In this talk, we will explain how diffraction patterns observed from cut and project sets (models for physical materials called quasicrystals) are determined by Diophantine approximation properties of the underlying constructions. The classical approach to calculating diffraction patterns seen from these objects assumes an infinite model, and for this reason, it is not the most practical, from an experimental point of view. Our approach (joint work with Michael Baake) quantifies precisely how much the diffraction patterns observed from finite patterns in cut and project sets deviate from the infinite models. Our methods are explicit and geared towards numerical computation, and they demonstrate the importance of Diophantine approximation to accurately determining complex phases and amplitudes of these diffraction images.