We have observed a strong (2%) angular modulation of the total backscattered conversion electron yield, measured as a function of the incidence angle of the 14.4 keV $\gamma$ rays from a ${}^{57}\mathrm{Co}$ Mössbauer source irradiating thin epitaxial ${}^{57}\mathrm{Fe}$ film grown on MgO(001). The measured 2D pattern is the first hologram of the local surrounding of the absorbing nuclei obtained due to nuclear resonant scattering of $\gamma$ rays. The real space holographic reconstruction shows distinct features corresponding to the nearest neighbor sites in the bcc $\alpha$-Fe structure.

X-ray fluorescence holography (XFH) is an atomic structure determination technique that combines the capabilities of X-ray diffraction and X-ray fluorescence spectroscopy. It provides a unique means of gaining fully three-dimensional information about the local atomic structure and lattice site positions of selected elements inside compound samples. In this work, we discuss experimental and theoretical aspects that are essential for the efficient recording and analysis of X-ray fluorescence holograms and review the most recent advances in XFH. We describe experiments performed with brilliant synchrotron radiation as well as with tabletop setups that employ conventional X-ray tubes.

Secondary extinction effects in x-ray holography with internal atomic reference are examined in the frame of multiple-scattering power transfer equations for a mosaic crystal. The calculations are compared with experimental holograms of an imperfect ${\mathrm{Cu}}_3\mathrm{Au}$ single crystal measured using x-ray fluorescence and total electron yields. It is shown that extinction effects in imperfect crystals can influence reconstructed real-space images in x-ray atom-resolving holography.

A new technique for high fidelity three-dimensional imaging of atomic structure with $\gamma$-ray holography is demonstrated. A complex hologram was constructed from holograms recorded for different values of the nuclear scattering amplitude on both sides of the ${}^{57}\mathrm{Fe}$ Mössbauer resonance. The holographic reconstruction was applied to this complex hologram resulting in a twin-image-free image of the bcc Fe local structure. The proposed procedure allows the removal of the twin images for all real space, making $\gamma$-ray holography an unambiguous tool for atomic and magnetic structure imaging.

Point projection is a mature geometry of x-ray imaging that is implemented in scientific and industrial applications. Objects to be imaged are placed near a microscopic x-ray source, and the magnification is accomplished by x-ray propagation towards a distant detector. The source size is a trade-off between the signal level and the spatial resolution. In this work, we demonstrate multipoint-projection x-ray imaging realized with an x-ray tube and compound structured microcapillary optics that generates nearly one thousand submicrometer secondary x-ray sources. The generated microbeams are multiplexed at the object. Demultiplexing of the transmitted beams, magnification, and phase contrast are achieved by the free-space propagation. A massive improvement in the signal-to-noise ratio, relative to a single secondary source, was achieved without a loss in spatial resolution. Hence, x-ray projections of highly absorbing samples at submicrometer spatial resolution could be recorded with only a few photons per detector pixel. For weakly absorbing samples, the multipoint-projection method enabled us to record, in a parallel way, replicated in-line x-ray holograms with incoherent radiation from an x-ray tube. Our method may enrich the panel of x-ray nanoscale imaging techniques and may be adopted for on-chip x-ray photonic devices.

Complex $\gamma$-ray holograms were recorded by tuning to the nuclear absorption lines of ${}^{57}\mathrm{Fe}$ in magnetite corresponding to different hyperfine fields. The numerical reconstruction of the holograms to real space provided three-dimensional images of local iron arrangements in octahedral and tetrahedral sublattices of magnetite. This direct site-selective imaging of atomic structure was performed using a tabletop experimental setup.