Linearization Point and Frequency Selection for Complex-Valued Electrical Capacitance Tomography

Benefiting from the ability to image the permittivity distribution of dielectric materials, electrical capacitance tomography (ECT) has been applied for multiphase flow metering for decades as a contactless method. However, the water-continuous flow brings challenges for ECT since the conductivity in water makes ECT fail to reconstruct the distribution. Therefore, complex-valued ECT (CV-ECT) is introduced to image both permittivity and conductivity distribution based on complex-valued capacitance measurements using the same sensor head of ECT. Different from conventional ECT, the investigation of excitation frequency and linearization point selection is vital for CV-ECT, as the conductivity information is coupled with permittivity and frequency. An eight-electrode CV-ECT system was set up to obtain measurements both in simulations and experiments. The measurements on different phantoms over different excitation frequencies were conducted, and the images were reconstructed to elaborate the selection of the linearization point and excitation frequency range.

I. Introduction

Electrical capacitance tomography (ECT) is known as a noninvasive imaging technique used to reconstruct the permittivity distribution of dielectric materials [1]. In conventional ECT, the capacitance measurements ignore the conductivity information and are mainly dependent on the permittivity within the region of interest (ROI). Thus, it is challenging for conventional ECT to measure the conductive phase of conductive/dielectric mixed multiphase flows when the measurements are mainly dependent on the conductivity of water rather than the permittivity [2]. To address this issue, some multimodality tomography systems, such as ECT/electrical resistance tomography (ERT) dual-modality and ECT/magnetic induction tomography (MIT) dual-modality systems, have been proposed [3]–[6], where ERT and MIT are used to provide conductivity information. Electrical impedance tomography (EIT) is another imaging technique widely used in medical imaging that can obtain complex impedance information [7]–[9]. In [10]–[12], a capacitively coupled ERT (CCERT) is proposed and applied to image the conductivity distribution without contact with liquids, which can be regarded as the combination of ECT and ERT, because it applied ECT sensors to collect resistance information. In addition, Marashdeh et al. [13], [14] proposed a multimodal tomography system based on ECT sensors, and then, the concept of displacement-current phase tomography (DCPT) was proposed in [15] and [16]. The phase information of complex admittance is used to reconstruct electrical parameter distribution, such as loss factor or permittivity [15], [17]. As for multifrequency measurements in ECT systems, Rasel et al. [18]–[20] proposed a method that can exploits differences between measurements obtained at distinct frequencies caused by the Maxwell–Wagner–Sillars effect to improve imaging quality. In [2] and [21], a complex-valued, multifrequency ECT (CVMF-ECT) system is proposed for simultaneous reconstruction of permittivity and conductivity using complex admittance data. Overall, these systems aim to utilize complex admittance information rather than just capacitance information or resistance information via contactless methods.