Keywords: 
• 叠层衍射 /
• 双随机编码 /
• 数字水印 /
• 鲁棒性

Abstract: 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.