Retrieving positions of closely packed sub-wavelength nanoparticles from their diffraction patterns

Distinguishing two objects or point sources located closer than the Rayleigh distance is impossible in conventional microscopy. Understandably, the task becomes increasingly harder with a growing number of particles placed in close proximity. It has been recently demonstrated that subwavelength nanoparticles in closely packed clusters can be counted by AI-enabled analysis of the diffraction patterns of coherent light scattered by the cluster. Here we show that deep learning analysis can determine the actual position of the nanoparticle in the cluster of subwavelength particles from a sing-shot diffraction pattern even if they are separated by distances below the Rayleigh resolution limit of a conventional microscope.