  We briefly review the diffraction of quasicrystals and then give an
elementary alternative proof of the diffraction formula for regular
cut-and-project sets, which is based on Bochner's theorem from Fourier
analysis. This clarifies a common view that the diffraction of a quasicrystal
is determined by the diffraction of its underlying lattice. To illustrate our
approach, we will also treat a number of well-known explicitly solvable
examples.
