Abstract

In this paper, we propose a new method for color image coding and synthesis based on fractional Fourier transforms and wavelength multiplexing with digital holography. A color image is divided into three channels and each channel, in which the information is encrypted with different wavelength, fractional orders and random phase masks, is independently encrypted or synthesized. The system parameters are additional keys and this method would improve the security of information encryption. The images are fused or subtracted by phase shifting technique. The possible optical implementations for color image encryption and synthesis are also proposed with some simulation results that show the possibility of the proposed idea.

© 2007 Optical Society of America

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References

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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).
  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. G. Unnikrishnan and K. Singh, "Double random fractional Fourier-domain encoding for optical security," Opt. Eng. 39, 2853-2859 (2000).
    [CrossRef]
  6. B. Hennelly and J. T. Sheridan, "Optical image encryption by random shifting in fractional Fourier domains," Opt. Lett. 28, 269-271 (2003).
    [CrossRef] [PubMed]
  7. E. Tajahuerce, O. Matoba, S. C. Verrall, and B. Javidi, "Optoeletronic information encryption with phase-shifting interferometry," Appl. Opt. 39, 2313-2320 (2000).
    [CrossRef]
  8. 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]
  9. B. Javidi and T. Nomura, "Securing information by use of digital holography," Opt. Lett. 25, 28-30 (2000).
    [CrossRef]
  10. X. Peng, L. F. Yu, and L. L. Cai, "Double-lock for image encryption with virtual optical wavelength," Opt. Express 10, 41-45 (2002).
  11. N. K. Nishchal, J. Joseph, and K. Singh, "Securing information using fractional Fourier transform in digital holography," Opt. Commun. 235, 253-259 (2004).
    [CrossRef]
  12. H. Kim, D. H. Kim, and Y. H. Lee, "Encryption of digital hologram of 3-D object by virtual optics," Opt. Express 12, 4912-4921 (2004).
    [CrossRef]
  13. L. F. Chen and D. M. Zhao, "Optical image encryption with Hartley transforms," Opt. Lett. 31, 3438-3440 (2006).
    [CrossRef] [PubMed]
  14. Y. Zhang, C. H. Zheng, and N. Tanno, "Optical encryption based on iterative fractional Fourier transform," Opt. Commun. 202, 277-285 (2002).
    [CrossRef]
  15. G. H. Situ and J. J. Zhang, "Multiple-image encryption by wavelength multiplexing," Opt. Lett. 30,1306-1308 (2005).
    [CrossRef] [PubMed]
  16. D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, and D. Brumm, "Optical image synthesis (complex amplitude addition and subtraction) by holographic Fourier transformation," Phys. Lett. 18, 116-118 (1965).
    [CrossRef]
  17. J. F. Ebersole, "Optical image subtraction," Opt. Eng. 14, 436-447 (1975).
  18. G. S. Pati, G. Unnikrishnan, and K. Singh, "Multichannel image addition and subtraction using joint-transform correlator architecture," Opt. Commun. 150, 33-37 (1998).
    [CrossRef]
  19. A. E. Chiou and P. Yeh, "Parallel image subtraction using a phase-conjugate Michelson interferometer," Opt. Lett. 11, 306-308 (1986).
    [CrossRef] [PubMed]
  20. S. H. Lee. S. K. Yao, and A. G. Milines, "Optical image synthesis (complex amplitude addition and subtraction) in real time by a diffraction-grating interferometric method," J. Opt. Soc. Am. A 60, 1037-1041 (1970).
    [CrossRef]
  21. S. T. Wu and F. T. S. Yu, "Image subtraction with an encoded extended incoherent source," Appl. Opt. 20, 4082-4088 (1981).
    [CrossRef] [PubMed]
  22. M. Y. Shih, A. Shishido, and I. C. Khoo, "All-optical image processing by means of a photosensitive nonlinear liquid-crystal film: edge enhancement and image addition-subtraction," Opt. Lett. 26, 1140-1142 (2001).
    [CrossRef]
  23. 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]
  24. 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. Express 14, 1476-1486 (2006).
    [CrossRef]
  25. S. Q. Zhang and M. A. Karim, "Color image encryption using double random phase encoding," Microwave Opt. Technol. Lett. 21, 318-323 (1999).
    [CrossRef]
  26. L. F. Chen and D. M. Zhao, "Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms," Opt. Express 14, 8552-8560 (2006).
    [CrossRef]
  27. W. M. Jin, L. H. Ma, and C. J. Yan, "Real color fractional Fourier transform holograms," Opt. Commun. 259, 513-516 (2006).
    [CrossRef]
  28. I. Yamaguchi, T. Matsumura, and J. Kato, "Phase-shifting color digital holography," Opt. Lett. 27, 1108-1110 (2002).
    [CrossRef]
  29. A.W. Lohmann, "Image rotation, Wigner rotation, and the fractional Fourier transform," J. Opt. Soc. Am. A 10, 2181-2186 (1993).
    [CrossRef]
  30. F. Zhang, I. Yamaguchi, and L. P. Yaroslavsky, "Algorithm for reconstruction of digital holograms with adjustable magnification," Opt. Lett. 29, 1668-1670 (2004).
    [CrossRef] [PubMed]

2006

2005

2004

2003

2002

2001

2000

1999

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

1998

G. S. Pati, G. Unnikrishnan, and K. Singh, "Multichannel image addition and subtraction using joint-transform correlator architecture," Opt. Commun. 150, 33-37 (1998).
[CrossRef]

1997

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

1995

1993

1986

1981

1975

J. F. Ebersole, "Optical image subtraction," Opt. Eng. 14, 436-447 (1975).

1970

S. H. Lee. S. K. Yao, and A. G. Milines, "Optical image synthesis (complex amplitude addition and subtraction) in real time by a diffraction-grating interferometric method," J. Opt. Soc. Am. A 60, 1037-1041 (1970).
[CrossRef]

1965

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, and D. Brumm, "Optical image synthesis (complex amplitude addition and subtraction) by holographic Fourier transformation," Phys. Lett. 18, 116-118 (1965).
[CrossRef]

Microwave Opt. Technol. Lett.

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

Appl. Opt.

Chin. Phys. Lett.

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]

J. Opt. Soc. Am. A

S. H. Lee. S. K. Yao, and A. G. Milines, "Optical image synthesis (complex amplitude addition and subtraction) in real time by a diffraction-grating interferometric method," J. Opt. Soc. Am. A 60, 1037-1041 (1970).
[CrossRef]

A.W. Lohmann, "Image rotation, Wigner rotation, and the fractional Fourier transform," J. Opt. Soc. Am. A 10, 2181-2186 (1993).
[CrossRef]

Opt. Commun.

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

G. S. Pati, G. Unnikrishnan, and K. Singh, "Multichannel image addition and subtraction using joint-transform correlator architecture," Opt. Commun. 150, 33-37 (1998).
[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]

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

Opt. Eng.

G. Unnikrishnan and K. Singh, "Double random fractional Fourier-domain encoding for optical security," Opt. Eng. 39, 2853-2859 (2000).
[CrossRef]

J. F. Ebersole, "Optical image subtraction," Opt. Eng. 14, 436-447 (1975).

Opt. Express

Opt. Lett.

L. F. Chen and D. M. Zhao, "Optical image encryption with Hartley transforms," Opt. Lett. 31, 3438-3440 (2006).
[CrossRef] [PubMed]

I. Yamaguchi, T. Matsumura, and J. Kato, "Phase-shifting color digital holography," Opt. Lett. 27, 1108-1110 (2002).
[CrossRef]

B. Hennelly and J. T. Sheridan, "Optical image encryption by random shifting in fractional Fourier domains," Opt. Lett. 28, 269-271 (2003).
[CrossRef] [PubMed]

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

F. Zhang, I. Yamaguchi, and L. P. Yaroslavsky, "Algorithm for reconstruction of digital holograms with adjustable magnification," Opt. Lett. 29, 1668-1670 (2004).
[CrossRef] [PubMed]

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

M. Y. Shih, A. Shishido, and I. C. Khoo, "All-optical image processing by means of a photosensitive nonlinear liquid-crystal film: edge enhancement and image addition-subtraction," Opt. Lett. 26, 1140-1142 (2001).
[CrossRef]

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]

B. Javidi and T. Nomura, "Securing information by use of digital holography," Opt. Lett. 25, 28-30 (2000).
[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]

A. E. Chiou and P. Yeh, "Parallel image subtraction using a phase-conjugate Michelson interferometer," Opt. Lett. 11, 306-308 (1986).
[CrossRef] [PubMed]

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]

Phys. Lett.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, and D. Brumm, "Optical image synthesis (complex amplitude addition and subtraction) by holographic Fourier transformation," Phys. Lett. 18, 116-118 (1965).
[CrossRef]

Phys. Today

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

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Figures (8)

Fig. 1.
Fig. 1.

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

Fig. 2.
Fig. 2.

Real color image decomposition: (a) an original color image with 800×600 pixels; (b) its red part; (c) its green part; (d) its blue part.

Fig. 3.
Fig. 3.

Encryption implementation with fractional Fourier hologram. BE: beam expander, BSs: beam splitters, Ms: mirrors, RPMs: random phases, I: input plane, O: output plane.

Fig. 4.
Fig. 4.

Color image encryption and decryption with on-axis fractional Fourier hologram. (a) An original color image with 1024×768 pixels; (b) its color encrypted fractional hologram; (c) key hologram; (d) recovered color image.

Fig. 5.
Fig. 5.

Color image encryption and decryption with off-axis fractional Fourier hologram. (a) Retrieved encrypted term; (b) retrieved random key; (c) wrong decryption result with all fractional orders simultaneously incorrect; (d) wrong decryption result with all random phases incorrect; (e) its wrong decryption result with both fractional orders and random phases incorrectly selected; (f)–(h) results with one channel incorrectly decrypted; (i)–(k) results with only one channel correctly decrypted; (l) correct decryption result.

Fig. 6.
Fig. 6.

Color image addition and subtraction. (a), (b) Original images with 1024×768 pixels; (c) their addition image; (d).addition image after post-processing; (e), (f) the other two original images with 257×255 pixels; (g) their subtraction image; (h).subtraction image after post-processing.

Fig. 7.
Fig. 7.

Color image encryption and addition. (a) Encrypted result of three added images; (b), (c) their incorrect decryption images; (d) result with one channel correctly decrypted; (e) result with two channels correctly decrypted; (f) their fused image with correct decryption.

Fig. 8.
Fig. 8.

Color image encryption and subtraction. (a) Encrypted result of two subtracted images; (b), (c) their incorrect decryption images; (d) result with one channel correctly decrypted; (e) result with two channels correctly decrypted; (f) their subtraction image with correct decryption.

Equations (20)

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g ( x 1 , y 1 ) = FrFT [ f ( x , y ) P ( x , y ) ] = f ( x , y ) P ( x , y ) exp ( i π x 2 + x 1 2 λ f s 1 tan ϕ 1 2 π i xx 1 λ f s 1 sin ϕ 1 )
× exp ( i π y 2 + y 1 2 λ f s 2 tan ϕ 2 2 π i yy 1 λ f s 2 sin ϕ 2 ) d x d y ,
I ( u , v ) = 1 + g ( x 1 , y 1 ) 2 + g * ( x 1 , y 1 ) Q ( u , v ) + g ( x 1 , y 1 ) Q * ( u , v ) .
h ( u , v ) = Q ( u , v ) + Q * ( u , v ) .
f ( x , y ) = IFrFT [ g ( x 1 , y 1 ) ] = g ( x 1 , y 1 ) Q * ( u , v ) Q ( u , v ) exp ( i π x 2 + x 1 2 λ f s 1 tan ( ϕ 1 ) 2 π i xx 1 λ f s 1 sin ( ϕ 1 ) )
× exp ( i π y 2 + y 1 2 λ f s 2 tan ( ϕ 2 ) 2 π i yy 1 λ f s 2 sin ( ϕ 2 ) ) d x 1 d y 1
= f ( x , y ) P ( x , y ) .
g ( x 1 , y 1 ) = FrFT [ f ( x , y ) ] = f ( x , y ) exp ( i π x 2 + x 1 2 λ f s 1 tan ϕ 1 2 π i xx 1 λ f s 1 sin ϕ 1 )
× exp ( i π y 2 + y 1 2 λ f s 2 tan ϕ 2 2 π i yy 1 λ f s 2 sin ϕ 2 ) d x d y .
I 1 ( u , v ) = 1 + g 1 ( x 1 , y 1 ) 2 + g 1 * ( x 1 , y 1 ) Q 1 ( u , v ) + g 1 ( x 1 , y 1 ) Q 1 * ( u , v ) ,
I 2 ( u , v ) = 1 + g 2 ( x 1 , y 1 ) 2 + g 2 * ( x 1 , y 1 ) Q 1 ( u , v ) exp ( i π ) + g 2 ( x 1 , y 1 ) Q 1 * ( u , v ) exp ( i π ) .
g 12 ( x 1 , y 1 ) = Q 1 * ( u , v ) Q 1 ( u , v ) [ g 1 ( x 1 , y 1 ) + g 2 ( x 1 , y 1 ) exp ( i π ) ]
= g 1 ( x 1 , y 1 ) + g 2 ( x 1 , y 1 ) ,
f 12 ( x , y ) = IFrFT [ g 12 ( x 1 , y 1 ) ] = g 12 ( x 1 , y 1 ) exp ( i π x 2 + x 1 2 λ f s 1 tan ( ϕ 1 ) 2 π i xx 1 λ f s 1 sin ( ϕ 1 ) )
× exp ( i π y 2 + y 1 2 λ f s 2 tan ( ϕ 2 ) 2 π i yy 1 λ f s 2 sin ( ϕ 2 ) ) d x 1 d y 1
= IFrFT [ g 1 ( x 1 , y 1 ) ] IFrFT [ g 2 ( x 1 , y 1 ) ]
= f 1 ( x , y ) f 2 ( x , y ) .
g 12 ( x 1 , y 1 ) = Q 1 * ( u , v ) Q 1 ( u , v ) [ g 1 ( x 1 , y 1 ) + g 2 ( x 1 , y 1 ) ] = g 1 ( x 1 , y 1 ) + g 2 ( x 1 , y 1 ) ,
f 12 ( x , y ) = IFrFT [ g 12 ( x 1 , y 1 ) ] = IFrFT [ g 1 ( x 1 , y 1 ) ] + IFrFT [ g 2 ( x 1 , y 1 ) ]
= f 1 ( x , y ) + f 2 ( x , y ) .

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