* These three authors contributed equally to this work Coherent Diffractive Imaging (CDI) is an algorithmic imaging technique where intricate features are reconstructed from measurements of the freely-diffracting intensity pattern [1-7]. An important goal of such lensless-imaging methods is to study the structure of molecules (including many proteins) that cannot be crystallized . Clearly, high spatial resolution and very fast measurement are key features for many applications of CDI. Ideally, one would want to perform CDI at the highest possible spatial resolution and in a single-shot measurement-such that the techniques could be applied to imaging at ultrafast rates. Undoubtedly, such capabilities would give rise to unprecedented possibilities. For example, observing molecules while they dissociate or undergo chemical reactions will considerably expand the knowledge in physics, chemistry and biology. However, the resolution of all current CDI techniques is limited by the diffraction limit, and therefore cannot resolve features smaller than one half the wavelength of the illuminating light , which is considered a fundamental limit in diffractive imaging . Moreover, combining CDI with current sub-wavelength imaging techniques would not allow for rapid single-shot measurements that are able to follow ultrafast dynamics, because such techniques rely on multiple exposures, either through mechanical scanning (e.g., Scanning Near-Field Microscope [11, 12], scanning a sub-wavelength "hot spot" [13-15]), or by using ensemble-averaging over multiple experiments with fluorescent particles [16, 17]. Here, we present sparsity-based single-shot sub-wavelength resolution in coherent diffraction microscopy: algorithmic reconstruction of sub-wavelength features from far-field intensity patterns of sparse optical objects. We experimentally demonstrate imaging of irregular and ordered arrangements of 100nm features with illumination wavelength of 532nm (green light), thereby obtaining resolutions several times better than the diffraction limit. The sparsity-based sub-wavelength imaging concept relies on minimization of the number of degrees of freedom, and operates on a single-shot basis [18-20]. Hence, it is suitable for capturing a series of ultrafast single-exposure images, and subsequently improving their resolution considerably beyond the diffraction limit. This work paves the way for ultrafast sub-wavelength CDI, via phase retrieval at the sub-wavelength scale. For example, sparsity-based methods could considerably improve the CDI resolution with x-ray free electron laser , without hardware modification. Conceptually, sparsity-based methods can enhance the resolution in all imaging systems, optical and non-optical.
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