## 2 Materials and Methods
### Data Acquisition  
The dataset used in this study was prepared by utilizing a novel MONDI system that reflected light, as discussed by [PERSON] et al. [28]. Figure 3a shows the inspection process using the MONDI system. The MONDI system inspected the specimen with a 15.5 \(\times\) 20.5 mm MO sensor with 0.6 mT of magnetic field saturation, a measurement range of approximately 0.03 to 5.0 kA/m, and a spatial resolution up to 1 \(\upmu\)m, over a magnetized specimen with an artificial defect. Magnetic flux leaks (MFLs) appeared around the defect when the specimen contained a defect, owing to the corresponding discontinuities [29]. Each MFL distorted the magnetic domain distribution of the MO sensor and made the domain unstable, following the distribution of the MFL, which duplicated the defect geometry [22]. A polarized optical system was used to observe the MO sensor based on the Faraday rotation effect. In general, when linearly polarized light propagates through a medium in the direction parallel to the applied magnetic field, the polarization plane is rotated by an angle (\(\theta_{F}\)) in proportion to the magnetic field (\(B\)) and sample thickness (\(d\)). The angle also depends on the Verdet constant (\(V\)), i.e., the strength coefficient of the Faraday effect in a particular material, as described by Equation (1) [30]. \[\theta_{F}=V\cdot B\cdot d \tag{1}\]  
Figure 2: Outline research methodology for magneto-optic nondestructive inspection (MONDI) system with pretrained convolutional neural network (CNN). This study utilized the polarized optical system by flashing 12 volts of polarized white light to a beam splitter that deflected light parallel to the MOF. The polarized light is influenced by the magnetic domain of the magneto-optical film (MOF) and rotated based on the Faraday rotation effect. The rotating plane light is reflected by the mirror layer of the MO sensor and reformed by an analyzer. Furthermore, the strength and direction of the magnetization can be obtained by estimating the rotation angle of the beam. The propagation of the light intensity through the polarizer, sample, and analyzer is defined mathematically by Equation (2), where \(I_{0}\) is the intensity of the incident light, and \(\alpha_{0}\) is the angle between the polarizer and analyzer [30]. The reflected light forms bright and dark areas according to the intensity of the rotation; these represent the crack geometry [22]. The reflection intensity can be described by analyzing the ratio of the upward and downward magnetized areas in the magnetic domain of the MO sensor [17] as explained by Equation (3), where \(H\) is the external magnetic field intensity, \(Hs\) is the intensity of the magnetic field saturating the MO sensors, and \(E\) is the electric field of the light transmitted to the analyzer. \[I=I_{0}\cos^{2}(\theta_{F}+\alpha_{0}) \tag{2}\]  
\[I_{output}=\frac{1}{2}\bigg{[}\frac{Hs+H}{Hs}E^{2}\cos^{2}(\alpha_{0}-\theta_ {F})+\frac{Hs-H}{H_{0}}E^{2}\cos^{2}(\alpha_{0}+\theta_{F})\bigg{]} \tag{3}\]  
Figure 3: Data acquisition process by capturing 4752 images from 11 specimens in 72 different directions of magnetizer and six current variations using MONDI system. (**a**) Visualization of MONDI system; (**b**) experimental setup; (**c**) geometry of the defect: A (semioval), B (rectangular), C (combination), D (triangle), and E (hole). The inspection in this study attempted to duplicate an actual industrial inspection process by involving variations in the magnetizer direction to determine the critical magnetizer angle, which is very important for understanding the distribution of the MFLs. The experiment was conducted using a carbon steel plate (ASTM A36) widely used for bridge structures and the marine industry, owing to its advantage of an increased service lifetime [31]. All of the specimens had a unique defect shape and dimensions; the specimens were classified as semioval, rectangular, combination shape, triangle, and hole defects (Figure 3c).