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Far-field analysis of small objects is severely constrained by the diffraction limit. Existing tools achieving sub-diffraction resolution often utilize point-by-point image reconstruction via scanning or labelling. Here, we present a new technique capable of fast and accurate characterization of two-dimensional structures with at least wavelength/25 theoretical resolution, based on a single far-field intensity measurement. Experimentally, we realized this technique resolving the smallest-available to us 180-nm-scale features with 845-nm laser light, reaching a resolution of wavelength/5. A comprehensive analysis of machine learning algorithms was performed to gain insight into the learning process and to understand the flow of subwavelength information through the system. Image parameterization, suitable for diffractive configurations and highly tolerant to random noise was developed. The proposed technique can be applied to new optical characterization tools with high spatial resolution, fast data acquisition and artificial intelligence, such as high-speed nanoscale metrology and quality control, and can be further developed to high-resolution spectroscopy 

Abstract Structured waves are ubiquitous for all areas of wave physics, both classical and quantum, where the wavefields are inhomogeneous and cannot be approximated by a single plane wave. Even the interference of two plane waves, or of a single inhomogeneous (evanescent) wave, provides a number of nontrivial phenomena and additional functionalities as compared to a single plane wave. Complex wavefields with inhomogeneities in the amplitude, phase, and polarization, including topological structures and singularities, underpin modern nanooptics and photonics, yet they are equally important, e.g., for quantum matter waves, acoustics, water waves, etc. Structured waves are crucial in optical and electron microscopy, wave propagation and scattering, imaging, communications, quantum optics, topological and non-Hermitian wave systems, quantum condensed-matter systems, optomechanics, plasmonics and metamaterials, optical and acoustic manipulation, and so forth. This Roadmap is written collectively by prominent researchers and aims to survey the role of structured waves in various areas of wave physics. Providing background, current research, and anticipating future developments, it will be of interest to a wide cross-disciplinary audience.