# 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
In summary, the different changes of the MSD diagrams not only validated the feasibility of detecting two different kinds of defects using the multi-electrode sensor (e.g., E21, E31 and E41) but also provided preliminary reasons to explain the multi-electrode sensor can discriminate the defects of the insulation layer and conducting surface. The FEM model of the multi-electrode sensor inspecting conducting specimen covered by insulation layer was shown in Figure 3c and the capacitance lines of E21, E31 and E41 obtained by using this FEM model were shown in Figure 6a-c respectively. In each single imaging diagram of Figure 6a-c, it hardly discriminated the defects of insulation layer and conducting surface. Even if the defect of the insulation layer could be discriminated through the concave shape of the capacitance lines shown in Figure 6b,c, the defect of conducting surface could not be completely discriminated through the convex shape of capacitance lines shown in Figure 6a-c. Comparing Figure 6a-c, the offset of any two adjacent electrode pairs (e.g., E21 and E31, E31 and E41), which was discussed in Figure 3b, was 6.5 mm. It is necessary to  
Figure 5: Measurement Sensitivity Distribution (MSD) diagrams of the multi-electrode sensor: E21 inspecting the specimen without defects (**a**), the defect located in the insulation layer (**b**) and the defect located on the surface of the conducting specimen (**c**); E31 inspecting the specimen without defects (**d**), the defect located in the insulation layer (**e**) and the defect located on the surface of the conducting specimen (**f**); E41 inspecting the specimen without defects (**g**), the defect located in the insulation layer (**h**) and the defect located on the surface of the conducting specimen (**i**). take position compensation for testing results, so that the corresponding abscissa of the different electrode pairs detecting the center of the same defect could be at the same position. The DCR is usually used to evaluate the performance of the conventional CI sensor under the condition of reducing the effect of external noise signals and it can evaluate the conventional CI sensor with different orders of magnitude on the same benchmark. The DCR can also be used to analyze the performance of the multi-electrode sensor and it is defined as follow  
\[DCR=\frac{y-yn}{yn} \tag{8}\]  
where, \(y\) is the measured value from the multi-electrode sensor inspecting the specimen which contains defects and \(yn\) is the mean value of the same multi-electrode sensor inspecting the specimen where there are no defects. Through position compensation, the DCR of E21, E31 and E41 were shown in Figure 6d. It was found that the DCR of the different electrode pairs detecting the center of two different kinds of defects presented different variation patterns. For the defect in the insulator layer, the DCR of the center of the defect showed a monotonous decreasing trend with the electrode pairs changing from E21 to E31 to E41. While for the defect in the conducting surface, the DCR of the center of the defect showed a monotonous increasing trend with the electrode pairs changing from E21 to E31 to E41. These different variation patterns showed that the multi-electrode sensor could completely discriminate the defects in the insulation layer and conducting surface, the reasons of which were preliminarily explained by the different changes of the MSD diagrams shown in Figure 5.  
Figure 6: Test results: (**a**) the capacitances of E21, (**b**) the capacitances of E31, (**c**) the capacitances of E41, (**d**) the DCRs of E21, E31 and E41; DCRs: Dynamic Change Rates.