  The coherence length of the thermal electromagnetic field near a planar
surface has a minimum value related to the nonlocal dielectric response of the
material. We perform two model calculations of the electric energy density and
the field's degree of spatial coherence. Above a polar crystal, the lattice
constant gives the minimum coherence length. It also gives the upper limit to
the near field energy density, cutting off its $1/z^3$ divergence. Near an
electron plasma described by the semiclassical Lindhard dielectric function,
the corresponding length scale is fixed by plasma screening to the Thomas-Fermi
length. The electron mean free path, however, sets a larger scale where
significant deviations from the local description are visible.
