An algorithm is developed for electrical impedance tomography (EIT) of finite cylinders with general cross-sectional boundaries and translationally uniform conductivity distributions. The electrodes for data collection are assumed to be placed around a cross-sectional plane; therefore, the axial variation of the boundary conditions and the potential field are expanded in Fourier series. For each Fourier component a two-dimensional (2-D) partial differential equation is derived. Thus the 3-D forward problem is solved as a succession of 2-D problems, and it is shown that the Fourier series can be truncated to provide substantial savings in computation time. The finite element method is adopted and the accuracy of the boundary potential differences (gradients) thus calculated is assessed by comparison to results obtained using cylindrical harmonic expansions for circular cylinders. A 1016-element and 541-node mesh is found to be optimal. The algorithm is applied to data collected from phantoms, and the errors incurred from the several assumptions of the method are investigated.

A new differential formulation of scattering from dielectric bodies is described. The problem is reduced to the solution of spatially varying state–space equations for the multipole coefficients of the scattered field. The equations are confined into the body, and the solution yields directly the scattering coefficient outside the body. The method is applied to spherically symmetrical objects. Numerical results are presented for plane wave scattering from Luneberg and Eaton lenses and a plasma-coated conducting sphere. The radiation properties of an electric and magnetic dipole antenna, respectively covered by a plasma and a dielectric layer, are studied. The numerical results show that the radiation of these antennas can be enhanced over the free-space radiation by adjusting the thickness and the density of the layer.

A novel differential formulation of electromagnetic scattering by rotationally symmetric penetrable bodies is presented. The formulation is essentially based on the representation of vector fields in terms of spherical vector wave functions. In regions where we have physical inhomogenity the representation is in terms of position‐dependent expansion coefficients. The differential equation system for these variable coefficients is deduced from the relevant wave equation. This system is numerically solved as an initial value problem, and the unknown constant expansion coefficients are found with a matrix inversion. The method was tested and validated on a number of problems, whose exact solutions are available, and the results obtained for scatterers for which no exact solutions are present were succesfully compared with the ones obtained by other methods.

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