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   <subfield code="a">For many years, x-ray microscopy has been attractive for materials studies with its ability to image thick samples and provide nanometer-scale resolution. However, the ability to manufacture high-resolution x-ray optics has been a hurdle to achieving the full potential of diffraction limited x-ray imaging. Recently, the advent of bright and coherent x-ray sources at synchrotrons and x-ray free electron lasers has enabled a lensless imaging technique called coherent diffractive imaging (CDI). Since it was first demonstrated in 1999, CDI has been rapidly developing into a materials imaging technique with resolutions approaching a few nanometers. This review provides an overview of the development of CDI and several applications to nanometer-scale imaging in two and three dimensions of biological and condensed mater materials. Also, we review the development of tabletop, coherent, soft x-ray sources that provide a complimentary and potentially more accessible source for nanometer-scale coherent imaging of materials.</subfield>
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