  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 ${\lambda}/200$.
