Robustness criterion for diffractive deep neural networks using normalized cutoff frequency

Robustness of diffractive deep neural networks (D²NNs) as a key performance for the deployment in real-world remains insufficiently elucidated. We propose a criterion to evaluate the robustness of D²NN using the normalized cutoff frequency (NCF), and reveal that the robustness is determined by the spatial frequency propagation characteristics of the light field. We demonstrate that despite differences in D²NN architectures, the same robustness of D²NNs is attributed to equal NCF values in classification and regression tasks. This principle is physically interpretable and widely applicable to linear and nonlinear D²NNs. The relationship between the robustness of D²NN and the spatial frequency bandwidth of the optical field is discovered, enabling efficient and accurate prediction of the robustness of large-scale D²NN models.