1. An X-ray imaging apparatus for imaging a subject comprising: a diffraction grating that forms an interference intensity distribution by diffracting an X-ray from an X-ray source; a shielding grating that forms a Moiré by partly shielding the X-ray from the diffraction grating; a detector that detects information of an intensity distribution of the Moiré by detecting the X-ray from the shielding grating; and a calculator that obtains information of a differential phase image of the subject by performing Fourier transform on the information of the intensity distribution of the Moiré detected by the detector, wherein the subject is placed between the X-ray source and the diffraction grating, or between the diffraction grating and the shielding grating.