A Limitation on Systems for Imaging Electrical Conductivity Distributions

The problem of reconstructing a two-dimensional distribution of electrical conductivity from impedance measurements made on the circumference of a circle enclosing the distribution is studied. It is shown to be, in general, impossible to uniquely reconstruct such conductivity distributions when employing certain recently proposed approaches based on the concept of computed tomography which is so successful when X-rays are used. The trouble is that the current stream-lines cannot usually be forced to be straight and paralel. It is indicated how ambiguities might be resolved by making moe extensive sets of measurements.