# Further Investigations into the Capacitive Imaging Technique Using a Multi-Electrode Sensor
## 3 Simulation Analysis of the Multi-Electrode Sensor for Defect Detection
### MSDs, the Capacitances and the DCRs  
Electrode pairs between the driving electrode (No.1) and the different sensing electrodes (No. 2-4) were abbreviated to E21, E31 and E41 respectively here after. It is inappropriate to use a single sensitivity value which is usually used to evaluate a sensor performance to characterize the multi-electrode sensor, as the measurement sensitivity value at each point in the probing area is position dependent and can be described as a measurement sensitivity distribution (MSD). The MSD, which describes how effectively each region in the probing area contributes to the measured charge signal on the sensing electrodes (No. 2-4), can also be considered as a 3D point spread function (PSF) in the imaging process and used to comprehensively evaluate the performance of the multi-electrode sensor [13]. The measurement sensitivity value \(S\) at a given position with coordinate (x, y, z) can be calculated using Equation (7). \[S(x,y,z)=-\overset{\rightarrow}{\xi}_{D}\cdot\overset{\rightarrow}{\xi}_{E} \tag{7}\]  
Where \(\xi_{D}\) and \(\xi_{E}\) are the electric fields in the position (x, y, z) when the driving and sensing electrodes are energized with excitation voltage of the same size respectively. As the angle between \(\xi_{D}\) and \(\xi_{E}\) can less than, equal to or greater than 90 degrees, the value of MSD which is the negative inner product of these two vector can be positive, zero and negative according to Equation (7). Figure 5: _Cont._As shown in Figure 5, the MSD diagrams of the multi-electrode sensor were obtained by 2D FEM models, which could be used to further explain the feasibility of detecting defects using the multi-electrode sensor. Comparing Figure 5a,b when E21 was used to inspect a defect in the insulation layer, the positive MSD (\"Zone A\" in Figure 5b) would extend to the upper boundary of the defect and the absolute value of negative MSD (\"Zone B\" in Figure 5b) would become larger. Comparing Figure 5a,c when E21 was used to inspect a defect on the surface of the conducting specimen, the area of the positive MSD (\"Zone A\" in Figure 5c) had no change. The negative MSD (\"Zone B\" in Figure 5c) had two different changes; one was that it spreads to the interior of the defect and the other was that it gathered at the intersection of the defect, the insulation layer and the conducting specimen. Comparing Figure 5d,e when E31 was used to inspect a defect in the insulation layer, the positive MSD (\"Zone A\" in Figure 5e) would extend to the upper boundary of the defect and the absolute value of negative MSD (\"Zone B\" in Figure 5e) would became larger. Comparing Figure 5d,f when E31 was used to inspect a defect on the surface of the conducting specimen, the area of the positive MSD (\"Zone A\" in Figure 5f) became a little larger. The negative MSD (\"Zone B\" in Figure 5f) had two different changes; one was that it spreads to the interior of the defect and the other was that it gathered at the intersection of the defect, the insulation layer and the conducting specimen. Comparing Figure 5g,h when E41 was used to inspect a defect in the insulation layer, the positive MSD (\"Zone A\" in Figure 5h) would extend to the upper boundary of the defect and the absolute value of negative MSD (\"Zone B\" in Figure 5h) would became larger. Comparing Figure 5g,i when E41 was used to inspect a defect on the surface of the conducting specimen, the area of the positive MSD (\"Zone A\" in Figure 5i) became larger. The negative MSD (\"Zone B\" in Figure 5i) had two different changes; one was that it spreads to the interior of the defect and the other was that it gathers at the intersection of the defect, the insulation layer and the conducting specimen.