Diffraction patterns produced by grazing scattering of fast atoms from insulator surfaces are used to examine the atom-surface interaction. The method is applied to He atoms colliding with a LiF(001) surface along axial crystallographic channels. The projectile-surface potential is obtained from an accurate DFT calculation, which includes polarization and surface relaxation. For the description of the collision process we employ the surface eikonal approximation, which takes into account quantum interference between different projectile paths. The dependence of projectile spectra on the parallel and perpendicular incident energies is experimentally and theoretically analyzed, determining the range of applicability of the proposed model.