Investigation of spatial resolution of electrical capacitance tomography based on the electromagnetic momentum (ECT-EMM)

Abstract

Electrical capacitance tomography (ECT) is a permittivity imaging method widely used in industrial inspection. The equations described by the ECT technique are nonlinear and ill-posed, which results in low image resolution. ECT can be considered an imaging method based on the Green’s reciprocity theorem, an energetic reciprocity theorem. ECT detects scalars, i.e. capacitances. Electromagnetic fields have both ‘energy’ and ‘momentum.’ In recent years, the electromagnetic momentum reciprocity theorem has enriched the electromagnetic reciprocity theorem. The electromagnetic momentum reciprocity theorem is an imaging method that detects vectors, i.e. capacitance gradients. Vectors contain richer information than scalars; thus, electrical capacitance tomography based on electromagnetic momentum (ECT-EMM) methods is expected to improve the resolution of permittivity imaging. This paper briefly describes the principle of the ECT-EMM technique for image reconstruction using sensitivity matrix gradient and capacitance gradient. Tikhonov regularisation algorithm is applied. The two methods, with and without capacitance measurements, are used to evaluate imaging resolution. Under different numbers of pixels and electrodes, typical permittivity distributions are used for reconstruction, and correlation coefficients are calculated. Simulations and experiments show that the ECT-EMM technique recognises object boundaries more clearly with high noise immunity. Five quality measures are used to evaluate the performance of the point spread function without capacitance measurements. Compared to ECT, the ECT-EMM technique is more sensitive to the central region away from the electrodes, recognises smaller minimum objects, and has smaller shape deformation.