We report on a new approach to large field-of-view laboratory-based X-ray phase-contrast imaging. The method is based upon the asymmetric mask design that enables the retrieval of the absorption, refraction and ultra-small- angle scattering properties of the sample without the need to move any component of the imaging system. The sample is scanned through the imaging system, which also removes possible aliasing problems that might arise from partial sample illumination when using the edge illumination technique. This concept can be extended to any desired number of apertures providing, at the same time, intensity projections at complementary illumination conditions. Experimental data simultaneously acquired at seven different illumination fractions are presented along with the results obtained from a numerical model that incorporates the actual detector performance. The ultimate shape of the illumination function is shown to be significantly dependent on these detector-specific characteristics. Based on this concept, a large field-of-view system was designed, which is also capable to cope with relatively high (100 kVp) X-ray energies. The imaging system obtained in this way, where the asymmetric mask design enables the data to be collected without moving any element of the instrumentation, adapts particularly well to those situations in medical, industrial and security imaging where the sample has to be scanned through the system.