Advances in the development of free-electron lasers offer the realistic prospect of high-resolution imaging to study the nanoworld on the time-scale of atomic motions. We identify X-ray Fourier Transform holography, (FTH) as a promising but, so far,
inefficient scheme to do this. We show that a uniformly redundant array (URA) placed next to the sample, multiplies the efficiency of X-ray FTH by more than one thousand (approaching that of a perfect lens) and provides holographic images with both amplitude- and phase-contrast information. The experiments reported here demonstrate this concept by imaging a nano-fabricated object at a synchrotron source, and a bacterial cell at a soft X-ray free-electron-laser, where illumination by a single 15 fs pulse was successfully used in producing the holographic image. We expect with upcoming hard X-ray lasers to achieve considerably higher spatial resolution and to obtain ultrafast movies of excited states of matter.
