IN conventional radiography, X-rays which pass through an object along different paths are differentially absorbed, and the intensity pattern of the emerging beam records the distribution of absorbing materials within the sample. An alternative approach is phase-contrast radiography, which instead records variations of the phase of the emerging radiation. Such an approach offers improved contrast sensitivity, especially when imaging weakly absorbing samples. Unfortunately, current phase-contrast imaging techniques1-11 generally require highly monochromatic plane-wave radiation and sophisticated X-ray optics, so their use is greatly restricted. Here we describe and demonstrate a simplified scheme for phase-contrast imaging based on an X-ray source having high spatial (but essentially no chromatic) coherence. The method is compatible with conventional polychromatic micro-focus X-ray tube sources, is well suited to large areas of irradiation, can operate with a lower absorbed dose than traditional X-ray imaging techniques, and should find broad application in clinical, biological and industrial settings.