Improved contrast in X-ray images can be obtained through phase contrast and dark-field imaging. Of the different methods for phase contrast imaging, the recently developed grating based interferometer is well suited for use at different X-ray sources, including a standard X-ray tube. This thesis explains the principles of a grating based interferometer, and the algorithms for tomographic reconstruction of differential phase contrast and dark-field images are derived. Experimental data recorded at three different X-ray sources are presented, and the data quality depending on source properties are discussed.