Bragg X-ray Fourier transform holography

Lens-less microscopy is now widely acknowledged to be an elegant solution to the so-called phase problem in X-ray crystallography. The method is based on the digital retrieval of the phase from the object's coherently diffracted intensity patterns, with the inversion being achieved through the use of time-consuming iterative algorithms. Fourier transform holography is a similar technique, but is essentially very quick and straightforward. Dr. V. Chamard (IM2NP, CNRS, Aix-Marseille Universite, France) and her colleagues recently demonstrated 3D imaging of a SiGe nanocrystal with Fourier transform holography. One unique point of the research is that they employed Bragg geometry, rather than forward scattering geometry, to obtain full 3D information. The technique requires that a reference crystal is placed near the object crystal to be imaged, and that the two crystals need to have comparable lattice parameters. They were successful in determining the electron density and the displacement field in 3D without suffering convergence problems, which are often the case with lens-less imaging iterative algorithms. For more information, see the paper, "Three-Dimensional X-Ray Fourier Transform Holography: The Bragg Case", V. Chamard et al., Phys. Rev. Lett. 104, 165501 (2010).