Parallel encryption and hierarchical retrieval for multi-channel images using an optical joint Fresnel transform correlator

We propose an optical encryption method allowing the parallel encryption and hierarchical retrieval for multi-channel images based on a joint Fresnel transform correlator. In our designed scheme, the linear phase shift operation for the phase masks is utilized to achieve the aim of ensuring that the center of the complex amplitude distributions from the same group can overlap with each other in Fresnel domain, and the phase retrieval algorithm for designing the phase masks is used to avoid the cross talk between multi-channel images. The optimized phase masks can be flexibly reconfigured on the spatial light modulator without increasing the additional optical hardware and system complexity. Our designed scheme can encrypt multi-channel images simultaneously into a single cipher-text, which can also be used to recover arbitrary original images with corresponding keys. Thus, this method can achieve the aim of the hierarchical retrieval of encrypted images from a single cipher-text. Moreover, because the encryption process does not require any transformative lenses and accurate alignment of optical elements, the encryption scheme is easy to be optically implemented. Furthermore, compared with the previous JTC-based cryptosystems, the Fresnel diffraction distance and the position of the key masks in our proposed scheme can both be utilized as the additional encryption keys, which can enhance the security effectively. The theoretical analysis and numeric simulation results both validate the feasibility and effectiveness of the designed scheme.