  Projected momentum distributions of electrons, i.e. Compton profiles above
the topmost atomic layer have recently become experimentally accessible by
kinetic electron emission in grazing-incidence scattering of atoms at
atomically flat single crystal metal surfaces. Sub-threshold emission by slow
projectiles was shown to be sensitive to high-momentum components of the local
Compton profile near the surface. We present a method to extract momentum
distribution, Compton profiles, and Wigner and Husimi phase space distributions
from ab-initio density-functional calculations of electronic structure. An
application for such distributions to scattering experiments is discussed.
