Retrieving positions of closely packed subwavelength nanoparticles from their diffraction patterns

Abstract

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 return the actual positions of nanoparticles in the cluster. The Pearson correlation coefficient between the ground truth and reconstructed positions of nanoparticles exceeds 0.7 for clusters of ten nanoparticles and 0.8 for clusters of two nanoparticles of 0.16λ in diameter, even if they are separated by distances below the Rayleigh resolution limit of 0.68λ, corresponding to a lens with numerical aperture NA = 0.9.