We demonstrate a hard-x-ray microscope that does not use a lens and is not limited to a small field of view or an object of finite size. The method does not suffer any of the physical constraints, convergence problems, or defocus ambiguities that often arise in conventional phase-retrieval diffractive imaging techniques. Calculation times are about a thousand times shorter than in current iterative algorithms. We need no a priori knowledge about the object, which can be a transmission function with both modulus and phase components. The technique has revolutionary implications for x-ray imaging of all classes of specimen.

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