “Diffraction selectivity of holograms with random phase encoding,” Opt. Commun. 175, 67–74 (2000).
[CrossRef]

Watson, C. I.

C. L. Wilson, C. I. Watson, E. G. Paek, “Combined optical and neural network fingerprint matching,” in Optical Pattern Recognition VIII, D. P. Casasent, T. Chao, eds., Proc. SPIE3073, 373–382 (1997).
[CrossRef]

White, A. D.

Wilson, C. L.

C. L. Wilson, C. I. Watson, E. G. Paek, “Combined optical and neural network fingerprint matching,” in Optical Pattern Recognition VIII, D. P. Casasent, T. Chao, eds., Proc. SPIE3073, 373–382 (1997).
[CrossRef]

Yamaguchi, I.

Yatagai, T.

Yoshikawa, N.

Zhang, T.

Appl. Opt. (6)

Appl. Phys. Lett. (1)

H. Lee, S. K. Jin, “Experimental study of volume holographic interconnects using random patterns,” Appl. Phys. Lett. 62, 2191–2193 (1993).
[CrossRef]

Math. Comput. (1)

J. W. Cooley, J. W. Tukey, “An algorithm for the machine calculation of complex Fourier series,” Math. Comput. 19, 297–301 (1965).
[CrossRef]

Opt. Commun. (2)

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

C. C. Sun, W. C. Su, B. Wang, Y. Ouyang, “Diffraction selectivity of holograms with random phase encoding,” Opt. Commun. 175, 67–74 (2000).
[CrossRef]

Opt. Eng. (1)

B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

Opt. Lett. (7)

Proc. SPIE. (1)

C. Denz, K. O. Mueller, F. Visinka, T. T. Tschudi, “Digital volume holographic data storage using phase-coded multiplexing,” Proc. SPIE. 3802, 142–147 (1999).
[CrossRef]

Other (3)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

J. Schwider, “Advanced evaluation techniques in interferometry,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1990), Vol. XXVIII, pp. 271–359.
[CrossRef]

C. L. Wilson, C. I. Watson, E. G. Paek, “Combined optical and neural network fingerprint matching,” in Optical Pattern Recognition VIII, D. P. Casasent, T. Chao, eds., Proc. SPIE3073, 373–382 (1997).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Phase-shifting holographic system to encrypt 3D information.

Fig. 2
Fig. 2

Location of the window in the hologram to generate different vertical perspectives. Perspectives along any other direction can be obtained in a similar way.

Fig. 3
Fig. 3

Image of the 3D object to be encrypted obtained by phase-shifting interferometry with the system in Fig. 1 without reference phase mask.

Fig. 4
Fig. 4

Gray-level representation of (a) the encrypted amplitude and (b) the encrypted phase of the 3D object in Fig. 3 by use of a random reference phase mask.

Fig. 5
Fig. 5

Representation of (a) the key amplitude and (b) the key phase of the random phase mask used to encrypt the information in Fig. 4.

Fig. 6
Fig. 6

(a) Result of decryption of the encrypted information contained in Fig. 4 with the key in Fig. 5. (b) Incorrect decryption with a wrong phase key.

Fig. 7
Fig. 7

Different perspectives of the 3D object obtained after decryption. Angles of view are (a) β = 0.7°, (b) β = 0°, and β = -0.7°.

Equations (17)

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UHx, y=AHx, yexpiϕHx, y=1iλ -  UOx, y; z×1zexpi 2πλ z×expπλzx-x2+(y-y)2dxdydz,
URx, y; Δφp=expiΔφpexpi πλLx2+y2×-  expiϕx, y×exp-i 2πλLxx+yydxdy,
URx, y; Δφp=ARx, yexpiφRx, y+Δφp=expiΔφpexpiΦx, y expi πλLx2+y2.
Ipx, y=AHx, y2+ARx, y2+2AHx, yARx, y×cosϕHx, y-φRx, y-Δφp.
ϕEx, y=ϕHx, y-φRx, y=arctanI4-I2I1-I3.
AEx, y=AHx, yARx, y=14I1-I32+I4-I221/2.
ϕKx, y=ϕCφRx, y=arc tanI4-I2I1-I3,
AKx, y=ACARx, y=14I1-I32+I4-I221/2
ϕDx, y=ϕEx, y-φKx, y,
ADx, y=AEx, yAKx, yif AKx, y  00otherwise.
ϕDx, y=arctanI4-I2I1-I3-I1-I3I4-I2I4-I2I4-I2-I1-I3I1-I3,
ADx, y=I1-I32+I4-I22I1-I32+(I4-I221/2
UOm, n=exp-iπλdΔx2m2+Δy2n2×m=0Nx-1n=0Ny-1 UDm, nexp-iπλdΔx2m2+Δy2n2exp-i2πmmNx+nnNy.
Δx=λdNx Δx,  Δy=λdNy Δy.
α=ax Δxd,  β=ay Δyd.
UDm, n; ax, ay=UDm, nrectm-axbx, n-ayby×expi 2πλdΔx2axm+Δy2ayn,
UOm, n; α, β=exp-iπλdΔx2m2+Δy2n2×m=0Nx-1n=0Ny-1 UDm, n; αdΔx, βdΔy×exp-iπλdΔx2m2+Δy2n2×exp-i2πmmNx+nnNy.

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