  Knowledge gained through X-ray crystallography fostered structural
determination of materials and greatly facilitated the development of modern
science and technology in the past century. Atomic details of sample structures
is achievable by X-ray crystallography, however, it is only applied to
crystalline structures. Imaging techniques based on X-ray coherent diffraction
or zone plates are capable of resolving the internal structure of
non-crystalline materials at nanoscales, but it is still a challenge to achieve
atomic resolution. Here we demonstrate a novel lensless Fourier-transform ghost
imaging method with pseudo-thermal hard X-rays by measuring the second-order
intensity correlation function of the light. We show that high resolution
Fourier-transform diffraction pattern of a complex amplitude sample can be
achieved at Fresnel region and the amplitude and phase distributions of a
sample in spatial domain can be retrieved successfully. The method of lensless
X-ray Fourier-transform ghost imaging extends X-ray crystallography to
non-crystalline samples, and its spatial resolution is limited only by the
wavelength of the X-ray, thus atomic resolution should be routinely obtainable.
Since highly coherent X-ray source is not required, comparing to conventional
X-ray coherent diffraction imaging, the method can be implemented with
laboratory X-ray sources, and it also provides a potential solution for
lensless diffraction imaging with fermions, such as neutron and electron where
the intensive coherent source usually is not available.
