How to Distinguish Perfect Quasi-Crystals from Twins and Other Structures Using Diffraction Experiments?

Performing diffraction experiments for various lengths of coherent scattering and using the scaling of peak intensities on a number of atoms one can experimentally distinguish quasi-crystals from the other structures (e.g. twins or random). For perfect quasi-crystals peak intensities scale as N$\text{}^{2}$, for other structures this scaling depends on concentration of atoms, behaving critical for Penrose concentration.