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The first successful operation of an X-ray interferometer under conditions of non-planar three-beam diffraction for phase-contrast X-ray microtomography is reported. Intrinsic phase differences of the reflections used cancel from the three-dimensional phase image of the specimen. With simultaneous hkl and hk\bar{l} reflections of a synchrotron radiation beam in a side-by-side geometry, the size of the usable field of view is doubled and the investigated specimen volume is increased by a factor of four. As an example, the reconstructed slice of a mouse kidney is shown in phase contrast at 71 keV. Optimized choices of three-beam reflections and matching interferometer geometries useful for applications are presented.

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