Exploiting phase degrees of freedom in cascaded diffractive optical elements for robust optical information encryption

Cascaded diffractive optical elements (DOEs) introduce additional degrees of freedom compared to a single DOE, providing an effective platform for rotation-angle multiplexed optical information encryption. However, cascaded DOE-based image reconstruction is highly sensitive to rotation misalignment, which limits its robustness in practical implementations. From a design perspective, this limitation arises from the insufficient utilization of the phase degrees of freedom provided by cascaded DOE. In this work, a double phase update algorithm is proposed for cascaded DOE design, in which all DOEs participate in phase updating during the iterative process. By more effectively exploiting the available phase degrees of freedom, the proposed method significantly enlarges the rotation tolerance while maintaining comparable reconstruction quality. Numerical simulations demonstrate that the rotation tolerance is extended from 1.21° to 2.78°, corresponding to an improvement of approximately 130%. These results indicate that the proposed design strategy provides an effective approach for improving the robustness of cascaded DOE-based optical information encryption.