X-ray phase-contrast imaging is a promising approach for improving soft-tissue contrast and lowering radiation dose in biomedical applications. While current tabletop imaging systems adapt to common x-ray tubes and large-area detectors by employing absorptive elements such as absorption gratings or monolithic crystals to filter the beam, we developed nanometric phase gratings which enable tabletop x-ray far-field interferometry with only phase-shifting elements, leading to a substantial enhancement in the performance of phase contrast imaging. In a general sense the method transfers the demands on the spatial coherence of the x-ray source and the detector resolution to the feature size of x-ray phase masks. We demonstrate its capabilities in hard x-ray imaging experiments at a fraction of clinical dose levels and present comparisons with the existing Talbot-Lau interferometer and with conventional digital radiography.