A Permittivity Imaging Method: Electrical Capacitance Tomography Based on Electromagnetic Momentum

Electrical capacitance tomography (ECT) is widely used in industrial two-phase flow detection. Noniterative algorithms have fast imaging speed but low image spatial resolution, while iterative algorithms improve image resolution by increasing the computation time. To increase the image resolution, one can either increase the complexity of the imaging algorithms or increase the observation data according to different imaging principles. ECT technique is an imaging technique based on Green’s reciprocity theorem, which detects scalar, i.e., capacitance. Green’s reciprocity theorem is an energy reciprocity theorem. In recent years, the momentum reciprocity theorem has been proposed. The imaging principle corresponding to the momentum reciprocity theorem detects vector, which is expected to obtain higher resolution permittivity images. A permittivity imaging method is proposed to better recognize the boundary of the object and reduce the complexity of the algorithm. The core of this method is ECT based on electromagnetic momentum (ECT-EMM). ECT-EMM is an imaging technique based on the EMM reciprocity theorem, which detects vector, i.e., capacitance gradient. We first obtain the capacitance gradient by the electrodes-moving scheme and the object-moving scheme. According to the principle of ECT-EMM, the permittivity gradient is reconstructed. Then, the permittivity distribution is recovered from the permittivity gradient. In this article, the principle of ECT-EMM is derived, and the object-moving scheme is used. Numerical simulation and experimental demonstration are performed using the Tikhonov regularization algorithm. The reconstructed images and quantitative metrics show that compared to ECT, the proposed method clearly reflects the boundaries of the two-phase flow and performs more stability with noise for certain objects.