Pushing the resolution limit of coherent diffractive imaging.

Coherent diffractive imaging (CDI), with its lensless geometry and theoretically perfect transfer function, is considered as one of the most promising paradigms to achieve the Abbe resolution limit. However, recent advances on pushing the resolution limit in high-numerical-aperture (NA) CDIs has thus far been challenging. Here, we report a nearly 0.9NA CDI with an optimized imaging factor (k = 0.501), pushing the Abbe resolution diffraction limit for the first time in ultra-high-NA scenarios. Leveraging this the ultra-high NA and the Abbe-limit k-factor, we demonstrate a record-high imaging resolution of 0.57 λ for CDIs. Our approach builds upon a novel computational framework termed 'rigorous Fraunhofer diffraction' that eliminates the Ewald sphere effect in CDIs, particularly for high NAs. Our framework transforms the general challenge of high-NA, resolution-limited CDIs from relying on approximate and complicated geometric corrections to a solvable problem through rigorous model-based computation.