| In electrical impedance tomography (EIT), the goal is to reconstruct an approximation to the spatially varying conductivity of the interior of an object by applying patterns of current and measuring the resulting voltages on its surface. We study the problem for an annulus, with electrodes placed on both the outer and inner boundaries. A reconstruction algorithm is proposed, which utilizes least squares and Newton's method to yield an approximate solution to a linearized version of the inverse conductivity problem for this geometry.; The boundary map which takes currents to voltages is analyzed for a homogeneous conductivity distribution using the Continuum and Gap models, and for a two-layer conductivity distribution using the Continuum model. For each of these cases, we show that eigenfunctions have a trigonometric form, with the restriction for the Gap model that an equal number of electrodes be placed on each of the two boundaries. For each eigenfunction, the ratio of current magnitude on the inner boundary to that on the outer boundary is a specific constant, which depends on the spatial frequency of the trigonometric function. The convergence of certain Gap model current patterns to Continuum model eigenfunctions is discussed.; The concept of distinguishability is used to show that the most effective current densities for detecting a difference between a homogeneous and a two-layer conductivity distribution in the Continuum model are the trigonometric current densities with low spatial frequency. The reconstruction algorithm is summarized, and reconstructions from both synthetic and experimental data are presented. |
