  In a fusion reactor internally coated with liquid metal, it will be important
to diagnose the thickness of the liquid at various locations in the vessel, as
a function of time, and possibly respond to counteract undesired bulging or
depletion. The electrical conductance between electrodes immersed in the liquid
metal can be used as a simple proxy for the local thickness. Here a matrix of
electrodes is shown to provide spatially resolved measurements of liquid metal
thickness in the absence of plasma. First a theory is developed for mxn
electrodes, and then it is experimentally demonstrated for 3x1 electrodes. The
experiments were carried out with Galinstan, but are easily extended to Lithium
or other liquid metals.
