  We demonstrate how a single scanning voltage probe can be used to map the
local conductivity and current density in a thin film with no a priori
knowledge of the geometry of the electrical contacts. With state-of-the-art
scanning voltage probes, under appropriate conditions such mapping should be
possible down to nanometer scales. The technique requires two non-colinear
voltage scans. When only one voltage map is available, determination of the
conductivity is not possible because the solution to the governing equation is
not unique. The only restriction on the technique is that the sheet
conductivity is a local function of position.
