Recently it was reported that deeply subwavelength features of free space superoscillatory electromagnetic fields can be observed experimentally and used in optical metrology with nanoscale resolution [Science 364, 771 (2019)]. Here we introduce a new type of imaging, termed Deeply Subwavelength Superoscillatory Imaging (DSSI), that reveals the fine structure of a physical object through its far-field scattering pattern under superoscillatory illumination. The object is reconstructed from intensity profiles of scattered light recorded for different positions of the object in the superoscillatory field. The reconstruction is performed with a convolutional neural network trained on a large number of scattering events. We show that DSSI offers resolution far beyond the conventional diffraction limit. In modelling experiments, a dimer comprising two subwavelength opaque particles is imaged with a resolution exceeding ${lambda}/200$.
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