We propose an algorithm for jointly designing two phase-only masks (POMs) that allow for the encryption and noise-free retrieval of triple images. The images required for optical retrieval are first stored in quick-response (QR) codes for noise-free retrieval and flexible readout. Two sparse POMs are respectively calculated from two different images used as references for authentication based on modified Gerchberg-Saxton algorithm (GSA) and pixel extraction, and are then used as support constraints in a modified double-phase retrieval algorithm (MPRA), together with the above-mentioned QR codes. No visible information about the target images or the reference images can be obtained from each of these authenticated POMs. This approach allows users to authenticate the two POMs used for image reconstruction without visual observation of the reference images. It also allows user to friendly access and readout with mobile devices.
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