Enhanced Three-Dimensional Double Random Phase Encryption: Overcoming Phase Information Loss in Zero-Amplitude Singularities for Simultaneous Two Primary Data

This paper proposes an advanced three-dimensional optical encryption technique based on double random phase encryption for the simultaneous encryption of two primary datasets. While conventional double random phase encryption offers high-speed encryption, it suffers from low data efficiency. To address this issue, the proposed method assigns the first primary dataset to the amplitude and the second to the phase. However, this approach faces a critical limitation: the phase information becomes undefined or lost when the amplitude is zero. Therefore, we introduce a biased amplitude encoding scheme for double random phase encryption to ensure the mathematical recoverability of the phase component. In the proposed method, a biased value ϵ is added to the amplitude part during the double random phase encryption encryption process and subsequently subtracted from the decrypted data to recover the two primary datasets. To verify the effectiveness of our approach, we employ synthetic aperture integral imaging and volumetric computational reconstruction. The experimental results show that while the first dataset remains lossless, the lossy characteristics of the second dataset are significantly mitigated.