## Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms

Optics Express, Vol. 14, Issue 19, pp. 8552-8560 (2006)

http://dx.doi.org/10.1364/OE.14.008552

Acrobat PDF (815 KB)

### 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

## 1. Introduction

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 techsnology,” Phys. Today **50**, 27–32 (1997). [CrossRef]

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]

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]

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

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]

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

21. W. M. Jin, L. H. Ma, and C. J. Yan, “Real color fractional Fourier transform holograms,” Opt. Commun. **259**, 513–516 (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]

## 2. Double random encryption and Fresnel transform holograms

*p*(

*x*,

*y*) and

*k*(

*x*,

*y*) are two independent white sequences uniformly distributed on the interval [0, 1

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]

*λ*is the wavelength of an incident beam, which is a monochromatic beam that corresponds to a certain color with the wavelength. So the decryption image would also be a single color picture, and its real color information is lost, which is shown in Fig. 1.

## 3. Color image encryption based on Fresnel transform holograms

*f*(

*x*,

*y*) can be decomposed into three components

*R*(

*x*,

*y*),

*G*(

*x*,

*y*) and

*B*(

*x*,

*y*), each component corresponds to one color (red, green or blue). To incorporate the color information, it is suggested by using a multichannel method to separate the image into red, green and blue three channels and each channel is to be independently encrypted. If the incident wavelength of each channel is close to the wavelength of basic color, the real color information can be recovered at the output plane in decryption.

_{4}should be chosen with high reflection index for red wavelengths and high transmission index for other wavelengths. I means the input plane, where the original color image is displayed. P and Ks are random phase masks, which are placed respectively at the input plane and Fresnel domains. Each color component passes through distances z

_{1}, z

_{2}, z

_{n}, where random phase masks K

_{1}, K

_{2}, K

_{n}, placed at corresponding Fresnel planes, it follows the basic theory of Fresnel transform and double random phase encryption method, which is mentioned in above section. All these three components join together, written on a hologram halide (H) with three corresponding reference beams. This pure optical setup can realize the encryption in real time but does not rely on electronics devices (such as CCD, Computer or SLM, etc.).

_{n}, z

_{n-1}z

_{2}, z

_{1}, with the phase masks K

_{n-1}K

_{2}, K

_{1}placed at corresponding positions in each channel. And finally the decryption image would be reconstructed at the output plane if all the keys were correct.

## 4. Numerical simulations and analyses

*λ*

_{1}=700nm, the system parameters are z

_{1}=17mm, z

_{2}=21mm, z

_{3}=30.5mm, respectively. And the parameters of other two channels are

*λ*

_{2}=546.1nm, z

_{1}=20mm, z

_{2}=25mm, z

_{3}=28mm;

*λ*

_{3}=435.8nm, z

_{1}=16mm, z

_{2}=23mm, z

_{3}=47.7mm, respectively.

*λ*

_{1},

*λ*

_{2},

*λ*

_{3}are the wavelengths of basic RGB color in the computer. The image is encrypted in three channels, and we can find the encrypted picture contains three noises (Red, Green and Blue). Here, z

_{1}, z

_{2}and z

_{3}in each channel should be chosen carefully to reduce the size mismatch regarding the propagation distance.

^{4}Near-field diffraction is regarded as a better choice. Size mismatch also exists in each channel because different wavelength is used. A desired scale factor of the output can be obtained by adjusting the parameters of distances. Figure 7(c) shows one of the incorrect decryption images when random phase masks are incorrect in decryption. Then Fig. 7(d) gives the result with some wrong distance parameters (z

_{1}=10mm, z

_{2}=20mm, z

_{3}=25mm; z

_{1}=15mm, z

_{2}=25mm, z

_{3}=17mm; z

_{1}=19mm, z

_{2}=13mm, z

_{3}=32mm). When random phase keys and system parameters are all wrong in decoding, the final decryption result is denoted in Fig. 7(e). Figure 7(f) is the correct decryption image.

*M*and

*N*are the pixels of the image, Δ

*x*and Δ

*y*are the pixel sizes. In this simulation, we give the MSEs of some decryption results. The MSE between the incorrect decryption image in Fig. 7(c) and original image in Fig. 7(a) is about 5.0860, and the corresponding MSE value between the correct decryption image in Fig. 7(f) and original image is about 5.1127×10

^{-27}. The values of MSE are also calculated for the partial color information recovery situations as in Fig. 8. The MSE between Fig. 8(e) and Fig. 8(a) is about 1.8667, and the value is 3.5294 between Fig. 8(f) and the original image. We note that the values of MSE well reflect the quality of the decrypted images.

## 5. Conclusion

_{1}, K

_{2}, K

_{n}, system parameters z

_{1}, z

_{2}, z

_{n}in each channel are important keys in encryption and decryption. When the keys are incorrect in decryption, the noise like information would appear at the output plane. When keys of only one or two channels are correct, the color information is distorted, and people also cannot obtain the correct information. The keys can be enlarged further by employing more phase masks placed at Fresnel domains in each channel, and the synthesized information can be encrypted, stored and transmitted with high security.

## Acknowledgment

## References and links

1. | P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. |

2. | B. Javidi, “Security information with optical techsnology,” Phys. Today |

3. | G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. |

4. | G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. |

5. | B. Hennelly and J. T. Sheridan, “Optical image encryption by random shifting in fractional Fourier domains,” Opt. Lett. |

6. | E. Tajahuerce, O. Matoba, S. C. Verrall, and B. Javidi, “Optoeletronic information encryption with phase-shifting interferometry,” Appl. Opt. |

7. | S. T. Liu, Q. L. Mi, and B. H. Zhu, “Optical image encryption with multistage and multichannel fractional Fourier-domain filtering,” Opt. Lett. |

8. | B. Javidi and T. Nomura, “Securing information by use of digital holography,” Opt. Lett. |

9. | X. Peng, L. F. Yu, and L. L. Cai, “Double-lock for image encryption with virtual optical wavelength,” Opt. Exp. |

10. | N. K. Nishchal, J. Joseph, and K. Singh, “Securing information using fractional Fourier transform in digital holography,” Opt. Commun. |

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. |

12. | H. Kim, D. H. Kim, and Y. H. Lee, “Encryption of digital hologram of 3-D object by virtual optics,” Opt. Exp. |

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. |

14. | L. F. Chen and D. M. Zhao, “Optical image encryption based on fractional wavelet transform,” Opt. Commun. |

15. | Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. |

16. | G. H. Situ and J. J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. |

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. |

18. | S. Q. Zhang and M. A. Karim, “Color image encryption using double random phase encoding,” Microwave Opt. Technol. Lett. |

19. | J. Nicolas, C. Iemmi, J. Compos, and M. J. Yzuel, “Optical encoding of color three-dimensional correlation,” Opt. Commun. |

20. | S. Ledesma, C. Iemmi, M. Villarreal, and J. Compos, “Multichannel correlation by color multiplexing,” Opt. Commun. |

21. | W. M. Jin, L. H. Ma, and C. J. Yan, “Real color fractional Fourier transform holograms,” Opt. Commun. |

**OCIS Codes**

(070.4560) Fourier optics and signal processing : Data processing by optical means

(090.0090) Holography : Holography

(100.2000) Image processing : Digital image processing

**ToC Category:**

Fourier Optics and Optical Signal Processing

**History**

Original Manuscript: June 19, 2006

Revised Manuscript: August 18, 2006

Manuscript Accepted: August 21, 2006

Published: September 18, 2006

**Citation**

Linfei Chen and Daomu Zhao, "Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms," Opt. Express **14**, 8552-8560 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-19-8552

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### References

- 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]
- B. Javidi, "Security information with optical technology," Phys. Today 50,27-32 (1997). [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]
- G. Situ and J. Zhang, "Double random-phase encoding in the Fresnel domain," Opt. Lett. 29, 1584-1586 (2004). [CrossRef] [PubMed]
- B. Hennelly and J. T. Sheridan, "Optical image encryption by random shifting in fractional Fourier domains," Opt. Lett. 28, 269-271 (2003). [CrossRef] [PubMed]
- E. Tajahuerce, O. Matoba, S. C. Verrall, and B. Javidi, "Optoeletronic information encryption with phase-shifting interferometry," Appl. Opt. 39, 2313-2320 (2000). [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]
- X. Peng, L. F. Yu, and L. L. Cai, "Double-lock for image encryption with virtual optical wavelength," Opt. Exp. 10, 41-45(2002).
- N. K. Nishchal, J. Joseph, and K. Singh, "Securing information using fractional Fourier transform in digital holography," Opt. Commun. 235, 253-259 (2004). [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]
- 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. 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]
- G. H. Situ and J. J. Zhang, "Multiple-image encryption by wavelength multiplexing," Opt. Lett. 30, 1306-1308 (2005). [CrossRef] [PubMed]
- 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]
- S. Q. Zhang and M. A. Karim, "Color image encryption using double random phase encoding," Microwave Opt. Technol. Lett. 21, 318-323 (1999). [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]
- 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]

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