Superresolution imaging using superoscillatory diffractive neural networks

Optical superoscillation enables far-field superresolution imaging beyond diffraction limits. However, existing superoscillatory lenses for spatial superresolution imaging systems still confront critical performance limitations due to the lack of advanced design methods and limited design degree of freedom. Here, we propose an optical superoscillatory diffractive neural network (SODNN) that achieves spatial superresolution for imaging beyond the diffraction limit with superior optical performance. SODNN is constructed by utilizing diffractive layers for optical interconnections and imaging samples or biological sensors for nonlinearity. This modulates the incident optical field to create optical superoscillation effects in three-dimensional (3D) space and generate the superresolved focal spots. By optimizing diffractive layers with 3D optical field constraints under an incident wavelength size of λ, we achieved a superoscillatory optical spot and needle with a full width at half-maximum of 0.407λ at the far-field distance over 400λ without sidelobes over the field of view and with a long depth of field over 10λ. Furthermore, the SODNN implements a multiwavelength and multifocus spot array that effectively avoids chromatic aberrations, achieving comprehensive performance improvement that surpasses the trade-off among performance indicators of conventional superoscillatory lens design methods. Our research work will inspire the development of intelligent optical instruments to facilitate the applications of imaging, sensing, perception, etc.