We adopt fringe counting from classical moiré interferometry on moiré patterns observed in scanning tunneling microscopy of strained thin films on single crystalline substrates. We analyze inhomogeneous strain distribution in islands of CeO2(111) on Cu(111) and identify a generic source of strain in heteroepitaxy--a thickness-dependent lattice constant of the growing film. This observation is mediated by the ability of ceria to glide on the Cu substrate. The moiré technique we are describing has a potential of nanometer-scale resolution of inhomogeneous two dimensional strain in incommensurate layered systems, notably in supported graphene.