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The rapid development of new sources of coherent X-rays, such as third-generation synchrotrons, high-harmonic-generation lasers and X-ray free-electron lasers, has led to the emergence of the new field of X-ray coherent science. The extension of coherent methods to the X-ray regime makes possible methods such as coherent diffraction, X-ray photon-correlation spectroscopy, speckle interferometry and ultrafast probing at atomic resolution and femtosecond timescales. Despite rapid improvements in the resolution that conventional X-ray optics can achieve, new methods for manipulating X-rays are required to push this to the atomic scale. Here we demonstrate a coherent imaging technique that enables us to image the complex field at the focus of an X-ray zone plate without the need for conventional X-ray lenses. There are no fundamental limits on the resolution of this lensless imaging technique other than the …