  We analyze electrostatic interaction between a sharp conducting tip and a
thin one-dimensional wire, e.g., a carbon nanotube, in a scanned gate
microscopy (SGM) experiment. The problem is analytically tractable if the wire
resides on a thin dielectric substrate above a metallic backgate. The
characteristic spatial scale of the electrostatic coupling to the tip is equal
to its height above the substrate. Numerical simulations indicate that imaging
of individual electrons by SGM is possible once the mean electron separation
exceeds this scale (typically, a few tens of nm). Differences between weakly
and strongly invasive SGM regimes are pointed out.
