Abstract

We propose what we believe is a new method for color image encryption by use of wavelength multiplexing based on lensless Fresnel transform holograms. An image is separated into three channels: red, green, and blue, and each channel is independently encrypted. The system parameters of Fresnel transforms and random phase masks in each channel are keys in image encryption and decryption. An optical color image coding configuration with multichannel implementation and an optoelectronic color image encryption architecture with single-channel implementation are presented. The keys can be added by iteratively employing the Fresnel transforms. Computer simulations are given to prove the possibility of the proposed idea.

© 2006 Optical Society of America

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  1. P. Refregier 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, "Security information with optical technology," Phys. Today 50,27-32 (1997).
    [CrossRef]
  3. G. Unnikrishnan, J. Joseph, and K. Singh, "Optical encryption by double-random phase encoding in the fractional Fourier domain," Opt. Lett. 25, 887-889 (2000).
    [CrossRef]
  4. G. Situ and J. Zhang, "Double random-phase encoding in the Fresnel domain," Opt. Lett. 29, 1584-1586 (2004).
    [CrossRef] [PubMed]
  5. B. Hennelly and J. T. Sheridan, "Optical image encryption by random shifting in fractional Fourier domains," Opt. Lett. 28, 269-271 (2003).
    [CrossRef] [PubMed]
  6. E. Tajahuerce, O. Matoba, S. C. Verrall, and B. Javidi, "Optoeletronic information encryption with phase-shifting interferometry," Appl. Opt. 39, 2313-2320 (2000).
    [CrossRef]
  7. S. T. Liu, Q. L. Mi, and B. H. Zhu, "Optical image encryption with multistage and multichannel fractional Fourier-domain filtering," Opt. Lett. 26, 1242-1244 (2001).
    [CrossRef]
  8. B. Javidi and T. Nomura, "Securing information by use of digital holography," Opt. Lett. 25, 28-30 (2000).
    [CrossRef]
  9. X. Peng, L. F. Yu, and L. L. Cai, "Double-lock for image encryption with virtual optical wavelength," Opt. Exp. 10, 41-45(2002).
  10. N. K. Nishchal, J. Joseph, and K. Singh, "Securing information using fractional Fourier transform in digital holography," Opt. Commun. 235, 253-259 (2004).
    [CrossRef]
  11. X. G. Wang, D. M. Zhao, F. Jing, and X. F. Wei, "Information synthesis (complex amplitude addition and subtraction) and encryption with digital holography and virtual optics," Opt. Exp. 14, 1476-1486 (2006).
    [CrossRef]
  12. H. Kim, D. H. Kim, and Y. H. Lee, "Encryption of digital hologram of 3-D object by virtual optics," Opt. Exp. 12, 4912-4921 (2004).
    [CrossRef]
  13. X. G. Wang, D. M. Zhao, and L. F. Chen, "Image encryption based on extended fractional Fourier transform and digital holography technique," Opt. Commun. 260, 449-453 (2006).
    [CrossRef]
  14. L. F. Chen and D. M. Zhao, "Optical image encryption based on fractional wavelet transform," Opt. Commun. 254, 361-367 (2005).
    [CrossRef]
  15. Y. Zhang, C. H. Zheng, and N. Tanno, "Optical encryption based on iterative fractional Fourier transform," Opt. Commun. 202, 277-285 (2002).
    [CrossRef]
  16. G. H. Situ and J. J. Zhang, "Multiple-image encryption by wavelength multiplexing," Opt. Lett. 30, 1306-1308 (2005).
    [CrossRef] [PubMed]
  17. L. F. Chen and D. M. Zhao, "Optical image addition and encryption by multi-exposure based on fractional Fourier transform hologram," Chin. Phys. Lett. 23, 603-606 (2006).
    [CrossRef]
  18. S. Q. Zhang and M. A. Karim, "Color image encryption using double random phase encoding," Microwave Opt. Technol. Lett. 21, 318-323 (1999).
    [CrossRef]
  19. J. Nicolas, C. Iemmi, J. Compos, and M. J. Yzuel, "Optical encoding of color three-dimensional correlation," Opt. Commun. 209, 35-43 (2002).
    [CrossRef]
  20. S. Ledesma, C. Iemmi, M. Villarreal, and J. Compos, "Multichannel correlation by color multiplexing," Opt. Commun. 166, 173-180 (1999).
    [CrossRef]
  21. W. M. Jin, L. H. Ma, and C. J. Yan, "Real color fractional Fourier transform holograms," Opt. Commun. 259, 513-516 (2006).
    [CrossRef]

2006 (4)

X. G. Wang, D. M. Zhao, F. Jing, and X. F. Wei, "Information synthesis (complex amplitude addition and subtraction) and encryption with digital holography and virtual optics," Opt. Exp. 14, 1476-1486 (2006).
[CrossRef]

X. G. Wang, D. M. Zhao, and L. F. Chen, "Image encryption based on extended fractional Fourier transform and digital holography technique," Opt. Commun. 260, 449-453 (2006).
[CrossRef]

L. F. Chen and D. M. Zhao, "Optical image addition and encryption by multi-exposure based on fractional Fourier transform hologram," Chin. Phys. Lett. 23, 603-606 (2006).
[CrossRef]

W. M. Jin, L. H. Ma, and C. J. Yan, "Real color fractional Fourier transform holograms," Opt. Commun. 259, 513-516 (2006).
[CrossRef]

2005 (2)

L. F. Chen and D. M. Zhao, "Optical image encryption based on fractional wavelet transform," Opt. Commun. 254, 361-367 (2005).
[CrossRef]

G. H. Situ and J. J. Zhang, "Multiple-image encryption by wavelength multiplexing," Opt. Lett. 30, 1306-1308 (2005).
[CrossRef] [PubMed]

2004 (3)

G. Situ and J. Zhang, "Double random-phase encoding in the Fresnel domain," Opt. Lett. 29, 1584-1586 (2004).
[CrossRef] [PubMed]

H. Kim, D. H. Kim, and Y. H. Lee, "Encryption of digital hologram of 3-D object by virtual optics," Opt. Exp. 12, 4912-4921 (2004).
[CrossRef]

N. K. Nishchal, J. Joseph, and K. Singh, "Securing information using fractional Fourier transform in digital holography," Opt. Commun. 235, 253-259 (2004).
[CrossRef]

2003 (1)

2002 (3)

X. Peng, L. F. Yu, and L. L. Cai, "Double-lock for image encryption with virtual optical wavelength," Opt. Exp. 10, 41-45(2002).

Y. Zhang, C. H. Zheng, and N. Tanno, "Optical encryption based on iterative fractional Fourier transform," Opt. Commun. 202, 277-285 (2002).
[CrossRef]

J. Nicolas, C. Iemmi, J. Compos, and M. J. Yzuel, "Optical encoding of color three-dimensional correlation," Opt. Commun. 209, 35-43 (2002).
[CrossRef]

2001 (1)

2000 (3)

1999 (2)

S. Ledesma, C. Iemmi, M. Villarreal, and J. Compos, "Multichannel correlation by color multiplexing," Opt. Commun. 166, 173-180 (1999).
[CrossRef]

S. Q. Zhang and M. A. Karim, "Color image encryption using double random phase encoding," Microwave Opt. Technol. Lett. 21, 318-323 (1999).
[CrossRef]

1997 (1)

B. Javidi, "Security information with optical technology," Phys. Today 50,27-32 (1997).
[CrossRef]

1995 (1)

Cai, L. L.

X. Peng, L. F. Yu, and L. L. Cai, "Double-lock for image encryption with virtual optical wavelength," Opt. Exp. 10, 41-45(2002).

Chen, L. F.

X. G. Wang, D. M. Zhao, and L. F. Chen, "Image encryption based on extended fractional Fourier transform and digital holography technique," Opt. Commun. 260, 449-453 (2006).
[CrossRef]

L. F. Chen and D. M. Zhao, "Optical image addition and encryption by multi-exposure based on fractional Fourier transform hologram," Chin. Phys. Lett. 23, 603-606 (2006).
[CrossRef]

L. F. Chen and D. M. Zhao, "Optical image encryption based on fractional wavelet transform," Opt. Commun. 254, 361-367 (2005).
[CrossRef]

Compos, J.

J. Nicolas, C. Iemmi, J. Compos, and M. J. Yzuel, "Optical encoding of color three-dimensional correlation," Opt. Commun. 209, 35-43 (2002).
[CrossRef]

S. Ledesma, C. Iemmi, M. Villarreal, and J. Compos, "Multichannel correlation by color multiplexing," Opt. Commun. 166, 173-180 (1999).
[CrossRef]

Hennelly, B.

Iemmi, C.

J. Nicolas, C. Iemmi, J. Compos, and M. J. Yzuel, "Optical encoding of color three-dimensional correlation," Opt. Commun. 209, 35-43 (2002).
[CrossRef]

S. Ledesma, C. Iemmi, M. Villarreal, and J. Compos, "Multichannel correlation by color multiplexing," Opt. Commun. 166, 173-180 (1999).
[CrossRef]

Javidi, B.

Jin, W. M.

W. M. Jin, L. H. Ma, and C. J. Yan, "Real color fractional Fourier transform holograms," Opt. Commun. 259, 513-516 (2006).
[CrossRef]

Jing, F.

X. G. Wang, D. M. Zhao, F. Jing, and X. F. Wei, "Information synthesis (complex amplitude addition and subtraction) and encryption with digital holography and virtual optics," Opt. Exp. 14, 1476-1486 (2006).
[CrossRef]

Joseph, J.

N. K. Nishchal, J. Joseph, and K. Singh, "Securing information using fractional Fourier transform in digital holography," Opt. Commun. 235, 253-259 (2004).
[CrossRef]

G. Unnikrishnan, J. Joseph, and K. Singh, "Optical encryption by double-random phase encoding in the fractional Fourier domain," Opt. Lett. 25, 887-889 (2000).
[CrossRef]

Karim, M. A.

S. Q. Zhang and M. A. Karim, "Color image encryption using double random phase encoding," Microwave Opt. Technol. Lett. 21, 318-323 (1999).
[CrossRef]

Kim, D. H.

H. Kim, D. H. Kim, and Y. H. Lee, "Encryption of digital hologram of 3-D object by virtual optics," Opt. Exp. 12, 4912-4921 (2004).
[CrossRef]

Kim, H.

H. Kim, D. H. Kim, and Y. H. Lee, "Encryption of digital hologram of 3-D object by virtual optics," Opt. Exp. 12, 4912-4921 (2004).
[CrossRef]

Ledesma, S.

S. Ledesma, C. Iemmi, M. Villarreal, and J. Compos, "Multichannel correlation by color multiplexing," Opt. Commun. 166, 173-180 (1999).
[CrossRef]

Lee, Y. H.

H. Kim, D. H. Kim, and Y. H. Lee, "Encryption of digital hologram of 3-D object by virtual optics," Opt. Exp. 12, 4912-4921 (2004).
[CrossRef]

Liu, S. T.

Ma, L. H.

W. M. Jin, L. H. Ma, and C. J. Yan, "Real color fractional Fourier transform holograms," Opt. Commun. 259, 513-516 (2006).
[CrossRef]

Matoba, O.

Mi, Q. L.

Nicolas, J.

J. Nicolas, C. Iemmi, J. Compos, and M. J. Yzuel, "Optical encoding of color three-dimensional correlation," Opt. Commun. 209, 35-43 (2002).
[CrossRef]

Nishchal, N. K.

N. K. Nishchal, J. Joseph, and K. Singh, "Securing information using fractional Fourier transform in digital holography," Opt. Commun. 235, 253-259 (2004).
[CrossRef]

Nomura, T.

Peng, X.

X. Peng, L. F. Yu, and L. L. Cai, "Double-lock for image encryption with virtual optical wavelength," Opt. Exp. 10, 41-45(2002).

Refregier, P.

Sheridan, J. T.

Singh, K.

N. K. Nishchal, J. Joseph, and K. Singh, "Securing information using fractional Fourier transform in digital holography," Opt. Commun. 235, 253-259 (2004).
[CrossRef]

G. Unnikrishnan, J. Joseph, and K. Singh, "Optical encryption by double-random phase encoding in the fractional Fourier domain," Opt. Lett. 25, 887-889 (2000).
[CrossRef]

Situ, G.

Situ, G. H.

Tajahuerce, E.

Tanno, N.

Y. Zhang, C. H. Zheng, and N. Tanno, "Optical encryption based on iterative fractional Fourier transform," Opt. Commun. 202, 277-285 (2002).
[CrossRef]

Unnikrishnan, G.

Verrall, S. C.

Villarreal, M.

S. Ledesma, C. Iemmi, M. Villarreal, and J. Compos, "Multichannel correlation by color multiplexing," Opt. Commun. 166, 173-180 (1999).
[CrossRef]

Wang, X. G.

X. G. Wang, D. M. Zhao, and L. F. Chen, "Image encryption based on extended fractional Fourier transform and digital holography technique," Opt. Commun. 260, 449-453 (2006).
[CrossRef]

X. G. Wang, D. M. Zhao, F. Jing, and X. F. Wei, "Information synthesis (complex amplitude addition and subtraction) and encryption with digital holography and virtual optics," Opt. Exp. 14, 1476-1486 (2006).
[CrossRef]

Wei, X. F.

X. G. Wang, D. M. Zhao, F. Jing, and X. F. Wei, "Information synthesis (complex amplitude addition and subtraction) and encryption with digital holography and virtual optics," Opt. Exp. 14, 1476-1486 (2006).
[CrossRef]

Yan, C. J.

W. M. Jin, L. H. Ma, and C. J. Yan, "Real color fractional Fourier transform holograms," Opt. Commun. 259, 513-516 (2006).
[CrossRef]

Yu, L. F.

X. Peng, L. F. Yu, and L. L. Cai, "Double-lock for image encryption with virtual optical wavelength," Opt. Exp. 10, 41-45(2002).

Yzuel, M. J.

J. Nicolas, C. Iemmi, J. Compos, and M. J. Yzuel, "Optical encoding of color three-dimensional correlation," Opt. Commun. 209, 35-43 (2002).
[CrossRef]

Zhang, J.

Zhang, J. J.

Zhang, S. Q.

S. Q. Zhang and M. A. Karim, "Color image encryption using double random phase encoding," Microwave Opt. Technol. Lett. 21, 318-323 (1999).
[CrossRef]

Zhang, Y.

Y. Zhang, C. H. Zheng, and N. Tanno, "Optical encryption based on iterative fractional Fourier transform," Opt. Commun. 202, 277-285 (2002).
[CrossRef]

Zhao, D. M.

X. G. Wang, D. M. Zhao, F. Jing, and X. F. Wei, "Information synthesis (complex amplitude addition and subtraction) and encryption with digital holography and virtual optics," Opt. Exp. 14, 1476-1486 (2006).
[CrossRef]

X. G. Wang, D. M. Zhao, and L. F. Chen, "Image encryption based on extended fractional Fourier transform and digital holography technique," Opt. Commun. 260, 449-453 (2006).
[CrossRef]

L. F. Chen and D. M. Zhao, "Optical image addition and encryption by multi-exposure based on fractional Fourier transform hologram," Chin. Phys. Lett. 23, 603-606 (2006).
[CrossRef]

L. F. Chen and D. M. Zhao, "Optical image encryption based on fractional wavelet transform," Opt. Commun. 254, 361-367 (2005).
[CrossRef]

Zheng, C. H.

Y. Zhang, C. H. Zheng, and N. Tanno, "Optical encryption based on iterative fractional Fourier transform," Opt. Commun. 202, 277-285 (2002).
[CrossRef]

Zhu, B. H.

Appl. Opt. (1)

Chin. Phys. Lett. (1)

L. F. Chen and D. M. Zhao, "Optical image addition and encryption by multi-exposure based on fractional Fourier transform hologram," Chin. Phys. Lett. 23, 603-606 (2006).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

S. Q. Zhang and M. A. Karim, "Color image encryption using double random phase encoding," Microwave Opt. Technol. Lett. 21, 318-323 (1999).
[CrossRef]

Opt. Commun. (7)

J. Nicolas, C. Iemmi, J. Compos, and M. J. Yzuel, "Optical encoding of color three-dimensional correlation," Opt. Commun. 209, 35-43 (2002).
[CrossRef]

S. Ledesma, C. Iemmi, M. Villarreal, and J. Compos, "Multichannel correlation by color multiplexing," Opt. Commun. 166, 173-180 (1999).
[CrossRef]

W. M. Jin, L. H. Ma, and C. J. Yan, "Real color fractional Fourier transform holograms," Opt. Commun. 259, 513-516 (2006).
[CrossRef]

X. G. Wang, D. M. Zhao, and L. F. Chen, "Image encryption based on extended fractional Fourier transform and digital holography technique," Opt. Commun. 260, 449-453 (2006).
[CrossRef]

L. F. Chen and D. M. Zhao, "Optical image encryption based on fractional wavelet transform," Opt. Commun. 254, 361-367 (2005).
[CrossRef]

Y. Zhang, C. H. Zheng, and N. Tanno, "Optical encryption based on iterative fractional Fourier transform," Opt. Commun. 202, 277-285 (2002).
[CrossRef]

N. K. Nishchal, J. Joseph, and K. Singh, "Securing information using fractional Fourier transform in digital holography," Opt. Commun. 235, 253-259 (2004).
[CrossRef]

Opt. Exp. (3)

X. G. Wang, D. M. Zhao, F. Jing, and X. F. Wei, "Information synthesis (complex amplitude addition and subtraction) and encryption with digital holography and virtual optics," Opt. Exp. 14, 1476-1486 (2006).
[CrossRef]

H. Kim, D. H. Kim, and Y. H. Lee, "Encryption of digital hologram of 3-D object by virtual optics," Opt. Exp. 12, 4912-4921 (2004).
[CrossRef]

X. Peng, L. F. Yu, and L. L. Cai, "Double-lock for image encryption with virtual optical wavelength," Opt. Exp. 10, 41-45(2002).

Opt. Lett. (7)

Phys. Today (1)

B. Javidi, "Security information with optical technology," Phys. Today 50,27-32 (1997).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

Image encryption and decryption by single wavelength illumination. (a) Original image with 256×256 pixels; (b) encrypted image with red wavelength; (c) and (d) correct and incorrect decryption images with red wavelength; (e) and (f) correct and incorrect decoding images with green wavelength; (g) and (h) right and wrong decryption results with blue wavelength.

Fig. 2.
Fig. 2.

Color image decomposition. R: Red; G: Green; B: Blue.

Fig. 3.
Fig. 3.

Schematic of optical color image encoding implementation. Ms: dichroic mirrors; I: Input plane; P and Ks: random phase masks; H: hologram halide.

Fig. 4.
Fig. 4.

Optoelectronic color image encryption architecture. SLM: Spatial Light Modulator; CCD: Charge-Coupled Device.

Fig. 5.
Fig. 5.

Optical color image decoding realization. O: Output plane.

Fig. 6.
Fig. 6.

Optoelectronic color image decryption configuration.

Fig. 7.
Fig. 7.

Color image coding and decoding results. (a) Original image with 512×512 pixels; (b) encrypted result; (c)–(e) incorrect decryption image; (f) correct decryption image.

Fig. 8.
Fig. 8.

Partial color image encryption and decryption results. (a) Original image with 500×362 pixels; (b) encryption image (c) result with red component incorrectly decrypted; (d) result with green component incorrectly decrypted; (e) result with blue component incorrectly decrypted; (f) only red component correctly decrypted; (g) only green component correctly decrypted; (h) only blue component correctly decrypted; (i) correct decryption.

Equations (14)

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

g ( x 2 , y 2 ) = FsT { FsT [ f ( x , y ) P ( x , y ) ; z 1 ] × K ( x 1 , y 1 ) ; z 2 } ,
f ' ( x , y ) = FsT { FsT [ g * ( x 2 , y 2 ) ; z 2 ] × K ( x 1 , y 1 ) ; z 1 } ,
FsT [ f ( x , y ) ; z ] = exp ( i 2 π z λ ) i λ z f ( x , y ) exp { i π λ z [ ( x 1 x ) 2 + ( y 1 y ) 2 ] } d x d y ,
P ( x , y ) = exp [ 2 π i p ( x , y ) ] , K ( x , y ) = exp [ 2 π i k ( x , y ) ] .
u ( x ' , y ' ) = 1 + g ( x 2 , y 2 ) 2
= 1 + g ( x 2 , y 2 ) 2 + g * ( x 2 , y 2 ) + g ( x 2 , y 2 ) .
g ( x n , y n ) = f ( x , y ) P ( x , y ) h ( x 1 , x ; y 1 , y ; z 1 )
× K 1 ( x 1 , y 1 ) h ( x 2 , x 1 ; y 2 , y 1 ; z 2 ) K 2 ( x 2 , y 2 )
× K n 1 ( x n 1 , y n 1 ) h ( x n , x n 1 ; y n , y n 1 ; z n ) d x d x 1 d x n 1 d y d y 1 d y n 1 ,
h ( x n , x n 1 ; y n , y n 1 ; z n ) = exp ( i 2 π z n λ ) i λ z n exp { i π λ z n [ ( x n x n 1 ) 2 + ( y n y n 1 ) 2 ] } ,
f ' ( x , y ) = g * ( x n , y n ) h ( x n 1 , x n ; y n 1 , y n ; z n )
× K n 1 ( x n 1 , y n 1 ) h ( x 1 , x 2 ; y 1 , y 2 ; z 2 ) K 1 ( x 1 , y 1 ) ,
× h ( x , x 1 ; y , y 1 ; z 1 ) d x n d x n 1 d x 1 d y n d y n 1 d y 1
MSE = m = 1 M n = 1 N [ f ( m Δ x , n Δ y ) f 0 ( m Δ x , n Δ y ) 2 ] m = 1 M n = 1 N [ f ( m Δ x , n Δ y ) 2 ] ,

Metrics