Three-dimensional electrical capacitance tomography

Three-dimensional electrical capacitance tomography (3D ECT)^[1][2] also known as electrical capacitance volume tomography (ECVT) is a non-invasive 3D imaging technology applied primarily to multiphase flows. It was introduced in the early 2000s as an extension of the conventional two-dimensional ECT.^[3] In conventional electrical capacitance tomography, sensor plates are distributed around a surface of interest. Measured capacitance between plate combinations is used to reconstruct 2D images (tomograms) of material distribution. Because the ECT sensor plates are required to have lengths on the order of the domain cross-section, 2D ECT does not provide the required resolution in the axial dimension. In ECT, the fringing field from the edges of the plates is viewed as a source of distortion to the final reconstructed image and is thus mitigated by guard electrodes. 3D ECT exploits this fringing field and expands it through 3D sensor designs that deliberately establish an electric field variation in all three dimensions. In 3D tomography, the data are acquired in 3D geometry, and the reconstruction algorithm produces the three-dimensional image directly, in contrast to 2D tomography, where 3D information might be obtained by stacking 2D slices reconstructed individually.

The image reconstruction algorithms are similar in nature to ECT; nevertheless, the reconstruction problem in 3D ECT is more complicated. The sensitivity matrix of an 3D sensor is more ill-conditioned, and the overall reconstruction problem is more ill-posed compared to ECT. The 3D ECT approach to sensor design allows direct 3D imaging of the outrounded geometry. The second commonly used name electrical capacitance volume tomography (ECVT) was introduced by W. Warsito, Q. Marashdeh, and L.-S. Fan in 2007.^[4]