Electrical capacitance tomography for sensors of square cross sections using Calderon's method

Calderon's method was generalized to electrical capacitance tomography (ECT) for sensors of square cross sections in this paper. It is a direct algorithm of image reconstruction, as neither matrix inversion nor an iterative process is required for image reconstruction. Since the major calculations are implemented in terms of a circular region, complicated calculations required by Calderon's method for a noncircular cross section are avoided. A unique conformal transformation was used to establish a map from a circular region to a square. Results were obtained for a sensor of square cross section by using the conformal transformation. Two approximations of the scattering transform used in Calderon's method were compared with simulated data. The Gauss-Legendre quadrature was applied to provide a fast-speed and high-quality image reconstruction. The reconstructed results validated the feasibility and effectiveness of the proposed treatment of Calderon's method in ECT with a sensor of noncircular cross section.