Abstract

We present a system for the implementation of phase-only optical decryption of an encrypted fixed phase mask. We achieve decryption by superimposing a decrypting phase key, implemented on a phase-only spatial light modulator with an encrypted phase mask in two equivalent image planes in an optical system. The decrypted phase information is retrieved by the generalized phase-contrast technique. We have constructed a compact experimental system that uses a 635-nm diode laser in which a fixed encrypted 0/π binary phase mask is decrypted by a binary phase key produced electronically on the spatial light modulator. The key is aligned by electronic scrolling of its position with respect to the mask.

© 2001 Optical Society of America

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References

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  1. B. Javidi, “Securing information with optical technologies,” Phys. Today 50, (3)27–32 (1997).
  2. R. L. van Renesse, Optical Document Security (Artech House, London, 1998).
  3. B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
    [CrossRef]
  4. P. Réfrégier, B. Javidi, “Optical encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
    [CrossRef]
  5. N. Towghi, B. Javidi, Z. Lou, “Fully phase encrypted image processor,” J. Opt. Soc. Am. A 16, 1915–1927 (1999).
    [CrossRef]
  6. O. Matoba, B. Javidi, “Encrypted optical storage with angular multiplexing,” Appl. Opt. 38, 7288–7293 (1999).
    [CrossRef]
  7. S. Lai, “Security holograms using an encoded reference wave,” Opt. Eng. 35, 2470–2472 (1996).
    [CrossRef]
  8. B. Javidi, T. Nomura, “Securing information by digital holography,” Opt. Lett. 25, 28–30 (2000).
    [CrossRef]
  9. D. Weber, J. Trolinger, “Novel implementation of non-linear joint transform correlators in optical security and validation,” Opt. Eng. 38, 62–68 (1999).
    [CrossRef]
  10. J. W. Han, C. S. Park, D. H. Ryu, E. S. Kim, “Optical image encryption based on xor operations,” Opt. Eng. 38, 47–54 (1999).
    [CrossRef]
  11. E. G. Johnson, J. D. Brasher, D. Gregory, P. Erbach, M. Duignan, G. Behrman, S. H. Lee, W. Dashner, P. Long, “Optical recognition of phase-encrypted biometrics,” Opt. Eng. 37, 18–26 (1998).
    [CrossRef]
  12. G. Unnikrishnan, J. Joseph, K. Singh, “Optical encryption system that uses phase conjugation in a photorefractive crystal,” Appl. Opt. 37, 8181–8186 (1998).
    [CrossRef]
  13. E. Tarahuerce, O. Matoba, S. C. Verrall, B. Javidi, “Optoelectronic information encryption with phase-shifting interferometry,” Appl. Opt. 39, 2313–2320 (2000).
    [CrossRef]
  14. J. Glückstad, “Phase contrast scrambling,” International PCT patent application WO 002339A1 (3July1998).
  15. J. Glückstad, “Image decrypting common path interferometer,” in Optical Pattern Recognition X, D. P. Casasent, T. Chao, eds., Proc. SPIE3715, 152–159 (1999).
    [CrossRef]
  16. P. C. Mogensen, J. Glückstad, “Phase-only optical encryption,” Opt. Lett. 25, 566–568 (2000).
    [CrossRef]
  17. P. C. Mogensen, J. Glückstad, “A phase based optical encryption system with polarization encoding,” Opt. Commun. 173, 177–183 (2000).
    [CrossRef]
  18. J. Glückstad, “Pattern generation by inverse phase contrast—comment,” Opt. Commun. 147, 16–19 (1998).
    [CrossRef]
  19. J. Glückstad, “Phase contrast image synthesis,” Opt. Commun. 130, 225–230 (1996).
    [CrossRef]
  20. J. Glückstad, L. Lading, H. Toyoda, T. Hara, “Lossless light projection,” Opt. Lett. 22, 1373–1375 (1997).
    [CrossRef]
  21. J. Glückstad, “Graphic method for analyzing common path interferometers,” Appl. Opt. 37, 8151–8152 (1998).
    [CrossRef]
  22. F. Zernike, “How I discovered phase contrast,” Science 121, 345–349 (1955).
    [CrossRef] [PubMed]
  23. L. G. Neto, “Implementation of image encryption using phase contrast techniques,” in Optical Pattern Recognition IX, D. P. Casasent, T. Chao, eds., Proc. SPIE3386, 284–289 (1998).
    [CrossRef]
  24. J. Glückstad, P. C. Mogensen, “Optimal phase contrast in common-path interferometry,” Appl. Opt. 40, 268–282 (2001).
    [CrossRef]
  25. J. Glückstad, P. C. Mogensen, “Reconfigurable ternary-phase array illuminator based on the generalised phase contrast method,” Opt. Commun. 173, 169–175 (2000).
    [CrossRef]
  26. Optics and Fluid Dynamics Department, Annual progress report R-793(EN) (Risø National Laboratory, Roskilde, Denmark, 1995).
  27. N. Mukohzaka, N. Yoshida, H. Toyoda, Y. Kobayashi, T. Hara, “Diffraction efficiency analysis of a parallel-aligned nematic-liquid-crystal spatial light modulator,” Appl. Opt. 33, 2804–2811 (1994).
    [CrossRef] [PubMed]
  28. Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
    [CrossRef]
  29. Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, M. Wu, “Compact high efficiency electrically addressable phase-only spatial light modulator,” in Diffractive/Holographic Technologies and Spatial Light Modulators VIII, I. Cindrich, S. H. Lee, R. L. Sutherland, eds., Proc. SPIE3951, 158–165 (2000).
    [CrossRef]
  30. P. C. Mogensen, J. Glückstad, “Practical implementation of phase-only optical encryption system,” in Optical Security and Counterfeit Deterence Techniques III, R. L. Van Renesse, W. A. Vliegenthart, eds., Proc. SPIE3973, 284–293 (2000).
    [CrossRef]
  31. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

2001 (1)

2000 (5)

J. Glückstad, P. C. Mogensen, “Reconfigurable ternary-phase array illuminator based on the generalised phase contrast method,” Opt. Commun. 173, 169–175 (2000).
[CrossRef]

B. Javidi, T. Nomura, “Securing information by digital holography,” Opt. Lett. 25, 28–30 (2000).
[CrossRef]

E. Tarahuerce, O. Matoba, S. C. Verrall, B. Javidi, “Optoelectronic information encryption with phase-shifting interferometry,” Appl. Opt. 39, 2313–2320 (2000).
[CrossRef]

P. C. Mogensen, J. Glückstad, “Phase-only optical encryption,” Opt. Lett. 25, 566–568 (2000).
[CrossRef]

P. C. Mogensen, J. Glückstad, “A phase based optical encryption system with polarization encoding,” Opt. Commun. 173, 177–183 (2000).
[CrossRef]

1999 (5)

D. Weber, J. Trolinger, “Novel implementation of non-linear joint transform correlators in optical security and validation,” Opt. Eng. 38, 62–68 (1999).
[CrossRef]

J. W. Han, C. S. Park, D. H. Ryu, E. S. Kim, “Optical image encryption based on xor operations,” Opt. Eng. 38, 47–54 (1999).
[CrossRef]

N. Towghi, B. Javidi, Z. Lou, “Fully phase encrypted image processor,” J. Opt. Soc. Am. A 16, 1915–1927 (1999).
[CrossRef]

O. Matoba, B. Javidi, “Encrypted optical storage with angular multiplexing,” Appl. Opt. 38, 7288–7293 (1999).
[CrossRef]

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

1998 (4)

E. G. Johnson, J. D. Brasher, D. Gregory, P. Erbach, M. Duignan, G. Behrman, S. H. Lee, W. Dashner, P. Long, “Optical recognition of phase-encrypted biometrics,” Opt. Eng. 37, 18–26 (1998).
[CrossRef]

G. Unnikrishnan, J. Joseph, K. Singh, “Optical encryption system that uses phase conjugation in a photorefractive crystal,” Appl. Opt. 37, 8181–8186 (1998).
[CrossRef]

J. Glückstad, “Pattern generation by inverse phase contrast—comment,” Opt. Commun. 147, 16–19 (1998).
[CrossRef]

J. Glückstad, “Graphic method for analyzing common path interferometers,” Appl. Opt. 37, 8151–8152 (1998).
[CrossRef]

1997 (2)

J. Glückstad, L. Lading, H. Toyoda, T. Hara, “Lossless light projection,” Opt. Lett. 22, 1373–1375 (1997).
[CrossRef]

B. Javidi, “Securing information with optical technologies,” Phys. Today 50, (3)27–32 (1997).

1996 (2)

S. Lai, “Security holograms using an encoded reference wave,” Opt. Eng. 35, 2470–2472 (1996).
[CrossRef]

J. Glückstad, “Phase contrast image synthesis,” Opt. Commun. 130, 225–230 (1996).
[CrossRef]

1995 (1)

1994 (2)

1955 (1)

F. Zernike, “How I discovered phase contrast,” Science 121, 345–349 (1955).
[CrossRef] [PubMed]

Behrman, G.

E. G. Johnson, J. D. Brasher, D. Gregory, P. Erbach, M. Duignan, G. Behrman, S. H. Lee, W. Dashner, P. Long, “Optical recognition of phase-encrypted biometrics,” Opt. Eng. 37, 18–26 (1998).
[CrossRef]

Brasher, J. D.

E. G. Johnson, J. D. Brasher, D. Gregory, P. Erbach, M. Duignan, G. Behrman, S. H. Lee, W. Dashner, P. Long, “Optical recognition of phase-encrypted biometrics,” Opt. Eng. 37, 18–26 (1998).
[CrossRef]

Dashner, W.

E. G. Johnson, J. D. Brasher, D. Gregory, P. Erbach, M. Duignan, G. Behrman, S. H. Lee, W. Dashner, P. Long, “Optical recognition of phase-encrypted biometrics,” Opt. Eng. 37, 18–26 (1998).
[CrossRef]

Duignan, M.

E. G. Johnson, J. D. Brasher, D. Gregory, P. Erbach, M. Duignan, G. Behrman, S. H. Lee, W. Dashner, P. Long, “Optical recognition of phase-encrypted biometrics,” Opt. Eng. 37, 18–26 (1998).
[CrossRef]

Erbach, P.

E. G. Johnson, J. D. Brasher, D. Gregory, P. Erbach, M. Duignan, G. Behrman, S. H. Lee, W. Dashner, P. Long, “Optical recognition of phase-encrypted biometrics,” Opt. Eng. 37, 18–26 (1998).
[CrossRef]

Fukuchi, N.

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, M. Wu, “Compact high efficiency electrically addressable phase-only spatial light modulator,” in Diffractive/Holographic Technologies and Spatial Light Modulators VIII, I. Cindrich, S. H. Lee, R. L. Sutherland, eds., Proc. SPIE3951, 158–165 (2000).
[CrossRef]

Glückstad, J.

J. Glückstad, P. C. Mogensen, “Optimal phase contrast in common-path interferometry,” Appl. Opt. 40, 268–282 (2001).
[CrossRef]

J. Glückstad, P. C. Mogensen, “Reconfigurable ternary-phase array illuminator based on the generalised phase contrast method,” Opt. Commun. 173, 169–175 (2000).
[CrossRef]

P. C. Mogensen, J. Glückstad, “Phase-only optical encryption,” Opt. Lett. 25, 566–568 (2000).
[CrossRef]

P. C. Mogensen, J. Glückstad, “A phase based optical encryption system with polarization encoding,” Opt. Commun. 173, 177–183 (2000).
[CrossRef]

J. Glückstad, “Pattern generation by inverse phase contrast—comment,” Opt. Commun. 147, 16–19 (1998).
[CrossRef]

J. Glückstad, “Graphic method for analyzing common path interferometers,” Appl. Opt. 37, 8151–8152 (1998).
[CrossRef]

J. Glückstad, L. Lading, H. Toyoda, T. Hara, “Lossless light projection,” Opt. Lett. 22, 1373–1375 (1997).
[CrossRef]

J. Glückstad, “Phase contrast image synthesis,” Opt. Commun. 130, 225–230 (1996).
[CrossRef]

J. Glückstad, “Phase contrast scrambling,” International PCT patent application WO 002339A1 (3July1998).

J. Glückstad, “Image decrypting common path interferometer,” in Optical Pattern Recognition X, D. P. Casasent, T. Chao, eds., Proc. SPIE3715, 152–159 (1999).
[CrossRef]

P. C. Mogensen, J. Glückstad, “Practical implementation of phase-only optical encryption system,” in Optical Security and Counterfeit Deterence Techniques III, R. L. Van Renesse, W. A. Vliegenthart, eds., Proc. SPIE3973, 284–293 (2000).
[CrossRef]

Goodman, J. W.

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

Gregory, D.

E. G. Johnson, J. D. Brasher, D. Gregory, P. Erbach, M. Duignan, G. Behrman, S. H. Lee, W. Dashner, P. Long, “Optical recognition of phase-encrypted biometrics,” Opt. Eng. 37, 18–26 (1998).
[CrossRef]

Han, J. W.

J. W. Han, C. S. Park, D. H. Ryu, E. S. Kim, “Optical image encryption based on xor operations,” Opt. Eng. 38, 47–54 (1999).
[CrossRef]

Hara, T.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

J. Glückstad, L. Lading, H. Toyoda, T. Hara, “Lossless light projection,” Opt. Lett. 22, 1373–1375 (1997).
[CrossRef]

N. Mukohzaka, N. Yoshida, H. Toyoda, Y. Kobayashi, T. Hara, “Diffraction efficiency analysis of a parallel-aligned nematic-liquid-crystal spatial light modulator,” Appl. Opt. 33, 2804–2811 (1994).
[CrossRef] [PubMed]

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, M. Wu, “Compact high efficiency electrically addressable phase-only spatial light modulator,” in Diffractive/Holographic Technologies and Spatial Light Modulators VIII, I. Cindrich, S. H. Lee, R. L. Sutherland, eds., Proc. SPIE3951, 158–165 (2000).
[CrossRef]

Horner, J. L.

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

Igasaki, Y.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, M. Wu, “Compact high efficiency electrically addressable phase-only spatial light modulator,” in Diffractive/Holographic Technologies and Spatial Light Modulators VIII, I. Cindrich, S. H. Lee, R. L. Sutherland, eds., Proc. SPIE3951, 158–165 (2000).
[CrossRef]

Inoue, T.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Javidi, B.

Johnson, E. G.

E. G. Johnson, J. D. Brasher, D. Gregory, P. Erbach, M. Duignan, G. Behrman, S. H. Lee, W. Dashner, P. Long, “Optical recognition of phase-encrypted biometrics,” Opt. Eng. 37, 18–26 (1998).
[CrossRef]

Joseph, J.

Kim, E. S.

J. W. Han, C. S. Park, D. H. Ryu, E. S. Kim, “Optical image encryption based on xor operations,” Opt. Eng. 38, 47–54 (1999).
[CrossRef]

Kobayashi, Y.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

N. Mukohzaka, N. Yoshida, H. Toyoda, Y. Kobayashi, T. Hara, “Diffraction efficiency analysis of a parallel-aligned nematic-liquid-crystal spatial light modulator,” Appl. Opt. 33, 2804–2811 (1994).
[CrossRef] [PubMed]

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, M. Wu, “Compact high efficiency electrically addressable phase-only spatial light modulator,” in Diffractive/Holographic Technologies and Spatial Light Modulators VIII, I. Cindrich, S. H. Lee, R. L. Sutherland, eds., Proc. SPIE3951, 158–165 (2000).
[CrossRef]

Lading, L.

Lai, S.

S. Lai, “Security holograms using an encoded reference wave,” Opt. Eng. 35, 2470–2472 (1996).
[CrossRef]

Lee, S. H.

E. G. Johnson, J. D. Brasher, D. Gregory, P. Erbach, M. Duignan, G. Behrman, S. H. Lee, W. Dashner, P. Long, “Optical recognition of phase-encrypted biometrics,” Opt. Eng. 37, 18–26 (1998).
[CrossRef]

Li, F.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Long, P.

E. G. Johnson, J. D. Brasher, D. Gregory, P. Erbach, M. Duignan, G. Behrman, S. H. Lee, W. Dashner, P. Long, “Optical recognition of phase-encrypted biometrics,” Opt. Eng. 37, 18–26 (1998).
[CrossRef]

Lou, Z.

Matoba, O.

Mogensen, P. C.

J. Glückstad, P. C. Mogensen, “Optimal phase contrast in common-path interferometry,” Appl. Opt. 40, 268–282 (2001).
[CrossRef]

J. Glückstad, P. C. Mogensen, “Reconfigurable ternary-phase array illuminator based on the generalised phase contrast method,” Opt. Commun. 173, 169–175 (2000).
[CrossRef]

P. C. Mogensen, J. Glückstad, “A phase based optical encryption system with polarization encoding,” Opt. Commun. 173, 177–183 (2000).
[CrossRef]

P. C. Mogensen, J. Glückstad, “Phase-only optical encryption,” Opt. Lett. 25, 566–568 (2000).
[CrossRef]

P. C. Mogensen, J. Glückstad, “Practical implementation of phase-only optical encryption system,” in Optical Security and Counterfeit Deterence Techniques III, R. L. Van Renesse, W. A. Vliegenthart, eds., Proc. SPIE3973, 284–293 (2000).
[CrossRef]

Mukohzaka, N.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

N. Mukohzaka, N. Yoshida, H. Toyoda, Y. Kobayashi, T. Hara, “Diffraction efficiency analysis of a parallel-aligned nematic-liquid-crystal spatial light modulator,” Appl. Opt. 33, 2804–2811 (1994).
[CrossRef] [PubMed]

Neto, L. G.

L. G. Neto, “Implementation of image encryption using phase contrast techniques,” in Optical Pattern Recognition IX, D. P. Casasent, T. Chao, eds., Proc. SPIE3386, 284–289 (1998).
[CrossRef]

Nomura, T.

Park, C. S.

J. W. Han, C. S. Park, D. H. Ryu, E. S. Kim, “Optical image encryption based on xor operations,” Opt. Eng. 38, 47–54 (1999).
[CrossRef]

Réfrégier, P.

Ryu, D. H.

J. W. Han, C. S. Park, D. H. Ryu, E. S. Kim, “Optical image encryption based on xor operations,” Opt. Eng. 38, 47–54 (1999).
[CrossRef]

Singh, K.

Tarahuerce, E.

Towghi, N.

Toyoda, H.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

J. Glückstad, L. Lading, H. Toyoda, T. Hara, “Lossless light projection,” Opt. Lett. 22, 1373–1375 (1997).
[CrossRef]

N. Mukohzaka, N. Yoshida, H. Toyoda, Y. Kobayashi, T. Hara, “Diffraction efficiency analysis of a parallel-aligned nematic-liquid-crystal spatial light modulator,” Appl. Opt. 33, 2804–2811 (1994).
[CrossRef] [PubMed]

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, M. Wu, “Compact high efficiency electrically addressable phase-only spatial light modulator,” in Diffractive/Holographic Technologies and Spatial Light Modulators VIII, I. Cindrich, S. H. Lee, R. L. Sutherland, eds., Proc. SPIE3951, 158–165 (2000).
[CrossRef]

Trolinger, J.

D. Weber, J. Trolinger, “Novel implementation of non-linear joint transform correlators in optical security and validation,” Opt. Eng. 38, 62–68 (1999).
[CrossRef]

Unnikrishnan, G.

van Renesse, R. L.

R. L. van Renesse, Optical Document Security (Artech House, London, 1998).

Verrall, S. C.

Weber, D.

D. Weber, J. Trolinger, “Novel implementation of non-linear joint transform correlators in optical security and validation,” Opt. Eng. 38, 62–68 (1999).
[CrossRef]

Wu, M.

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, M. Wu, “Compact high efficiency electrically addressable phase-only spatial light modulator,” in Diffractive/Holographic Technologies and Spatial Light Modulators VIII, I. Cindrich, S. H. Lee, R. L. Sutherland, eds., Proc. SPIE3951, 158–165 (2000).
[CrossRef]

Yoshida, N.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

N. Mukohzaka, N. Yoshida, H. Toyoda, Y. Kobayashi, T. Hara, “Diffraction efficiency analysis of a parallel-aligned nematic-liquid-crystal spatial light modulator,” Appl. Opt. 33, 2804–2811 (1994).
[CrossRef] [PubMed]

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, M. Wu, “Compact high efficiency electrically addressable phase-only spatial light modulator,” in Diffractive/Holographic Technologies and Spatial Light Modulators VIII, I. Cindrich, S. H. Lee, R. L. Sutherland, eds., Proc. SPIE3951, 158–165 (2000).
[CrossRef]

Zernike, F.

F. Zernike, “How I discovered phase contrast,” Science 121, 345–349 (1955).
[CrossRef] [PubMed]

Appl. Opt. (6)

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

Opt. Commun. (4)

J. Glückstad, P. C. Mogensen, “Reconfigurable ternary-phase array illuminator based on the generalised phase contrast method,” Opt. Commun. 173, 169–175 (2000).
[CrossRef]

P. C. Mogensen, J. Glückstad, “A phase based optical encryption system with polarization encoding,” Opt. Commun. 173, 177–183 (2000).
[CrossRef]

J. Glückstad, “Pattern generation by inverse phase contrast—comment,” Opt. Commun. 147, 16–19 (1998).
[CrossRef]

J. Glückstad, “Phase contrast image synthesis,” Opt. Commun. 130, 225–230 (1996).
[CrossRef]

Opt. Eng. (5)

S. Lai, “Security holograms using an encoded reference wave,” Opt. Eng. 35, 2470–2472 (1996).
[CrossRef]

D. Weber, J. Trolinger, “Novel implementation of non-linear joint transform correlators in optical security and validation,” Opt. Eng. 38, 62–68 (1999).
[CrossRef]

J. W. Han, C. S. Park, D. H. Ryu, E. S. Kim, “Optical image encryption based on xor operations,” Opt. Eng. 38, 47–54 (1999).
[CrossRef]

E. G. Johnson, J. D. Brasher, D. Gregory, P. Erbach, M. Duignan, G. Behrman, S. H. Lee, W. Dashner, P. Long, “Optical recognition of phase-encrypted biometrics,” Opt. Eng. 37, 18–26 (1998).
[CrossRef]

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

Opt. Lett. (4)

Opt. Rev. (1)

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Phys. Today (1)

B. Javidi, “Securing information with optical technologies,” Phys. Today 50, (3)27–32 (1997).

Science (1)

F. Zernike, “How I discovered phase contrast,” Science 121, 345–349 (1955).
[CrossRef] [PubMed]

Other (8)

L. G. Neto, “Implementation of image encryption using phase contrast techniques,” in Optical Pattern Recognition IX, D. P. Casasent, T. Chao, eds., Proc. SPIE3386, 284–289 (1998).
[CrossRef]

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, M. Wu, “Compact high efficiency electrically addressable phase-only spatial light modulator,” in Diffractive/Holographic Technologies and Spatial Light Modulators VIII, I. Cindrich, S. H. Lee, R. L. Sutherland, eds., Proc. SPIE3951, 158–165 (2000).
[CrossRef]

P. C. Mogensen, J. Glückstad, “Practical implementation of phase-only optical encryption system,” in Optical Security and Counterfeit Deterence Techniques III, R. L. Van Renesse, W. A. Vliegenthart, eds., Proc. SPIE3973, 284–293 (2000).
[CrossRef]

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

Optics and Fluid Dynamics Department, Annual progress report R-793(EN) (Risø National Laboratory, Roskilde, Denmark, 1995).

R. L. van Renesse, Optical Document Security (Artech House, London, 1998).

J. Glückstad, “Phase contrast scrambling,” International PCT patent application WO 002339A1 (3July1998).

J. Glückstad, “Image decrypting common path interferometer,” in Optical Pattern Recognition X, D. P. Casasent, T. Chao, eds., Proc. SPIE3715, 152–159 (1999).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Generic optical encryption setup. An encrypted phase mask is decrypted by the application of the correct phase key. The decrypted phase information is then retrieved by the generalized phase-contrast technique in which a phase-contrast filter (PCF) placed in a 4-f setup is used to generate an intensity pattern that contains the decrypted information at the output of the optical system.

Fig. 2
Fig. 2

Generalized phase-contrast system based on a 4-f optical system (lenses L1 and L2). The decrypted wave front is shown as an aperture truncated phase function ϕ(x, y), which generates an intensity distribution I(x′, y′) in the observation plane by a filtering operation in the Fourier plane. The values of the filter parameters (A, B, θ) determine the type of filtering operation.

Fig. 3
Fig. 3

Fixed phase mask, shown as (a) a schematic cross section and (b) a plan view of a typical binary pixelated phase-shifting pattern. The fixed mask consists of a λ/2 layer of a photoresist (PR) deposited upon an optical flat, one side of which has been antireflection (AR) coated at the laser wavelength. An incident wave front is thus modulated by the fixed mask, generating a spatially varying binary 0/π phase perturbation of the wave front.

Fig. 4
Fig. 4

Experimental setup for the decryption of a fixed binary phase mask. The light source is a 635-nm diode laser (LD), which is expanded and spatially filtered to produce a collimated beam. The fixed phase mask is imaged onto the SLM by lenses L1 and L2 through aperture Ir1. When it is aligned correctly, the key that is implemented on the SLM decrypts the information in the mask. The decrypted phase information is then retrieved with a PCF in a standard 4-f setup (lenses L3 and L4) to generate an intensity distribution in the plane of the CCD camera.

Fig. 5
Fig. 5

Decryption of a 17 × 9 pixel fixed mask with a 17 × 9 pixel dynamic key. (a) A successful decryption that reveals the letters RISØ, (b) an image of the fixed phase mask viewed with the PCF, and (c) the corresponding image for the decrypting key. If the PCF is misplaced, the decrypted information is not visualized (d). The fixed mask size is 3 mm × 3 mm.

Fig. 6
Fig. 6

Plot of visibility V as a function of modulated area F π for a binary 0/π input wave front. The curves correspond to the experimentally estimated K = 0.68 and the optimal K = 1.0. The points that correspond to the experimental values for F π in the images in Figs. 5(a)5(c) are superimposed upon the K = 0.68 curve, clearly showing the loss in visibility when F π and the aperture are not matched.

Fig. 7
Fig. 7

Unsuccessful decryption of (a) the fixed mask occurs when (b) the incorrect key is applied to the fixed mask. In this case the incorrect key is simply the correct key shown in Fig. 5 rotated through an angle of 180°. An incorrect phase shift in the key will also fail to yield a complete decryption of the fixed mask. Examples of the results of application of keys with approximate phase shifts of π/2 and 2π are shown in (c) and (d), respectively.

Equations (16)

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ax, y=circr/Δrexpiϕx, y.
Hfx, fy=A1+BA-1 expiθ-1circfr/Δfr.
Ix, yA2|expiϕ˜x, ycircr/Δr+gr|α¯|BA-1 expiθ-1|2,
α¯=πΔr2-1πΔr2expiϕx, ydxdy=|α¯|expiϕα¯,ϕ˜=ϕ-ϕα¯.
K=grcentral region1-J01.22πη.
Ix, yA2|expiϕ˜x, y+K|α¯|BA-1 expiθ-1|2.
Ix, y|expiϕ˜x, y+K|α¯|expiθ-1|2.
Ix, y|expiϕ˜x, y-1|20; 4.
Ix, y|expiϕ˜x, y|2=1.
Ix, y|expiϕ˜x, y-2K|α¯2.
Imaxx, y=1+2K|α¯|2,
Iminx, y=1-2K|α¯|2.
V=Imax-IminImax+Imin.
V=4K|α¯|1+4K2|α¯|2-1.
V=4K|1-2Fπ|1+4K21-2Fπ2-1.
w=1.22λf/Δr,

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