Abstract

Objects acting as inputs of encrypting optical systems can be regarded as having two independent channels: amplitude and phase. In this context, we can use the term “complex objects” to refer these input objects. In this work we explore the way to perform an undercover operation where one channel (amplitude) is used to depict decoy information to confuse intruders, while the other (phase) operates with the true information. Besides, we use the Gerchberg–Saxton algorithm to transform the amplitude and phase encrypted information into pure phase data, therefore increasing the efficiency of the technique as only a single matrix containing these data needs to be sent. Finally, as an example to show the potential of the method, we combine the separate channels in a multiplexing technique with the Gerchberg–Saxton algorithm to generate an efficient multiuser secure process.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Réfrégier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20, 767-769 (1995).
    [CrossRef] [PubMed]
  2. B. Javidi, G. Zhang, and J. Li, “Encrypted optical memory using double-random phase encoding,” Appl. Opt. 36, 1054-1058 (1997).
    [CrossRef] [PubMed]
  3. O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24, 762-764 (1999).
    [CrossRef]
  4. E. Tajahuerce and B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39, 6595-6601 (2000).
    [CrossRef]
  5. R. Arizaga, R. Henao, and R. Torroba, “Fully digital encryption technique,” Opt. Commun. 221, 43-47 (2003).
    [CrossRef]
  6. J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260, 109-112 (2006).
    [CrossRef]
  7. J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiple image encryption using an aperture-modulated optical system,” Opt. Commun. 261, 29-33 (2006).
    [CrossRef]
  8. N. Takai and Y. Mifune, “Digital watermarking by a holographic technique,” Appl. Opt. 41, 865-873 (2002).
    [CrossRef] [PubMed]
  9. R. Arizaga and R. Torroba, “Validation through a binary key code and a polarization sensitive digital technique,” Opt. Commun. 215, 31-36 (2003).
    [CrossRef]
  10. H. Kim and Y. H. Lee, “Optimal watermarking of digital hologram of 3-D object,” Opt. Express 13, 2881-2886 (2005).
    [CrossRef] [PubMed]
  11. N. Towghi, B. Javidi, and Z. Luo, “Fully phase encrypted image processor,” J. Opt. Soc. Am. A 16, 1915-1927 (1999).
    [CrossRef]
  12. B. Javidi, N. Towghi, N. Maghzi, and S. C. Verrall, “Error-reduction techniques and error analysis for fully phase- and amplitude-based encryption,” Appl. Opt. 39, 4117-4130(2000).
    [CrossRef]
  13. X. Tan, O. Matoba, T. Shimma, K. Kuroda, and B. Javidi, “Secure optical storage that uses fully phase encryption,” Appl. Opt. 39, 6689-6694 (2000).
    [CrossRef]
  14. P. C. Mogensen and J. Glückstad, “phase-only optical encryption,” Opt. Lett. 25, 566-568 (2000).
    [CrossRef]
  15. N. K. Nishchal, J. Joseph, and K. Singh, “Optical phase encryption by phase contrast using electrically addressed spatial light modulator,” Opt. Commun. 217, 117-122(2003).
    [CrossRef]
  16. J. F. Barrera, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encryption technique by combining random amplitude and phase masks,” Optik (Jena) 120, 351-355 (2009).
    [CrossRef]
  17. T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39, 2031-2035(2000).
    [CrossRef]
  18. T. Nomura and B. Javidi, “Optical encryption system with a binary key code,” Appl. Opt. 39, 4783-4787 (2000).
    [CrossRef]
  19. N. K. Nischal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42, 1583-1588 (2003).
    [CrossRef]
  20. R. W. Gerchberg and W. O. Saxton, “Phase determination from image and diffraction plane pictures in the electron microscope,” Optik (Jena) 34, 275-284 (1971).
  21. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 227-246 (1972).
  22. C. H. Yeh, H. T. Chang, H. C. Chien, and C. J. Kuo, “Design of cascaded phase keys for a hierarchical security system,” Appl. Opt. 41, 6128-6134 (2002).
    [CrossRef] [PubMed]
  23. X. F. Meng, L. Z. Cai, X. L. Yang, X. X. Shen, and G. Y. Dong, “Information security system by iterative multiple-phase retrieval and pixel random permutation,” Appl. Opt. 45, 3289-3297 (2006).
    [CrossRef] [PubMed]
  24. M. Singh and A. Kumar, “Optical encryption and decryption using a sandwich random phase diffuser in the Fourier plane,” Opt. Eng. 46, 055201 (2007).
    [CrossRef]
  25. M. Singh, A. Kumar, and K. Singh, “Multiplexing in optical encryption by using an aperture system and a rotating sandwich random phase diffuser in the Fourier plane,” Opt. Lasers Eng. 46, 243-251 (2008).
    [CrossRef]

2009 (1)

J. F. Barrera, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encryption technique by combining random amplitude and phase masks,” Optik (Jena) 120, 351-355 (2009).
[CrossRef]

2008 (1)

M. Singh, A. Kumar, and K. Singh, “Multiplexing in optical encryption by using an aperture system and a rotating sandwich random phase diffuser in the Fourier plane,” Opt. Lasers Eng. 46, 243-251 (2008).
[CrossRef]

2007 (1)

M. Singh and A. Kumar, “Optical encryption and decryption using a sandwich random phase diffuser in the Fourier plane,” Opt. Eng. 46, 055201 (2007).
[CrossRef]

2006 (3)

X. F. Meng, L. Z. Cai, X. L. Yang, X. X. Shen, and G. Y. Dong, “Information security system by iterative multiple-phase retrieval and pixel random permutation,” Appl. Opt. 45, 3289-3297 (2006).
[CrossRef] [PubMed]

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260, 109-112 (2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiple image encryption using an aperture-modulated optical system,” Opt. Commun. 261, 29-33 (2006).
[CrossRef]

2005 (1)

2003 (4)

N. K. Nischal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42, 1583-1588 (2003).
[CrossRef]

R. Arizaga, R. Henao, and R. Torroba, “Fully digital encryption technique,” Opt. Commun. 221, 43-47 (2003).
[CrossRef]

R. Arizaga and R. Torroba, “Validation through a binary key code and a polarization sensitive digital technique,” Opt. Commun. 215, 31-36 (2003).
[CrossRef]

N. K. Nishchal, J. Joseph, and K. Singh, “Optical phase encryption by phase contrast using electrically addressed spatial light modulator,” Opt. Commun. 217, 117-122(2003).
[CrossRef]

2002 (2)

2000 (6)

1999 (2)

1997 (1)

1995 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 227-246 (1972).

1971 (1)

R. W. Gerchberg and W. O. Saxton, “Phase determination from image and diffraction plane pictures in the electron microscope,” Optik (Jena) 34, 275-284 (1971).

Arizaga, R.

R. Arizaga, R. Henao, and R. Torroba, “Fully digital encryption technique,” Opt. Commun. 221, 43-47 (2003).
[CrossRef]

R. Arizaga and R. Torroba, “Validation through a binary key code and a polarization sensitive digital technique,” Opt. Commun. 215, 31-36 (2003).
[CrossRef]

Barrera, J. F.

J. F. Barrera, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encryption technique by combining random amplitude and phase masks,” Optik (Jena) 120, 351-355 (2009).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiple image encryption using an aperture-modulated optical system,” Opt. Commun. 261, 29-33 (2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260, 109-112 (2006).
[CrossRef]

Bolognini, N.

J. F. Barrera, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encryption technique by combining random amplitude and phase masks,” Optik (Jena) 120, 351-355 (2009).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260, 109-112 (2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiple image encryption using an aperture-modulated optical system,” Opt. Commun. 261, 29-33 (2006).
[CrossRef]

Cai, L. Z.

Chang, H. T.

Chien, H. C.

Dong, G. Y.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 227-246 (1972).

R. W. Gerchberg and W. O. Saxton, “Phase determination from image and diffraction plane pictures in the electron microscope,” Optik (Jena) 34, 275-284 (1971).

Glückstad, J.

Henao, R.

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiple image encryption using an aperture-modulated optical system,” Opt. Commun. 261, 29-33 (2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260, 109-112 (2006).
[CrossRef]

R. Arizaga, R. Henao, and R. Torroba, “Fully digital encryption technique,” Opt. Commun. 221, 43-47 (2003).
[CrossRef]

Javidi, B.

Joseph, J.

N. K. Nischal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42, 1583-1588 (2003).
[CrossRef]

N. K. Nishchal, J. Joseph, and K. Singh, “Optical phase encryption by phase contrast using electrically addressed spatial light modulator,” Opt. Commun. 217, 117-122(2003).
[CrossRef]

Kim, H.

Kumar, A.

M. Singh, A. Kumar, and K. Singh, “Multiplexing in optical encryption by using an aperture system and a rotating sandwich random phase diffuser in the Fourier plane,” Opt. Lasers Eng. 46, 243-251 (2008).
[CrossRef]

M. Singh and A. Kumar, “Optical encryption and decryption using a sandwich random phase diffuser in the Fourier plane,” Opt. Eng. 46, 055201 (2007).
[CrossRef]

Kuo, C. J.

Kuroda, K.

Lee, Y. H.

Li, J.

Luo, Z.

Maghzi, N.

Matoba, O.

Meng, X. F.

Mifune, Y.

Mogensen, P. C.

Nischal, N. K.

N. K. Nischal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42, 1583-1588 (2003).
[CrossRef]

Nishchal, N. K.

N. K. Nishchal, J. Joseph, and K. Singh, “Optical phase encryption by phase contrast using electrically addressed spatial light modulator,” Opt. Commun. 217, 117-122(2003).
[CrossRef]

Nomura, T.

T. Nomura and B. Javidi, “Optical encryption system with a binary key code,” Appl. Opt. 39, 4783-4787 (2000).
[CrossRef]

T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39, 2031-2035(2000).
[CrossRef]

Réfrégier, P.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 227-246 (1972).

R. W. Gerchberg and W. O. Saxton, “Phase determination from image and diffraction plane pictures in the electron microscope,” Optik (Jena) 34, 275-284 (1971).

Shen, X. X.

Shimma, T.

Singh, K.

M. Singh, A. Kumar, and K. Singh, “Multiplexing in optical encryption by using an aperture system and a rotating sandwich random phase diffuser in the Fourier plane,” Opt. Lasers Eng. 46, 243-251 (2008).
[CrossRef]

N. K. Nishchal, J. Joseph, and K. Singh, “Optical phase encryption by phase contrast using electrically addressed spatial light modulator,” Opt. Commun. 217, 117-122(2003).
[CrossRef]

N. K. Nischal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42, 1583-1588 (2003).
[CrossRef]

Singh, M.

M. Singh, A. Kumar, and K. Singh, “Multiplexing in optical encryption by using an aperture system and a rotating sandwich random phase diffuser in the Fourier plane,” Opt. Lasers Eng. 46, 243-251 (2008).
[CrossRef]

M. Singh and A. Kumar, “Optical encryption and decryption using a sandwich random phase diffuser in the Fourier plane,” Opt. Eng. 46, 055201 (2007).
[CrossRef]

Tajahuerce, E.

Takai, N.

Tan, X.

Tebaldi, M.

J. F. Barrera, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encryption technique by combining random amplitude and phase masks,” Optik (Jena) 120, 351-355 (2009).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiple image encryption using an aperture-modulated optical system,” Opt. Commun. 261, 29-33 (2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260, 109-112 (2006).
[CrossRef]

Torroba, R.

J. F. Barrera, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encryption technique by combining random amplitude and phase masks,” Optik (Jena) 120, 351-355 (2009).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260, 109-112 (2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiple image encryption using an aperture-modulated optical system,” Opt. Commun. 261, 29-33 (2006).
[CrossRef]

R. Arizaga and R. Torroba, “Validation through a binary key code and a polarization sensitive digital technique,” Opt. Commun. 215, 31-36 (2003).
[CrossRef]

R. Arizaga, R. Henao, and R. Torroba, “Fully digital encryption technique,” Opt. Commun. 221, 43-47 (2003).
[CrossRef]

Towghi, N.

Verrall, S. C.

Yang, X. L.

Yeh, C. H.

Zhang, G.

Appl. Opt. (8)

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

Opt. Commun. (5)

R. Arizaga and R. Torroba, “Validation through a binary key code and a polarization sensitive digital technique,” Opt. Commun. 215, 31-36 (2003).
[CrossRef]

R. Arizaga, R. Henao, and R. Torroba, “Fully digital encryption technique,” Opt. Commun. 221, 43-47 (2003).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encrypted data by using polarized light,” Opt. Commun. 260, 109-112 (2006).
[CrossRef]

J. F. Barrera, R. Henao, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiple image encryption using an aperture-modulated optical system,” Opt. Commun. 261, 29-33 (2006).
[CrossRef]

N. K. Nishchal, J. Joseph, and K. Singh, “Optical phase encryption by phase contrast using electrically addressed spatial light modulator,” Opt. Commun. 217, 117-122(2003).
[CrossRef]

Opt. Eng. (3)

T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39, 2031-2035(2000).
[CrossRef]

M. Singh and A. Kumar, “Optical encryption and decryption using a sandwich random phase diffuser in the Fourier plane,” Opt. Eng. 46, 055201 (2007).
[CrossRef]

N. K. Nischal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42, 1583-1588 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (1)

M. Singh, A. Kumar, and K. Singh, “Multiplexing in optical encryption by using an aperture system and a rotating sandwich random phase diffuser in the Fourier plane,” Opt. Lasers Eng. 46, 243-251 (2008).
[CrossRef]

Opt. Lett. (3)

Optik (Jena) (3)

R. W. Gerchberg and W. O. Saxton, “Phase determination from image and diffraction plane pictures in the electron microscope,” Optik (Jena) 34, 275-284 (1971).

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 227-246 (1972).

J. F. Barrera, M. Tebaldi, R. Torroba, and N. Bolognini, “Multiplexing encryption technique by combining random amplitude and phase masks,” Optik (Jena) 120, 351-355 (2009).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Double phase mask encrypting architecture: R 1 and R 2 , encrypting masks; L, transforming lens with focal length f; * denotes complex conjugate. The upper and lower parts describe the complex encrypyting and decrypting procedures respectively.

Fig. 2
Fig. 2

Block diagram for (a) encryption and (b) decryption. FT represents the Fourier transform operation, and * denotes complex conjugate.

Fig. 3
Fig. 3

(a) and (b) Binary amplitude and phase, respectively, of the complex input object (note the message in the bars in the phase information); (c) reconstructed amplitude using only the Fourier-plane coding mask, observing no traces of the phase component; (d) phase component reconstructed using the input-plane phase mask.

Fig. 4
Fig. 4

Block diagram showing the sequence (clockwise) when applying the Gerchberg–Saxton algorithm. FT and FT 1 represent the direct and inverse Fourier transform operation, respectively.

Fig. 5
Fig. 5

Image of an input complex object to be encrypted and phase transformed with the aid of the Gerchberg–Saxton algorithm. (a) and (b) Amplitude and phase of the object, respectively. (c) Pure phase element obtained after applying the Gerchberg–Saxton algorithm over the complex encrypted object. The resulting decrypted image corresponding to the input complex object is shown in (d) amplitude and (e) phase.

Fig. 6
Fig. 6

Flow charts depicting the multiplexing procedure for a three-input case: CO 1 , CO 2 , and CO 3 , complex input objects; I , Fourier transform; R 1 , R 2 , R 3 , and R 4 , random phase masks; E 1 , E 2 , and E 3 encrypted complex objects; M, multiplexed encrypted information; *, complex conjugate.

Fig. 7
Fig. 7

Images of two input complex objects to be encrypted, multiplexed, and phase transformed with the aid of the Gerchberg–Saxton algorithm. (a) and (b) Amplitude and phase of one object, respectively; (c) and (d) second object amplitude and phase, respectively.

Fig. 8
Fig. 8

Resulting decrypted images corresponding to the objects shown in Fig. 7. The reconstructions depict in (a) and (c) the objects amplitudes, and in (b) and (d) their respective phases.

Fig. 9
Fig. 9

NMSE curve as a fuction of the percentage of random noise affecting the pure phase multiplexing.

Equations (10)

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

g ( v , ω ) = FT v , w { f ( x , y ) · exp [ i 2 π q ( x , y ) ] · exp [ i 2 π p ( x , y ) ] } · exp [ i 2 π b ( v , w ) ] ,
ψ a ( x , y ) = { f ( x , y ) · exp [ i 2 π q ( x , y ) ] · R 1 ( x , y ) } FT x , y { R 2 ( v , w ) } ,
k ( v , w ) = FT v , w * { f ( x , y ) · exp [ i 2 π q ( x , y ) ] · R 1 ( x , y ) } · R 2 * ( v , w ) ,
D ( x , y ) = f * ( x , y ) · exp [ i 2 π q ( x , y ) ] · R 1 * ( x , y ) .
CO * ( x , y ) = f * ( x , y ) · exp [ i 2 π q ( x , y ) ] .
M ( x , y ) = [ CO 1 ( x , y ) · R 1 ( x , y ) ] FT x , y { R 2 ( v , w ) · R 3 ( v , w ) } + [ CO 2 ( x , y ) · R 1 ( x , y ) ] FT x , y { R 2 ( v , w ) · R 4 ( v , w ) } + [ CO 3 ( x , y ) · R 1 ( x , y ) ] FT x , y { R 2 ( v , w ) R 3 ( v , w ) · R 4 ( v , w ) } .
k m ( v , w ) = [ FT v , w * { CO 1 ( x , y ) · R 1 ( x , y ) } · R 2 * ( v , w ) · R 3 * ( v , w ) + [ FT v , w * { CO 2 ( x , y ) · R 1 ( x , y ) } · R 2 * ( v , w ) · R 4 * ( v , w ) + [ FT v , w * { CO 3 ( x , y ) · R 1 ( x , y ) } · R 2 * ( v , w ) · R 3 * ( v , w ) R 4 * ( v , w ) .
D 1 ( x , y ) = CO 1 * ( x , y ) · R 1 * ( x , y ) + [ CO 2 * ( x , y ) · R 1 * ( x , y ) ] FT x , y { R 4 * ( v , w ) · R 3 ( v , w ) } + [ CO 3 * ( x , y ) · R 1 * ( x , y ) ] FT x , y { R 4 * ( v , w ) } .
NMSE = 1 K · m , n N | D ( m , n ) D ( m , n ) | 2 ,
K = m , n N | D ( m , n ) D w ( m , n ) | 2 .

Metrics