Reconstruction of diffraction patterns by using the Helmholz–Kirchhoff integral theorem

Abstract

A new method to obtain three-dimensional information on atomic arrangement from a monochromatic Laue pattern based on the Helmholz–Kirchhoff integral theorem is presented and experimentally proved by applying the algorithm to the thermal diffuse scattering from a single crystal. The advantage given by the possibility of collecting all the required data on a position-sensitive detector in one shot opens new perspectives for studies of fast physical or chemical processes in three dimensions. The reduced exposure time can also avoid radiation damage of organic specimens, and, in conjunction with an ultra-bright beam from the next generation of X-ray free-electron lasers, makes the method suitable for structural studies with individual atomic clusters. This approach can also be used, by observing the thermal diffuse scattering or order diffuse scattering from both non-crystalline samples and `imperfect' crystals, for the investigation of short-range ordered arrangements of atoms.