Super-resolution imaging using super-oscillatory diffractive neural networks

The Abbe-Rayleigh diffraction limit of traditional optical equipment has always been an obstacle to the study of micro-/nano-scale objects [1, 2]. Near-field microscopic imaging techniques, such as contact photography [3] and scanning near-field imaging (SNOM) [4, 5], capture evanescent fields by placing a probe or light-sensitive material extremely close to the object to achieve nanoscale resolution, which is not possible for imaging inside biological samples or encapsulated micro-/nano-structures. Far-field microscopic imaging technology is not restricted by the above bottlenecks. Some typical far-field microscopic imaging techniques, such as single-molecule localization (SML) microscopy [6, 7] or stimulated emission depletion (STED) [8, 9], have demonstrated the possibility of nanoscale imaging without capturing evanescent fields. However, SML microscopy and STED typically require intense beams to excite, deplete, or bleach fluorophores in a sample that produces photobleaching and phototoxicity in living samples. Optical super-oscillations are rapid sub-wavelength spatial variations of light intensity and phase that occur in complex electromagnetic fields formed by the precise interference of coherent waves, which provide an advanced method for far-field super-resolution imaging beyond the diffraction limit [10, 11]. To generate optical super-oscillation, the complicated lens design methods [12-14] or Fresnel zone plate (FZP) optimization design methods, including optimizing algorithms [15-18] or optimization-free algorithms [19, 20], have been proposed.