At a corrugated metal or semiconductor surface, incident waves are split into beams reflected by the surface and exponentially damped waves penetrating the vacuum region. A probing tip approaching this surface from the vacuum side collects these damped waves, resulting in a tunneling current flow between the surface and the tip. By relying on arguments like those used to derive resolution criteria for optical instruments, a similar formula can be found for free-electron-like metals. For a surface with a weak sinusoidal corrugation with amplitude hs 2, the amplitude Δd 2 of the observed corrugation of the equicurrent surface decreases as Δ d hs= exp[-π2( φ2m h2)- 1 2 (d+rt a2], where φ=U-EF is the averaged lo (work function), U the potential, EF the Fermi energy, a the corrugation period, d the distance between the surface and tip. and rt the tip radius. The validity of this formula is confirmed by numerical computations of tunneling through a corrugated barrier. © 1984.