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An X-ray Talbot interferometer consisting of two capillary plates, which were used as X-ray amplitude gratings, was evaluated for X-ray phase imaging. A theoretical aspect of capillary X-ray Talbot interferometry is presented with a preliminary operation result using synchrotron radiation. A two-dimensional X-ray Talbot effect, or self-imaging effect, which was the basis of Talbot interferometry, was observed with the capillary plate, and moiré images formed by the X-ray Talbot interferometer exhibited contrasts corresponding to the differential phase shift caused by phase objects placed in front of the interferometer. Finally, the possibility of quantitative phase measurement with a fringe scanning technique is discussed.