Holographic x-ray image reconstruction through the application of differential and integral operators.

We introduce a noniterative image-reconstruction technique for coherent diffractive imaging. Through the application of differential and integral operators, an extended reference can be used to recover the complex-valued transmissivity of an object, in closed form, from a measurement of its far-field (Fraunhofer) diffraction intensity. We demonstrate the feasibility of this approach, using a reference of a pair of crossed wires and slits, through numerical simulations and a soft x-ray coherent diffractive imaging experiment.