Abstract

A technique that combines the high speed and the high security of optical encryption with the advantages of electronic transmission, storage, and decryption is introduced. Digital phase-shifting interferometry is used for efficient recording of phase and amplitude information with an intensity recording device. The encryption is performed by use of two random phase codes, one in the object plane and another in the Fresnel domain, providing high security in the encrypted image and a key with many degrees of freedom. We describe how our technique can be adapted to encrypt either the Fraunhofer or the Fresnel diffraction pattern of the input. Electronic decryption can be performed with a one-step fast Fourier transform reconstruction procedure. Experimental results for both systems including a lensless setup are shown.

© 2000 Optical Society of America

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1999 (3)

1998 (2)

1997 (2)

1996 (1)

U. Schnars, T. M. Kreis, W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35, 977–982 (1996).
[CrossRef]

1995 (3)

1994 (3)

1993 (2)

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

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

1992 (1)

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 (3)

1987 (1)

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[CrossRef]

1979 (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.

Bollaro, F.

Brangaccio, D. J.

Bruning, J. H.

Chavel, P.

Ph. Lalanne, H. Richard, J. C. Rodier, P. Chavel, J. Taboury, K. Madani, P. Garda, F. Devos, “2D generation of random numbers by multimode fiber speckle for silicon arrays of processing elements,” Opt. Commun. 76, 387–394 (1990).
[CrossRef]

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]

Creath, K.

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. XXVI, pp. 349–393.
[CrossRef]

Cuche, E.

Denz, C.

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.

Devos, F.

Ph. Lalanne, H. Richard, J. C. Rodier, P. Chavel, J. Taboury, K. Madani, P. Garda, F. Devos, “2D generation of random numbers by multimode fiber speckle for silicon arrays of processing elements,” Opt. Commun. 76, 387–394 (1990).
[CrossRef]

Fainman, Y.

Ford, J. E.

Gallagher, J. E.

Garda, P.

Ph. Lalanne, H. Richard, J. C. Rodier, P. Chavel, J. Taboury, K. Madani, P. Garda, F. Devos, “2D generation of random numbers by multimode fiber speckle for silicon arrays of processing elements,” Opt. Commun. 76, 387–394 (1990).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Goudail, F.

Hagler, M. O.

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.

U. Schnars, T. M. Kreis, W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35, 977–982 (1996).
[CrossRef]

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]

Kang, Y. H.

Kawai, H.

Kim, K. H.

Kreis, T. M.

U. Schnars, T. M. Kreis, W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35, 977–982 (1996).
[CrossRef]

Krile, T. F.

Lalanne, Ph.

Ph. Lalanne, H. Richard, J. C. Rodier, P. Chavel, J. Taboury, K. Madani, P. Garda, F. Devos, “2D generation of random numbers by multimode fiber speckle for silicon arrays of processing elements,” Opt. Commun. 76, 387–394 (1990).
[CrossRef]

Lee, B.

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.

Madani, K.

Ph. Lalanne, H. Richard, J. C. Rodier, P. Chavel, J. Taboury, K. Madani, P. Garda, F. Devos, “2D generation of random numbers by multimode fiber speckle for silicon arrays of processing elements,” Opt. Commun. 76, 387–394 (1990).
[CrossRef]

Marron, J. C.

Matoba, O.

Ohzu, H.

Onural, L.

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[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]

Pedrini, G.

G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital double-pulsed holographic interferometry for vibration analysis,” J. Mod. Opt. 40, 367–374 (1995).
[CrossRef]

Psaltis, D.

Qiao, Y.

Redus, W. D.

Réfrégier, Ph.

Richard, H.

Ph. Lalanne, H. Richard, J. C. Rodier, P. Chavel, J. Taboury, K. Madani, P. Garda, F. Devos, “2D generation of random numbers by multimode fiber speckle for silicon arrays of processing elements,” Opt. Commun. 76, 387–394 (1990).
[CrossRef]

Rodier, J. C.

Ph. Lalanne, H. Richard, J. C. Rodier, P. Chavel, J. Taboury, K. Madani, P. Garda, F. Devos, “2D generation of random numbers by multimode fiber speckle for silicon arrays of processing elements,” Opt. Commun. 76, 387–394 (1990).
[CrossRef]

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.

Schroeder, K. S.

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]

Scott, P. D.

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[CrossRef]

Taboury, J.

Ph. Lalanne, H. Richard, J. C. Rodier, P. Chavel, J. Taboury, K. Madani, P. Garda, F. Devos, “2D generation of random numbers by multimode fiber speckle for silicon arrays of processing elements,” Opt. Commun. 76, 387–394 (1990).
[CrossRef]

Takaki, Y.

Tiziani, H. J.

G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital double-pulsed holographic interferometry for vibration analysis,” J. Mod. Opt. 40, 367–374 (1995).
[CrossRef]

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]

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]

Walkup, J. F.

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.

Zou, Y. L.

G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital double-pulsed holographic interferometry for vibration analysis,” J. Mod. Opt. 40, 367–374 (1995).
[CrossRef]

Appl. Opt. (7)

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]

J. Mod. Opt. (1)

G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital double-pulsed holographic interferometry for vibration analysis,” J. Mod. Opt. 40, 367–374 (1995).
[CrossRef]

J. Opt. Soc. Am. A (2)

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]

Ph. Lalanne, H. Richard, J. C. Rodier, P. Chavel, J. Taboury, K. Madani, P. Garda, F. Devos, “2D generation of random numbers by multimode fiber speckle for silicon arrays of processing elements,” Opt. Commun. 76, 387–394 (1990).
[CrossRef]

Opt. Eng. (3)

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

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[CrossRef]

U. Schnars, T. M. Kreis, W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35, 977–982 (1996).
[CrossRef]

Opt. Lett. (8)

Other (6)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. XXVI, pp. 349–393.
[CrossRef]

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

H. J. Caulfield, ed., Handbook of Optical Holography (Academic, London, 1979).

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]

J. L. Horner, B. Javidi, eds., Optical Engineering Special Issue on Optical Security (SPIE, Bellingham, Wash., 1999), Vol. 38.

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Figures (10)

Fig. 1
Fig. 1

Phase-shifting interferometer configured to perform Fourier encryption of the input image with two random phase masks. λ/2 and λ4 are half- and quarter-wave plates, respectively.

Fig. 2
Fig. 2

Four-step phase-shifting technique with retarder plates.

Fig. 3
Fig. 3

Diagram of the encryption–decryption procedure: (a) encryption, (b) obtaining the key, and (c) decryption.

Fig. 4
Fig. 4

Phase-shifting interferometer to perform Fresnel encryption of the input image. The input and the random phase masks generate Fresnel diffraction patterns at the output plane.

Fig. 5
Fig. 5

Information to be encrypted by Fourier transformation of the input. The gray-level image has been obtained by digital phase-shifting interferometry with the optical system in Fig. 1 without the reference phase mask.

Fig. 6
Fig. 6

Encrypted images of the input in Fig. 5: (a) gray-level representation of the phase distribution obtained by phase-shifting interferometry and (b) amplitude distribution. Picture (c) shows the reconstruction of the input object from the complex amplitude distribution associated with the previous images.

Fig. 7
Fig. 7

Key and decryption of the information in Fig. 5: (a) gray-level representation of the phase distribution of the key at the output plane obtained by phase-shifting interferometry and (b) amplitude distribution. Picture (c) shows the reconstruction of the input object when the phase and the amplitude distribution in Fig. 6 are corrected with the key.

Fig. 8
Fig. 8

Information to be encrypted by Fresnel propagation of the input signal. The gray-level image has been obtained by digital phase-shifting interferometry with the optical system in Fig. 4 without the reference phase mask.

Fig. 9
Fig. 9

Encrypted images of the information in Fig. 8 obtained by phase-shifting interferometry with the system in Fig. 4: (a) gray-level representation of the phase distribution and (b) amplitude distribution. Picture (c) shows an attempt to reconstruct the input object from the complex amplitude distribution associated with the previous images.

Fig. 10
Fig. 10

Key and decryption of the information in Fig. 8 with the optical system in Fig. 4: (a) gray-level representation of the phase distribution of the key at the output plane and (b) amplitude distribution of the key. Picture (c) shows the successful reconstruction of the input object when the phase and amplitude distribution in Fig. 9 are corrected with the previous key.

Equations (15)

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UOx, y=expi πf1-dfx2+y2×-tx, yexpiϕ1x, y×exp-i 2πλfxx+yydxdy,
URx, y; α=expiαexpi πλzx2+y2×-expiϕ2x, yexpi πλzx2+y2×exp-i 2πλzxx+yydxdy,
Ix, y; α=|UOx, y+URx, y; α|2,
Ix, y; α=AOx, y2+ARx, y2+2AOx, y×ARx, ycosϕOx, y-φx, y-α.
ϕE(x, y)=ϕO(x, y)-φ(x, y)=arctanI(x, y;-3π/2)-I(x, y;-π/2)I(x, y; 0)-I(x, y; -π).
AEx, y=AOx, yARx, y=14Ix, y; 0-Ix, y;-πcosϕOx, y-φx, y,
Ix, y; α=|AC expiϕC+URx, y; α|2,
ϕKx, y=ϕC-φx, y= arctanIx, y; -3 π/2-Ix, y; -π/2Ix, y; 0-Ix, y; -π,
AKx, y=ACARx, y=14Ix, y; 0-Ix, y; -πcosϕO-φx, y,
ϕOx, y=ϕEx, y-ϕKx, y,
AOx, y=AEx, yAKx, yif AKx, y00otherwise.
|tm, n|2=m=0N-1n=0N-1 UOm, n×expi 2πNmm+nn2,
Δx=λfNΔx=λfT,
UOx, y=expi πλdx2+y2-tx, y×expiϕ1x, yexpi πλdx2+y2×exp-i 2πλdxx+yydxdy.
|tm, n|2=m=0N-1n=0N-1 UOm, nexpiπ Δx2λdm2+n2×expi 2πNmm+nn2,

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