We present a computationally efficient method to incorporate
density-functional theory into the calculation of reflectivity in low-energy
electron microscopy. The reflectivity is determined by matching plane waves
representing the electron beams to the Kohn-Sham wave functions calculated for
a finite slab in a supercell. We show that the observed quantum interference
effects in the reflectivity spectra of a few layers of graphene on a substrate
can be reproduced well by the calculations using a moderate slab thickness.