X-ray Fourier ptychography.

To a large extent, the performance of imaging systems is determined by their objectives, which affect properties as varied as collection efficiency, resolving power, and image distortions. Such limitations can be addressed by so-called aperture synthesis, a technique used, for instance, in radar, astronomy, and, increasingly, microscopy. Here, we apply such techniques to x-ray imaging and demonstrate how Fourier ptychography can be used at transmission x-ray microscopes to increase resolution, provide quantitative absorption and phase contrast, and allow for corrections of lens aberrations. We anticipate that such methods will find common and frequent applications, alleviating a number of limitations imposed by x-ray optical elements, offering an alternative approach to phase contrast imaging, and providing novel opportunities to mitigate radiation damage.