Prompted by recent experimental developments, a theory of surface scattering of fast atoms at grazing incidence is developed. The theory gives rise to a quantum-mechanical limit for ordered surfaces that describes coherent diffraction peaks whose thermal attenuation is governed by a Debye-Waller factor, however, this Debye-Waller factor has values much larger than would be calculated using simple models. A classical limit for incoherent scattering is obtained for high energies and temperatures. Between these limiting classical and quantum cases is another regime in which diffraction features appear that are broadened by the motion in the fast direction of the scattered beam but whose intensity is not governed by a Debye-Waller factor. All of these limits appear to be accessible within the range of currently available experimental conditions.

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The relative diffraction peak intensities of He atoms with an incident beam energy of 65 meV diffracted from a microfabricated 100 nm-period transmission grating are analyzed using both Fresnel and Fraunhofer diffraction theory. The projected slit width could be varied from 50 nm down to less than 1 nm by inclining the grating at angles up to ⌰ 0 ϭ42°with respect to the incident beam. Good agreement between calculated and measured peak intensities, up to the sixth order, is obtained by accounting for random deviations in the slit positions, and averaging over the velocity spread of the incident beam as well as the spatial extent of the nozzle beam source. It is demonstrated that He atom beam diffraction together with simple transmission measurements is an excellent means of characterizing such gratings including a detailed determination of the slit width, the bar shape, and random as well as periodic disorder.