Reconstructing the geometric configuration of three dimensional interface using electrical capacitance tomography

SUMMARY Electrical capacitance tomography is a promising visualization technique to image the internal permittivity distribution using boundary capacitance measurements. Because of its advantages of noninvasive, noninstructive, no radiation, and low cost, it has been successfully applied in many industrial processes. Currently, the commonly used algorithms in electrical capacitance tomography are based on the pixel/volume-wise parameterization of the permittivity. When the permittivity is piecewise constant, it is difficult to enhance the spatial resolution. In the paper, a shape-based algorithm is presented to directly reconstruct the geometric configuration of the smooth interface between two layered materials. By parameterizing the interface shape using Bezier surface, the unknown shape is iteratively approached using Levenberg–Marquardt method. To improve the computational efficiency, the forward problem is solved using a cornice boundary integral equation, and a fast Jacobian calculation method is derived using the reciprocity theorem and some integral transform technique. The numerical results demonstrate that the presented method has ability to reconstruct the smooth and continuous three-dimensional interfaces with a good accuracy and high convergence, even when the permittivity values of the reconstructed substances are also unknown. Copyright © 2013 John Wiley & Sons, Ltd.