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.

We report the experimental demonstration of deeply subwavelength far-field optical microscopy of unlabelled samples. We beat the ~λ/2 diffraction limit of conventional optical microscopy several times over by recording the intensity pattern of coherent light scattered from the object into the far-field. We retrieve information about the object with a deep learning neural network trained on scattering events from a large set of known objects. The microscopy retrieves dimensions of the imaged object probabilistically. Widths of the sub-wavelength components of the dimer are measured with precision of λ/10 with probability higher that 95% and with precision of λ/20 with probability of better that 77%. The ability to image at the nanometer scale using visible light remains a long-standing fundamental challenge for optics. Despite over 400 years of developments in microscopy, subwavelength optical imaging is only possible through the use of near-field probes [1] or fluorescent labels [2,3]. Moreover, combining the latter with artificial intelligence approaches has shown to improve imaging resolution [4,5]. However, fluorescence-based and near-field methods exlude many applications. Several other techniques have been developed to break through the "diffraction limit" of conventional microscopes [6-8], which however led only to modest enhancement of resolution in far-field techniques [9,10]. The distinction between far-field and near-field imaging techniques is important. In the context of imaging, the near-field and far-field zones are regions of the electromagnetic field around an object, resulting from radiation scattering on the object. The near-field consists of non-A

Microscopes and various forms of interferometers have been used for decades in optical metrology of objects that are typically larger than the wavelength of light λ. Metrology of sub-wavelength objects, however, was deemed impossible due to the diffraction limit. We report the measurement of the physical size of sub-wavelength objects with deeply sub-wavelength accuracy by analyzing the diffraction pattern of coherent light scattered by the objects with deep learning enabled analysis. With a 633 nm laser, we show that the width of sub-wavelength slits in an opaque screen can be measured with an accuracy of ∼ λ/130 for a single-shot measurement or ∼ λ/260 (i.e., 2.4 nm) when combining measurements of diffraction patterns at different distances from the object, thus challenging the accuracy of scanning electron microscopy and ion beam lithography. In numerical experiments, we show that the technique could reach an accuracy beyond λ/1000. It is suitable for high-rate non-contact measurements of nanometric sizes of randomly positioned objects in smart manufacturing applications with integrated metrology and processing tools.

We propose two-dimensional gratings comprised of a large number of identical and similarly oriented hexagonal holes for the high order diffraction suppression. An analytical study of the diffraction property for such gratings, based on both square and triangle arrays, is described. The dependence of the high order diffraction property on the hole shape and size is investigated. Notably, theoretical calculation reveals that the 2nd, 3rd and 4th order diffractions adjacent to the 1st order diffraction can be completely suppressed, and the 5th order diffraction efficiency is as low as 0.01%, which will be submerged in the background noise for most practical applications. The 1st order diffraction intensity efficiency 6.93% can be achieved as the hexagonal holes along y-axis connect with each other. For the case of b=P_y/3, the 1st order diffraction intensity efficiency is 3.08%. The experimental results are also presented, confirming the theoretical predictions. Especially, our two-dimensional gratings have the ability to form free-standing structures which are highly desired for the x-ray region. Comparing with the grating of the square array, the grating of the triangle array is easy to be fabricated by silicon planar process due to the large spacing between any two adjacent holes. Our results should be of great interest in a wide spectrum unscrambling from the infrared to the x-ray region.

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