  The spatial distributions of anti-bonding $\pi^\ast$ and $\sigma^\ast$ states
in epitaxial graphene multilayers are mapped using electron energy-loss
spectroscopy in a scanning transmission electron microscope. Inelastic
channeling simulations validate the interpretation of the spatially-resolved
signals in terms of electronic orbitals, and demonstrate the crucial effect of
the material thickness on the experimental capability to resolve the
distribution of unoccupied states. This work illustrates the current potential
of core-level electron energy-loss spectroscopy towards the direct
visualization of electronic orbitals in a wide range of materials, of huge
interest to better understand chemical bonding among many other properties at
interfaces and defects in solids.
