# Further Investigations into the Capacitive Imaging Technique Using a Multi-Electrode Sensor
## 3 Simulation Analysis of the Multi-Electrode Sensor for Defect Detection
### FEM Models and the Electric Potential Lines
1) and the different sensing electrodes (No. 2-4) respectively. They are at different positions, which can cause shifted features in the corresponding capacitive images when imaging the same defect. L23 was the distance between CL12 and CL13 and L34 was the distance between CL13 and CL14. L23 and L34, which were the offsets of test results of adjacent electrode pairs, were equal to 6.5 mm. Note that, when detecting the same defect by using the multi-electrode sensor, position compensation according to L23 and L34 should be used to align the detected features for direct comparison. The 2D model describing a multi-electrode sensor to detect a conducting specimen covered by an insulation layer is shown in Figure 3c. There were two kinds of defects in the specimen, one located in insulation layer and the other located on the surface of conducting specimen. The two defects were all 8 mm \(\times\) 5 mm and the horizontal center distance of them was 60 mm. The insulation layer, which was fiberglass, was 230 mm \(\times\) 10 mm. The conducting specimen, which was aluminum plate (grounded), was also 230 mm \(\times\) 10 mm. The lift-off, which was the distance between the multi-electrode sensor and insulation layer, was always 2 mm. As the quasi-electric field assumes that there is no coupling between the magnetic field and the electric field, the distributions of electric potential lines can be formed under the driving electrode (No. 1) by using the multi-electrode sensor. Because of the quasi-electric field, the driving electrode (No. 1) was connected to 10 V DC and the sensing electrodes (No. 2-4) were all connected to 0 V DC in the FEM models. In the actual experiments, when one sensing electrode was selected by the MUX (with its potential set to be 0 V), the other two sensing electrodes were in floating potential state. In FE models, although \"floating potential\" is also available, due to the fact that it was difficult to determine the voltage value of the floating potential which was susceptible to the influence of the surrounding environment (e.g., human and metals) in the actual environment, the two inactive sensing electrodes were connected to 0 V DC in simulation. The electric potential diagrams of the multi-electrode sensor are shown in Figure 4.The electric potential lines are mainly concentrated around the driving electrode (No. 1), which was caused by 10 V DC. The changes of the electric potential lines around the driving electrode (No. 1) could cause the changes of the capacitances between the driving electrode (No. 1) and the different sensing electrodes (No. 2-4), which could in principle validate the feasibility of defecting defects by using the multi-electrode sensor. Comparing Figure 4a,b, it was found that if there was a defect located in the  
Figure 3: (a) the front view of the multi-electrode sensor, (b) the cross-section of the multi-electrode sensor and (c) the multi-electrode sensor inspecting the conducting specimen covered by the insulation layer. insulation layer, the electric potential lines would be distorted in the boundary between the defect and insulation layer. The distortion of the electric potential lines shows that the multi-electrode electrode could in principle detect the defect located in the insulation layer. Comparing Figure 4a,c, it was found that if there was a defect on the surface of the conducting specimen, the electric potential lines would downward extend to the surface of the conducting specimen. The changes in the electric potential lines show that the multi-electrode sensor could in principle detect the defect located on the surface of the conducting specimen. In summary, the simulation diagrams of electric potential lines validated the feasibility of the multi-electrode sensor detecting the defects which were located in the insulation layer and on the surface of the conducting specimen.