Design of Electrode Arrays for 3D Capacitance Tomography in Planar Domains

Electrode design is investigated for electrical capacitance tomography on a 1 mm-thick 3D planar domain. Arrays of square electrodes are located on both sides of the domain, which is filled with dielectric material. Anomalies of interest are voids in the material with low dielectric constant. Simulated tomography is conducted with various electrode patterns over a range of electrode sizes in order to compare performance. The high-aspect-ratio domain requires a large finite element mesh for simulating electric fields and for defining spatial sensitivity responses of electrode pairs. Compared to the canonical 2D pipe cross-section problem, this high-aspect-ratio system requires solving the reconstruction problem on a much larger mesh and is more severely underdetermined. An efficient methodology for characterizing the sensitivity responses of various electrode pairs is developed. An image reconstruction algorithm creates binary images by sequentially composing a list of occupied cells, conditioned with a cell-to-cell energy formulation. A parametric study of four candidate electrode patterns is conducted using electrode sizes between 0.8 mm and 1.6 mm, in which each potential design is used to perform tomographic reconstruction of 100 images. A new image-error metric is proposed, which is used to evaluate each electrode design. It is found that an electrode matrix pattern on each substrate, with the patterns offset, results in lower mean image error than other candidate patterns.