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  1. Abstract One of the most significant developments in life sciences—the discovery of bacteria and protists—was accomplished by Antoni van Leeuwenhoek in the 17thcentury using a single ball lens microscope. It is shown that the full potential of single lens designs can be realized in a contact mode of imaging by ball lenses with a refractive index of n≈ 2, suitable for developing compact cellphone‐based microscopes. The quality of imaging is comparable to basic compound microscopes, but with a narrower field‐of‐view, and is demonstrated for various biomedical samples. The maximal magnification (M > 50) with the highest resolution (≈0.66 µm atλ= 589 nm) is achieved for imaging of nanoplasmonic structures by ball lenses made from LASFN35 glass, the index of which is tuned nearn =2 using chromatic dispersion. Due to limitations of geometrical optics, the imaging theory is developed based on an exact numerical solution of the Maxwell equations, including spherical aberration and the nearfield coupling of a point source. The modeling is performed using multiscale analysis: from the field propagation inside ball lenses with diameters 30 < D/λ < 4000 to the formation of the diffracted field at distances of ≈105λ. It is shown that such imaging enables the transition from pixel‐ to diffraction‐limited resolution in cellphone microscopy. 
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  2. Abstract Label‐free super‐resolution (LFSR) imaging relies on light‐scattering processes in nanoscale objects without a need for fluorescent (FL) staining required in super‐resolved FL microscopy. The objectives of this Roadmap are to present a comprehensive vision of the developments, the state‐of‐the‐art in this field, and to discuss the resolution boundaries and hurdles that need to be overcome to break the classical diffraction limit of the label‐free imaging. The scope of this Roadmap spans from the advanced interference detection techniques, where the diffraction‐limited lateral resolution is combined with unsurpassed axial and temporal resolution, to techniques with true lateral super‐resolution capability that are based on understanding resolution as an information science problem, on using novel structured illumination, near‐field scanning, and nonlinear optics approaches, and on designing superlenses based on nanoplasmonics, metamaterials, transformation optics, and microsphere‐assisted approaches. To this end, this Roadmap brings under the same umbrella researchers from the physics and biomedical optics communities in which such studies have often been developing separately. The ultimate intent of this paper is to create a vision for the current and future developments of LFSR imaging based on its physical mechanisms and to create a great opening for the series of articles in this field. 
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