Fig. 1. (a) Schematic diagram of DPENet. The DPENet consists of two parts: spatial differentiator and all-optical processor. POL, polarizer; DWPs, dual Wollaston prisms; QWP, quarter-wave plate. (b) Edge detection system based on a DIC microscope. (c) Ray-tracing diagram of DWPs. α, structural angle of prisms; γ, refraction angle. (d) Schematic diagram of forward- and backpropagation of a three-layer D²NN.

Fig. 2. (a) Convergence plots of DPENet and ANN; (b) intensity of each layer of D²NN processor. The complex light field is directly phase-only modulated by D²NN, but only the intensity distribution of each layer is shown. (c) Phase parameters of each layer of D²NN obtained by training.

Fig. 3. (a) Perpendicular directions of edges of the MNIST; (b) and (c) are the partial results of capital letters; (d) and (e) are the partial results of lowercase letters; (f) PR curves of MNIST and NIST; the table shows the F-scores for the different testing data sets.

Fig. 4. (a) Results of edge detection for resolution test charts. Scale bars, 5 µm. (b)–(e) Edges under the splitting beams at a distance of 1, 2, 4, and 6 pixels, respectively; (f) resolution of edge imaging with different scales.

Fig. 5. Results of edge extraction of pathological sections. (a) Environmental noise in the acquisition conditions; (b) the cell nucleus damage leads to detection confusion.