  The X-ray free electron lasers (XFEL) can enable diffractive structural
determination of protein crystals or single molecules that are too
radiation-sensitive for conventional X-ray analysis. However the electronic
form factor could have been modified during the ultrashort X-ray pulse due to
photoionization and electron cascade caused by the intense X-ray pulse. For
general X-ray imaging techniques, to minimize radiation damage effect is of
major concern to ensure faithful reconstruction of the structure. Here we show
that a radiation-damage-free diffraction can be achieved with an atomic spatial
resolution, by using X-ray parametric down-conversion (XPDC), and two-color
two-photon ghost diffraction. We illustrate that the formation of the
diffraction patterns satisfies a condition analogous to the Bragg equation,
with a resolution that could be as fine as the lattice length scale of several
Angstrom. Because the samples are illuminated by the optical photons of low
energy, they can be free of radiation damage.
