Fig. 1. (a) Project objective: design a generalized training set for a neural network, which can later be used for general image reconstruction without retraining and can operate in real time. (b) Schematic of hybrid vision camera where light from an object is transmitted through a diffractive encoder (DE). Sensors capture two transmitted images that are combined as inputs to the trained neural network, which reconstruct the object from the detector-plane images. (c) This project employs two pairs of diffractive encoders: one with low SVD-entropy (lens and topological charge m=1 and 3) and the other with high SVD-entropy (uniformly distributed random pattern).

Fig. 2. Reconstructed images from (a), (b), (c) MNIST handwritten and (d), (e), (f) fashion MNIST datasets with random, Fourier, and vortex bases, respectively. The vortex basis provides edge enhancement for object detection. (g) Ground truth and (h) reconstructed images from the CIFAR-10 dataset using the vortex training bases and a vortex mask as the encoder.

Fig. 3. (a)–(c) Sample training images XR, XF, and XV or random, Fourier, and vortex training sets. (d)–(f) Corresponding training and validation curves.

Fig. 4. (a) Single “hot” pixel response of the random model and (b) single-pixel response of the vortex model, which demonstrates sharp edges and resolves high-contrast objects. (c) Comparison of reconstruction error for different levels of noise given high-entropy random UTS and random mask and lower SVD-entropy vortex UTS and vortex mask. This error corresponds to the scenario in which shot noise dominates the background noise.

Fig. 5. (a) SVD-entropy of a structured pattern composed of the phase of a vortex (modulus 0, 2π) and a Gaussian mask with radius of w2. A few-pixel pattern has almost zero entropy, and the SVD-entropy saturates for a vortex depending on the topological charge. (b) Illustration of these patterns with w2=5×10−3, 5×10−2, 5×10−1, and 5 corresponding to SVD-entropy values of 0.94, 1.8, 2.6, and 2.7. The SVD-entropy strongly relates to the length of the edge dislocations of an image. (c) Histogram of the SVD-entropy in the vortex XV, Fourier XF, and random XR generalized training sets implemented in this project.

Fig. 6. (a) Schematic of experimental reconstruction with UTS. There is no spatial filter or polarizer, images are noisy, and at this wavelength, the modulation dynamic range is only α=π. This was done intentionally to simulate poor experimental conditions with background light. (b) Sample of random UTS images and (c) sample of reconstructed images produced by random patterns, which are not learned by the simple neural network model experimentally. On the other hand, (d) simpler images with fewer edges are (e) reconstructed by the neural network. (f) Sample of ground truth images and (g) discernable reconstructed patterns when the neural network is trained by the vortex dataset.