Reconstruction of the three-dimensional inclusion shapes using electrical capacitance tomography

Electrical capacitance tomography (ECT) is an industrial visualization technology that non-destructively measures the permittivity distributions within a closed vessel. Due to its advantages of good portability, high speed and low cost, ECT has been successfully applied in many industrial processes. In the paper, a shape-based method is presented to reconstruct the geometric configurations of three-dimensional inclusions using ECT. In contrast to the pixel-based methods, the presented method treats the inclusions' permittivity values as known and parameterizes their surfaces using spherical harmonics. By selecting the coefficients of the spherical harmonics as unknowns, the optimal inclusion surface shape is iteratively searched using the Levenberg–Marquardt method. To improve the computational efficiency, a fast Jacobian matrix calculation method is derived based on the reciprocity theorem. To enhance the stability, a multi-stage strategy is proposed to increase the spherical harmonics degrees gradually. Both numerical and experimental tests are conducted to test the reconstruction performance and the factors influencing the reconstruction are further discussed based on the results.