Z. Liu, L. Xu, Q. Guo, C. Lin, and S. Liu, “Image watermarking by using phase retrieval algorithm in gyrator transform domain,” Opt. Commun. 283, 4923–4927(2010).

[CrossRef]

Z. Liu, L. Xu, C. Lin, and S. Liu, “Image encryption by encoding with a nonuniform optical beam in gyrator transform domains,” Appl. Opt. 49, 5632–5637 (2010).

[CrossRef]
[PubMed]

H. E. Hwang, H. T. Chang, and W. N. Lie, “Multiple-image encryption and multiplexing using a modified Gerchberg–Saxton algorithm and phase modulation in Fresnel-transform domain,” Opt. Lett. 34, 3917–3919 (2009).

[CrossRef]
[PubMed]

M. Joshi, C. Shakher, and K. Singh, “Logarithms-based RGB image encryption in the fractional Fourier domain: a non-linear approach,” Opt. Lasers Eng. 47, 721–727(2009).

[CrossRef]

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (2009).

[CrossRef]

X. Meng, L. Cai, Y. Wang, X. Yang, X. Xu, G. Dong, X. Shen, H. Zhang, and X. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A 9, 1070–1075(2007).

[CrossRef]

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

[CrossRef]

Y. Li, K. Kreske, and J. Rosen, “Security and encryption optical systems based on a correlator with significant output images,” Appl. Opt. 39, 5295–5301 (2000).

[CrossRef]

B. Javidi and T. Nomura, “Polarization encoding for optical security systems,” Opt. Eng. 39, 2439–2443 (2000).

[CrossRef]

P. C. Mogensen and J. Gluckstad, “Phase-only optical encryption,” Opt. Lett. 25, 566–568 (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]

S. Q. Zhang and M. A. Karim, “Color image encryption using double random phase encoding,” Microw. Opt. Technol. Lett. 21, 318–323 (1999).

[CrossRef]

D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407–414 (1997).

[CrossRef]

X. Meng, L. Cai, Y. Wang, X. Yang, X. Xu, G. Dong, X. Shen, H. Zhang, and X. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A 9, 1070–1075(2007).

[CrossRef]

X. Peng, L. Yu, and L. Cai, “Double-lock for image encryption with virtual optical wavelength,” Opt. Express 10, 41–45 (2002).

[PubMed]

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (2009).

[CrossRef]

X. Meng, L. Cai, Y. Wang, X. Yang, X. Xu, G. Dong, X. Shen, H. Zhang, and X. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A 9, 1070–1075(2007).

[CrossRef]

X. Meng, L. Cai, Y. Wang, X. Yang, X. Xu, G. Dong, X. Shen, H. Zhang, and X. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A 9, 1070–1075(2007).

[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Z. Liu, L. Xu, Q. Guo, C. Lin, and S. Liu, “Image watermarking by using phase retrieval algorithm in gyrator transform domain,” Opt. Commun. 283, 4923–4927(2010).

[CrossRef]

B. Javidi and T. Nomura, “Polarization encoding for optical security systems,” Opt. Eng. 39, 2439–2443 (2000).

[CrossRef]

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

[CrossRef]

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]

M. Joshi, C. Shakher, and K. Singh, “Logarithms-based RGB image encryption in the fractional Fourier domain: a non-linear approach,” Opt. Lasers Eng. 47, 721–727(2009).

[CrossRef]

S. Q. Zhang and M. A. Karim, “Color image encryption using double random phase encoding,” Microw. Opt. Technol. Lett. 21, 318–323 (1999).

[CrossRef]

D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407–414 (1997).

[CrossRef]

Z. Liu, L. Xu, C. Lin, and S. Liu, “Image encryption by encoding with a nonuniform optical beam in gyrator transform domains,” Appl. Opt. 49, 5632–5637 (2010).

[CrossRef]
[PubMed]

Z. Liu, L. Xu, Q. Guo, C. Lin, and S. Liu, “Image watermarking by using phase retrieval algorithm in gyrator transform domain,” Opt. Commun. 283, 4923–4927(2010).

[CrossRef]

Z. Liu, L. Xu, Q. Guo, C. Lin, and S. Liu, “Image watermarking by using phase retrieval algorithm in gyrator transform domain,” Opt. Commun. 283, 4923–4927(2010).

[CrossRef]

Z. Liu, L. Xu, C. Lin, and S. Liu, “Image encryption by encoding with a nonuniform optical beam in gyrator transform domains,” Appl. Opt. 49, 5632–5637 (2010).

[CrossRef]
[PubMed]

Z. Liu, L. Xu, C. Lin, and S. Liu, “Image encryption by encoding with a nonuniform optical beam in gyrator transform domains,” Appl. Opt. 49, 5632–5637 (2010).

[CrossRef]
[PubMed]

Z. Liu, L. Xu, Q. Guo, C. Lin, and S. Liu, “Image watermarking by using phase retrieval algorithm in gyrator transform domain,” Opt. Commun. 283, 4923–4927(2010).

[CrossRef]

D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407–414 (1997).

[CrossRef]

X. Meng, L. Cai, Y. Wang, X. Yang, X. Xu, G. Dong, X. Shen, H. Zhang, and X. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A 9, 1070–1075(2007).

[CrossRef]

B. Javidi and T. Nomura, “Polarization encoding for optical security systems,” Opt. Eng. 39, 2439–2443 (2000).

[CrossRef]

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (2009).

[CrossRef]

M. Joshi, C. Shakher, and K. Singh, “Logarithms-based RGB image encryption in the fractional Fourier domain: a non-linear approach,” Opt. Lasers Eng. 47, 721–727(2009).

[CrossRef]

X. Meng, L. Cai, Y. Wang, X. Yang, X. Xu, G. Dong, X. Shen, H. Zhang, and X. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A 9, 1070–1075(2007).

[CrossRef]

M. Joshi, C. Shakher, and K. Singh, “Logarithms-based RGB image encryption in the fractional Fourier domain: a non-linear approach,” Opt. Lasers Eng. 47, 721–727(2009).

[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]

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (2009).

[CrossRef]

X. Meng, L. Cai, Y. Wang, X. Yang, X. Xu, G. Dong, X. Shen, H. Zhang, and X. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A 9, 1070–1075(2007).

[CrossRef]

Z. Liu, L. Xu, Q. Guo, C. Lin, and S. Liu, “Image watermarking by using phase retrieval algorithm in gyrator transform domain,” Opt. Commun. 283, 4923–4927(2010).

[CrossRef]

Z. Liu, L. Xu, C. Lin, and S. Liu, “Image encryption by encoding with a nonuniform optical beam in gyrator transform domains,” Appl. Opt. 49, 5632–5637 (2010).

[CrossRef]
[PubMed]

X. Meng, L. Cai, Y. Wang, X. Yang, X. Xu, G. Dong, X. Shen, H. Zhang, and X. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A 9, 1070–1075(2007).

[CrossRef]

X. Meng, L. Cai, Y. Wang, X. Yang, X. Xu, G. Dong, X. Shen, H. Zhang, and X. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A 9, 1070–1075(2007).

[CrossRef]

D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407–414 (1997).

[CrossRef]

X. Meng, L. Cai, Y. Wang, X. Yang, X. Xu, G. Dong, X. Shen, H. Zhang, and X. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A 9, 1070–1075(2007).

[CrossRef]

S. Q. Zhang and M. A. Karim, “Color image encryption using double random phase encoding,” Microw. Opt. Technol. Lett. 21, 318–323 (1999).

[CrossRef]

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

[CrossRef]

Y. Li, K. Kreske, and J. Rosen, “Security and encryption optical systems based on a correlator with significant output images,” Appl. Opt. 39, 5295–5301 (2000).

[CrossRef]

Z. Liu, L. Xu, C. Lin, and S. Liu, “Image encryption by encoding with a nonuniform optical beam in gyrator transform domains,” Appl. Opt. 49, 5632–5637 (2010).

[CrossRef]
[PubMed]

D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407–414 (1997).

[CrossRef]

X. Meng, L. Cai, Y. Wang, X. Yang, X. Xu, G. Dong, X. Shen, H. Zhang, and X. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A 9, 1070–1075(2007).

[CrossRef]

S. Q. Zhang and M. A. Karim, “Color image encryption using double random phase encoding,” Microw. Opt. Technol. Lett. 21, 318–323 (1999).

[CrossRef]

G. Situ and J. Zhang, “A lensless optical security system based on computer- generated phase only masks,” Opt. Commun. 232, 115–122 (2004).

[CrossRef]

Z. Liu, L. Xu, Q. Guo, C. Lin, and S. Liu, “Image watermarking by using phase retrieval algorithm in gyrator transform domain,” Opt. Commun. 283, 4923–4927(2010).

[CrossRef]

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (2009).

[CrossRef]

B. Javidi and T. Nomura, “Polarization encoding for optical security systems,” Opt. Eng. 39, 2439–2443 (2000).

[CrossRef]

M. Joshi, C. Shakher, and K. Singh, “Logarithms-based RGB image encryption in the fractional Fourier domain: a non-linear approach,” Opt. Lasers Eng. 47, 721–727(2009).

[CrossRef]

H. E. Hwang, H. T. Chang, and W. N. Lie, “Multiple-image encryption and multiplexing using a modified Gerchberg–Saxton algorithm and phase modulation in Fresnel-transform domain,” Opt. Lett. 34, 3917–3919 (2009).

[CrossRef]
[PubMed]

P. C. Mogensen and J. Gluckstad, “Phase-only optical encryption,” Opt. Lett. 25, 566–568 (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]

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]

G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29, 1584–1586 (2004).

[CrossRef]
[PubMed]

C. L. Mela and C. Iemmi, “Optical encryption using phase-shifting interferometry in a joint transform correlator,” Opt. Lett. 31, 2562–2564 (2006).

[CrossRef]
[PubMed]

H.P.Herzig, ed., Micro-Optics (Taylor & Francis, 1996).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).