  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.
