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Abstract
Reconstruction of a radially varying conductivity in a circular cylinder is considered by exciting the cylinder with a quasi-static current and measuring the potential distribution on the surface. A nonlinear integral equation is derived from which the conductivity distribution may be obtained from Fourier harmonics of the surface potential. A linear version is used for studies of uniqueness, resolution and accuracy. Using the orthogonality of shifted Legendre polynomials an explicit solution for the conductivity is given, avoiding numerical inversion problems. The solution is only unique if the conductivity on the axis is known. The resolution is determined by the maximum number N of Fourier harmonics, and the sensitivity of the solution increases rapidly with N. The nonlinear version, although non-unique in principle, is solved numerically by iteration with a considerable improvement of the reconstruction.