We propose a new 2-step phase-shifting digital holographic optical encryption technique and analyze tolerance error for this cipher system. 2-step phase-shifting digital holograms are acquired by moving the PZT mirror with phase step of 0 or ${\pi}$/2 in the reference beam path of the Mach-Zehnder type interferometer. Digital hologram with the encrypted information is Fourier transform hologram and is recorded on CCD camera with 256 gray-level quantized intensities. The decryption performance of binary bit data and image data is analyzed by considering error factors. One of the most important errors is quantization error in detecting the digital hologram intensity on CCD. The more the number of quantization error pixels and the variation of gray-level increase, the more the number of error bits increases for decryption. Computer experiments show the results to be carried out encryption and decryption with the proposed method and the graph to analyze the tolerance of the quantization error in the system.

Keywords: Optical encryption, Digital holography, Phase-shifting interferometry, Cipher system,

OCIS codes: 090.0090; 090.2880; 070.0070; 070.4560; 170.3010

1. B. Javidi and J. L. Horner, "Optical pattern recognition for validation and security verification," Opt. Eng. 33, 1752-1756 (1994).
   
2. J. F. Heanue, M. C. Bashaw, and L. Hesselink, "Encrypted holographic data storage based on orthogonal-phase-code multiplexing," Appl. Opt. 34, 6012-6015 (1995).
   
3. P. Refregier and B. Javidi, "Optical image encryption based on input plane and Fourier plane random encoding," Opt. Lett. 20, 767-769 (1995).
   
4. B. Javidi, A. Sergent, and E. Ahouzi, "Performance of double phase encoding encryption technique using binarized encrypted images," Opt. Eng. 37, 565-569 (1998).
   
5. D. Weber and J. Trolinger, "Novel implementation of nonlinear joint transform correlators in optical security and validation," Opt. Eng. 38, 62-68 (1999).
   
6. E. Cuche, F. Bevilacqua, and C. Depeursinge, "Digital holography for quantitative phase-contrast imaging," Opt. Lett. 24, 291-293 (1999).
   
7. B. Javidi and T. Nomura, "Securing information by means of digital holography," Opt. Lett. 25, 28-30 (2000).
   
8. G. Unnikrishnan and K. Singh, "Double random fractional Fourier domain encoding for optical security," Opt. Eng. 39, 2853-2859 (2000).
   
9. G.-S. Lin, H. T. Chang, W.-N. Lie, and C.-H. Chuang, "Public-key-based optical image cryptosystem based on data embedding techniques," Opt. Eng. 42, 2331-2339 (2003).
   
10. U. Schnars and W. Jueptner, "Direct recording of holograms by a CCD target and numerical reconstruction," Appl. Opt. 33, 179-181 (1994).
    
11. P. Hariharan, "Digital phase-shifting interferometry : a simple error compensating phase calculation algorithm," Appl. Opt. 26, 2504-0505 (1987).
    
12. I. Yamaguchi and T. Zhang, "Phase-shifting digital holography," Opt. Lett. 22, 610-612 (1998).
13. H. J. Lee and S. G. Gil, "Error analysis for optical security by means of 4-step phase-shfting digital hologaphy," J. Opt. Soc. Korea 10, 118-123 (2006).
    
14. S. K. Gil, S. H. Jeon, N. Kim, and J. R. Jeong, "Successive encryption and transmission with phase-shifting digital holography," Proc. SPIE 6136, 339-346 (2006).
15. S. K. Gil, H. J. Byun, H. J. Lee, S. H. Jeon, and J. R. Jeong, "Optical encryption of binary data information with 2-step phase-shifting digital holography," Proc. SPIE 6488, 648812 (2007).
16. J.-P. Liu, T.-C. Poon, G.-S. Jhou, and P.-J. Chen, "Comparison of two-, three, and four-exposure guadrature phase-shifting holography," Appl. Opt. 50, 2443-2450 (2011).
    
17. M.-O. Jeong, N. Kim, and J.-H. Park, "Elemental image synthesis for integral imaging using phase-shifting digital holography," J. Opt. Soc. Korea 12, 275-280 (2008).
    
18. S. H. Jeon, Y. G. Hwang, and S. K. Gil, "Optical encryption of gray-level image using on-axis and 2-f digital holography with two-step phase-shifting method," Opt. Rev. 15, 181-186 (2008).
    
19. S. H. Jeon and S. K. Gil, "Measurement of a mirror surface topography using 2-frame phase-shifting digital interferometry," J. Opt. Soc. Korea 13, 245-250 (2009).
    
20. S. H. Jeon and S. K. Gil, "QPSK modulation based optical image cryptosystem using phase-shifting digital holography," J. Opt. Soc. Korea 14, 97-103 (2010).