Phase contrast (PC) imaging is one of the most exciting emerging x-ray imaging techniques, with the potential of removing some of the main limitations of conventional radiology. After extensive experimentation carried out particularly at synchrotron radiation (SR) facilities, the scientific community agrees that it is now time to translate these ideas towards the first clinical implementations. In this framework, a complete model, based on Fresnel/Kirchoff diffraction integrals, was devised. This model accounts for source dimensions, beam spectrum and divergence and detector point spread function (PSF), and can thus be applied to any x-ray imaging system. In particular, by accepting in input the above parameters along with the ones describing the sample, the model can be used to optimize the geometry of the set-up, i.e. to assess the source-to-sample and sample-to-detector distances which maximize feature detection. The model was evaluated by acquiring a range of images of different samples with a laboratory source, and a good agreement was found between simulated and experimental data in all cases. In order to maximize the generality of the results, all acquisitions were carried out using a polychromatic source and an energy-resolving detector; in this way, a range of monochromatic images could be obtained as well as polychromatic images, which can be created by integrating different parts of the acquired spectra. One of the most notable results obtained is that in many practical cases polychromatic PC imaging can provide the same image quality as its monochromatic counterpart. This is an important step in the wider application of PC using conventional sources.