# Further Investigations into the Capacitive Imaging Technique Using a Multi-Electrode Sensor
## 1 Introduction  
Insulation layer is a protective structure for metal pipeline to resist corrosion [1; 2; 3]. It is used to insulate metal pipeline from corrosion environment such as moisture content, to restrain the occurrence of corrosion on the surface of metal pipeline and finally to achieve the purpose of controlling corrosion [4]. Due to defects in pipeline production, external mechanical action, disturbance or pressure of soil, wear of rock, bacterial invasion and other factors, the defects of the insulator layer and metal surface often occur [5; 6; 7; 8]. Therefore, it is very useful to detect the defects both in insulator layer and metal surface. When there are defects in the insulator layer, it is necessary to replace the insulator layer. When there are defects in the metal surface, it is necessary to replace the insulator layer and metal pipeline at the same time. Discriminating the defects in the insulator layer and metal surface is thus beneficial to take appropriate remedial measures to reduce maintenance cost and improve production efficiency [9]. It is a challenging work for conventional NDE technique and capacitive imaging (CI) technique has been proven to be a feasible technique in previous work [10; 11; 12; 13]. As a novel non-destructive testing (NDT) technique, CI has been used for oil pipelines, storage tanks, nuclear power stations and new armor in recent years [14; 15; 16; 17; 18]. It has many advantages, such as easy to implement, cost effective, environment friendly and non-contact [10; 12]. The CI can not only detect surface defects in a conductor but also detect internal defects in a non-conductor [11]. A conventional CI sensor consists of two co-planar electrodes, one being the driving electrode and the other being the sensing electrode [13]. The detection principle of CI is shown in Figure 1. An AC voltage is applied to the driving electrode and the sensing electrode is connected to a measurement circuit. As shown in Figure 1a, when the CI sensor detects a non-conducting specimen, the fringing electric field emanates from the driving electrode and terminates at the sensing electrode. The fringing electric field can reach the inside of the non-conducting specimen through the air gap. If there is a defect inside the non-conducting specimen, it will influence the distribution of the fringing electric field and thus impacts the charge on the sensing electrode. As shown in Figure 1b, when the CI sensor detects the conducting specimen covered by an insulation layer, the fringing electric field emanates from the driving electrode and terminates at the sensing electrode and on the surface of the conducting specimen. If a defect exists on the surface of the conducting specimen, it will also influence the distribution of the fringing electric field and thus impacts the charge on the sensing electrode. In summary, all the changes of the charge can be used to detect the defects within the insulation layer and metal surface. Note that for a clearer illustration, only the effective electric field lines, which originated from the driving electrode and terminated on the sensing electrode, were included in Figure 1. Field lines that terminated at the ground and infinity have minimal impact on the measured values and were omitted from the illustrative figure. It is very difficult to accurately compare the defects at the different depths in the insulation layer and discriminate the defects within the insulation layer and metal surface using the conventional CI sensor with a single sensing electrode, because using a single pair of electrodes is hard to obtain more information about the defects. In order to solve the above problems, the multi-electrode sensor which can give more information about the defects in the depth direction was proposed and briefly introduced in Section 2. The finite element method (FEM) models were then constructed by COMSOL Multiphysics (COMSOL Co., Ltd.).