Fig. 1. (a) Complex-valued universal linear transformations using spatially incoherent diffractive optical networks. (b) Amplitude and phase of the target complex-valued linear transformation. (c) Mosaicking and demosaicking processes. (d)–(e) Image encryption. (d) Complex-valued images are digitally encrypted (A−1), and subsequently decrypted using the diffractive system that performs A (diffractive key). (e) The encryption is performed through the spatially incoherent diffractive network (diffractive lock), and the decryption is performed digitally (digital key).

Fig. 2. Performance of spatially incoherent diffractive networks on arbitrary complex-valued linear transformations. (a) The all-optical linear transformation error as a function of the number of diffractive features (N). The red dot represents the design corresponding to the results shown in (b)–(d). (b) The phase profiles of the K=4 diffractive layers of the optimized model (N=2×2Ni,rNo,r). (c) Evaluation of the resulting all-optical intensity transformation, i.e., the spatially varying PSFs. (d) The complex linear transformation evaluation. For εr and ε, |·|2 represents an element-wise operation.

Fig. 3. Image encryption with the letters “U” and “C” encoded into amplitude and phase, respectively, of the complex-valued image. (a) The input, target, output, and the approximatn error, both in complex and real nonnegative (intensity) domains. The original information is represented by o, while i is obtained by digital encrypting o following Fig. 1(d). (b) The input, output (resulting from optical encryption), and digitally decrypted output and the error between the input and the decrypted output. The result of digital decryption matches the input information. The second row shows the corresponding input, target, and output intensities and the approximation error. |·|2 represents an element-wise operation.