Hard X-ray dark-field imaging with incoherent sample illumination

We report on a non-interferometric technique enabling dark-field imaging by using incoherent illumination and two achromatic optical elements. The simultaneous retrieval of absorption and differential phase images in the hard X-ray regime is also provided. We show that three projection images are sufficient to separate three signals: absorption, differential phase, and scattering. The method is highly efficient, also in terms of the dose delivered to the sample, flexible, robust against environmental vibrations, and scalable. It can be easily implemented in laboratories and translated into commercial systems, lending itself to a wide range of applications.