Fig. 2

Training results and experimental data collection. a The loss curves of training set and validation set versus updating epochs. The learning rate is tuned dynamically every 15 epochs. The POAM converges after dozens of epochs and the inset indicates that the neural network is not overfitting. The loss value is the sum of 300 (one batch) samples. b Final designs of the optical diffractive network. (b1 - b5) Five cascaded diffractive layers with a fixed distance of \(40{\uplambda }\) between two successive layers. (b6) The gradient distributions of the 5th layer. PS: Color-encoded gradient map. (b7) Phase value distributions of 5 diffractive layers. c The optical setup for generating experimental structured light. CW laser, continuous-wave laser; BE, beam expander; HWP, half-wave plate; BS, beam splitter; SLM, spatial light modulator; P, polarizer; L1, L2, lens. For each data sample, we reconstruct the complex optical fields using 4-step phase shift method as depicted in the inset (I₁, I₂, I₃, I₄). See details in Supplementary Note 1. d Four selective reconstruction results based on c, which are single mode (TC = 5), multiplexed (mul.) mode (TC =\(-\)4, \(-\)1, equal weights), mul. mode (TC =\(-\)4, \(-\)3, 2, 5, equal weights), mul. mode (TC = \(-\)10 ~ 10, random weights), from left to right