Freeform diffractive deep neural networks with intrinsically smooth layers plus a curvature constraint.

Conventional diffractive deep neural networks (D2NNs) rely on discretized phase distributions, which often lead to fabrication challenges, significant speckle noise, and sensitivity to perturbations. To overcome these limitations, we propose a D2NN architecture based on smoothly freeform surfaces with C2 continuity. Specifically, we employ multi-level cubic B‑splines to represent the phase distribution of each diffractive layer, which naturally yields a smooth phase profile while preserving high design freedom. An explicit curvature constraint is further imposed to regularize the surface curvature, which facilitates fabrication by, e.g., diamond turning. Results show that, compared with a discrete-phase D2NN, our method even achieves a slightly higher accuracy of 95.97% on MNIST, while being more robust against alignment errors.