ar X iv : 1 31 1 . 43 73 v 1 [ m at h - ph ] 1 8 N ov 2 01 3 Recent progress in mathematical

Diffraction methods [13] continue to provide the main tool for the structure analysis of solids. The corresponding inverse problem of determining a structure from its diffraction is difficult and, in general, does not define a structure uniquely. Kinematic diffraction, an approximation that is reasonable for X-ray diffraction where multiple scattering effects can be neglected, is well suited for a mathematical approach via measures. Measures are generalisations of the classic concept of Lebesgue measure used in volume integration and provide a natural mathematical concept to quantify the distribution of matter in space as well as the distribution of scattering intensity. This mathematical approach to diffraction was pioneered by Hof [16] and has substantially been developed since the discovery of quasicrystals required an extension of the methods used to compute the diffraction of perfectly periodic crystals.