## 3 Experiments, Results and Discussion
### Effects of Magnetic Particle Concentration on Magnetic Particle Indication Images  
In order to systematically investigate how different magnetic particle concentrations in the suspension influence on the captured images, the magnetic particle suspension was prepared at both higher and lower concentrations than the recommended one by the MPI international standards ISO 9934, so as to determine the optimal magnetic particle concentration range [24]. Magnetic particle suspensions with the concentrations of 0.50 mL/L, 1.00 mL/L, 10.00 mL/L, and 40.00 mL/L were used as the test samples. According to the standard and practical experience, the general magnetic powder concentration is usually 3-6 mL/L. In this study, the concentration is far beyond the standard stipulated concentration. The workpiece magnetic field strength was 2400 A/m. The corresponding magnetic particle indication images captured by a high-resolution CCD are displayed in Figure 9.  
It is clear from Figure 9a,b that when the concentration of fluorescent magnetic particles in the suspension was very low (0.50 mL/L and 1.00 mL/L), few magnetic particles accumulated on the cracks of the workpiece. Therefore, magnetic particle indication images were blurry, the brightness of the indication was very low, the background fluorescence was weak, and the cracks were difficult to identify [25]. On the contrary, when the concentration of fluorescent magnetic particles in the suspension was very high (10.00 mL/L and 40.00 mL/L), due to the presence of a large amount of magnetic particles on the test piece surface, the background fluorescence was too strong, the magnetic particle indication on the crack had no obvious boundary with the background, and the contrast of the crack indications against the background, therefore, the cracks were difficult to identify. The above  
Figure 9: Photographs of magnetic particle indications at different magnetic particle concentrations: (a) 0.50 mL/L, (b) 1.00 mL/L, (c) 10.00 mL/L, (d) 40.00 mL/L. two types of extreme magnetic particle concentrations were not conducive to differentiating crack indications from the captured images [26; 27; 28]. The recommended values specified in MPI international standards are mostly empirical values based on human observation, and no quantitative method is available to determine the appropriate magnetic particle concentration in the suspensions [3; 29; 30]. Therefore, in order to revise the magnetic particle inspection standard, reveal the influences of magnetic particle concentrations in the suspension on the quality of crack indications, and guide the development of automated MPI technologies, it is necessary to comprehensively and systematically analyze the changes of the magnetic particle concentration in a suspension during the inspection process. In the present experiment, a controlled variable method was used for this purpose. The gray scale values of the crack images were analyzed in MATLAB so as to obtain different values of magnetic particle indication image evaluation parameters, such as indication gray scale value as well as background gray scale value, and the corresponding results are summarized in Table 2. The definition of the image contrast \(C_{j}\) is as:  
\[C_{j}=\sqrt{\frac{\sum_{i=1}^{N}(x_{i}-\overline{x})^{2}}{N}} \tag{28}\]  
where \(N\) is the number of pixels, \(x_{i}\) is the grayscale of the sampling point, and the \(\overline{x}\) represents the average gray scale value. When the magnetic particle concentration in the suspension was low (1-15 mL/L), it is clear from Figure 10 that as the magnetic particles got higher, all parameters, including the gray scale value of crack indication and the background gray scale value increased rapidly.