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We propose a method for watermarking algorithm using ptychographical imaging. The proposed method uses four probes and one fake probe for illumination, orderly. And five weighted double phase-encoded hidden images are added to a host image that is referred to as the transmitted image. Specifically, the amplitude of the transmitted image contains encoded and attenuated watermark image. And the phase of the transmitted image is the host image due to the application of the fake probe. We develop an analytical presentation for the experimental principle using mathematical derivation of the fake probe and ptychographical imaging. We test analytically the distortion of the transmitted image that is due to noise jamming and the effect of the occlusion of the pixels of the transmitted image. Moreover, we discuss the impact of the probe number and probe overlap rate on system robustness, respectively. Results of computer simulations are presented. First, the amplitude and phase of the watermark image are extracted well. Second, the contradiction between watermark imperceptible and watermark extraction quality can be resolved. Third, the simulations illustrate the system ability to extract the watermark image under distortions and the robustness of the transmitted image against removal trials. Furthermore, the robustness of the system is improved, as the number or overlap rate of the probe increases. In the end, the proposed method is applied to GIF images.
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Keywords:
- ptychographical imaging /
- double random coding /
- optical watermark /
- robust
[1] Takai N, Mifune Y 2002 Appl. Opt. 41 865
[2] Kishk S, Javidi B 2002 Appl. Opt. 41 5462
[3] Kishk S, Javidi B 2003 Opt. Lett. 28 167
[4] Kishk S, Javidi B 2003 Opt. Express 11 874
[5] Clemente P, Durán V, Torres-Company V, Tajahuerce E, Lancis J 2010 Opt. Lett. 35 2391
[6] Chen W, Chen X, Sheppard C J R 2010 Opt. Lett. 35 3817
[7] Hua L-L, Xu N, Yang G 2014 Chin. Phys. B 23 064201
[8] Shi Y, Li T, Wang Y, Gao Q, Zhang S, Li H 2013 Opt. Lett. 38 1425
[9] Refregier P, Javidi B 1995 Opt. Lett. 20 767
[10] Chang H T, Tsan C L 2005 Appl. Opt. 44 6211
[11] Situ G, Zhang J 2005 Opt. Commun. 245 55
[12] He M Z, Cai L Z, Liu Q, Wang X C, Meng X F 2005 Opt. Commun. 247 29
[13] Kim H, Lee Y H 2005 Opt. Express 13 2881
[14] Shi Y S, Situ G H, Zhang J J 2007 Opt. Lett. 32 1914
[15] Shi X Y, Zhao D M 2011 Appl. Opt. 50 766
[16] Wang Y L, Shi Y S, Li T, Gao Q K, Xiao J, Zhang S G 2013 Acta Phys. Sin. 62 064206 (in Chinese) [王雅丽, 史祎诗, 李拓, 高乾坤, 肖俊, 张三国 2013 62 064206]
[17] Gao Q, Wang Y, Li T, Shi Y 2014 Appl Opt. 53 4700
[18] Hoppe W 1969 Acta Cryst. A 25 495
[19] Hoppe W 1982 Ultramicroscopy. 10 187
[20] Faulkner H M L, Rodenburg J M 2004 Phys. Rev. Lett. 93 023903
[21] Rodenburg J M, Faulkner H M L 2004 Appl. Phys. Lett. 85 4795
[22] Rodenburg J M, Hurst A C, Cullis A G 2007 Ultramicroscopy. 107 227
[23] Rodenburg J M, Hurst A C, Cullis A G, Dobson B R, Pfeiffer F, Bunk O, David C, Jefimovs K, Johnson I 2007 Phys. Rev. Lett. 98 034801
[24] Thibault P, Dierolf M, Menzel A, Bunk O, David C, Pfeiffer F 2008 Science 321 379
[25] Maiden A M, Rodenburg J M, Humphry M J 2010 Opt. Lett. 35 2585
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[1] Takai N, Mifune Y 2002 Appl. Opt. 41 865
[2] Kishk S, Javidi B 2002 Appl. Opt. 41 5462
[3] Kishk S, Javidi B 2003 Opt. Lett. 28 167
[4] Kishk S, Javidi B 2003 Opt. Express 11 874
[5] Clemente P, Durán V, Torres-Company V, Tajahuerce E, Lancis J 2010 Opt. Lett. 35 2391
[6] Chen W, Chen X, Sheppard C J R 2010 Opt. Lett. 35 3817
[7] Hua L-L, Xu N, Yang G 2014 Chin. Phys. B 23 064201
[8] Shi Y, Li T, Wang Y, Gao Q, Zhang S, Li H 2013 Opt. Lett. 38 1425
[9] Refregier P, Javidi B 1995 Opt. Lett. 20 767
[10] Chang H T, Tsan C L 2005 Appl. Opt. 44 6211
[11] Situ G, Zhang J 2005 Opt. Commun. 245 55
[12] He M Z, Cai L Z, Liu Q, Wang X C, Meng X F 2005 Opt. Commun. 247 29
[13] Kim H, Lee Y H 2005 Opt. Express 13 2881
[14] Shi Y S, Situ G H, Zhang J J 2007 Opt. Lett. 32 1914
[15] Shi X Y, Zhao D M 2011 Appl. Opt. 50 766
[16] Wang Y L, Shi Y S, Li T, Gao Q K, Xiao J, Zhang S G 2013 Acta Phys. Sin. 62 064206 (in Chinese) [王雅丽, 史祎诗, 李拓, 高乾坤, 肖俊, 张三国 2013 62 064206]
[17] Gao Q, Wang Y, Li T, Shi Y 2014 Appl Opt. 53 4700
[18] Hoppe W 1969 Acta Cryst. A 25 495
[19] Hoppe W 1982 Ultramicroscopy. 10 187
[20] Faulkner H M L, Rodenburg J M 2004 Phys. Rev. Lett. 93 023903
[21] Rodenburg J M, Faulkner H M L 2004 Appl. Phys. Lett. 85 4795
[22] Rodenburg J M, Hurst A C, Cullis A G 2007 Ultramicroscopy. 107 227
[23] Rodenburg J M, Hurst A C, Cullis A G, Dobson B R, Pfeiffer F, Bunk O, David C, Jefimovs K, Johnson I 2007 Phys. Rev. Lett. 98 034801
[24] Thibault P, Dierolf M, Menzel A, Bunk O, David C, Pfeiffer F 2008 Science 321 379
[25] Maiden A M, Rodenburg J M, Humphry M J 2010 Opt. Lett. 35 2585
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