Described here is a method for performing phase contrast imaging using an array of independently controllable x-ray sources. The array of x-ray sources can be controlled to produce a distinct spatial pattern of x-ray radiation and thus can be used to encode phase contrast signals without the need for a coded aperture. The lack of coded aperture increases the flexibility of the imaging method. For instance, because a fixed, coded aperture is not required, the angular resolution of the imaging technique can be increased as compared to coded-aperture imaging. Moreover, the lack of a radioopaque coded aperture increases the photon flux that reaches the subject, thereby increasing the attainable signal-to-noise ratio.