  The Talbot effect, in which a wave imprinted with transverse periodicity
reconstructs itself at regular intervals, is a diffraction phenomenon that
occurs in many physical systems. Here we present the first observation of the
Talbot effect for electron de Broglie waves behind a nanofabricated
transmission grating. This was thought to be difficult because of Coulomb
interactions between electrons and nanostructure gratings, yet we were able to
map out the entire near-field interference pattern, the "Talbot carpet", behind
a grating. We did this using a Talbot interferometer, in which Talbot
interference fringes from one grating are moire'-filtered by a 2nd grating.
This arrangement has served for optical, X-ray, and atom interferometry, but
never before for electrons. Talbot interferometers are particularly sensitive
to distortions of the incident wavefronts, and to illustrate this we used our
Talbot interferometer to measure the wavefront curvature of a weakly focused
electron beam. Here we report how this wavefront curvature demagnified the
Talbot revivals, and we discuss applications for electron Talbot
interferometers.
