Unlabeled Far-Field Deeply Subwavelength Topological Microscopy (DSTM).

A nonintrusive far-field optical microscopy resolving structures at the nanometer scale would revolutionize biomedicine and nanotechnology but is not yet available. Here, a new type of microscopy is introduced, which reveals the fine structure of an object through its far-field scattering pattern under illumination with light containing deeply subwavelength singularity features. The object is reconstructed by a neural network trained on a large number of scattering events. In numerical experiments on imaging of a dimer, resolving powers better than λ/200, i.e., two orders of magnitude beyond the conventional "diffraction limit" of λ/2, are demonstrated. It is shown that imaging is tolerant to noise and is achievable with low dynamic range light intensity detectors. Proof-of-principle experimental confirmation of DSTM is provided with a training set of small size, yet sufficient to achieve resolution five-fold better than the diffraction limit. In principle, deep learning reconstruction can be extended to objects of random shape and shall be particularly efficient in microscopy of a priori known shapes, such as those found in routine tasks of machine vision, smart manufacturing, and particle counting for life sciences applications.