# Three-Dimensional Imaging of Metallic Grain by Stacking the Microscopic Images
## 1 Introduction  
Predicting, comprehending, and monitoring the microstructure and mechanical properties, such as heterogeneous microstructure, ductility decreases, the concentration of residual stress, brittleness, and deterioration of toughness, of critical structures, such as heat exchangers, power plants, the oil and gas industry, chemical engineering, and especially nuclear power plants, is important to ensure safety and avoid failures that can lead to environmental disasters, causalities, and financial losses. To prevent and avert such risks, and to ensure the continued safety and integrity of these structures, periodic inspections are required [1, 2, 3, 4]. Numerous non-destructive methods can be used for microstructure characterization. In most cases, non-destructive testing cannot directly determine material characteristics, which are established by destructive testing. To quantify material properties non-destructively, non-destructive methods must be correlated with destructively measured standard data. The limitation and disadvantage of destructive methods are that they do not allow the characterization of the evolution of material properties of the same specimen when successively damaged [3], and they are not easily applicable to characterize the mechanical behavior of materials, if possible, with restricted, difficult and expensive access, even using a numerical simulation, such as the finite element method. The finite element method is used to analyze the relationship between the load, stress-strain, and resistance to failure of a structure [5, 6, 7, 8]. Meanwhile, according to conventional studies, the size and shape of the microstructure affect the strength, toughness, and creepresistance of the structure [9; 10; 11]. However, it is not easy to reflect and demonstrate this with the finite element method [12; 13; 14; 15]. This is because the factor used in the finite element method is the shape of the structure and does not include the microstructure of the structure itself. Therefore, we have not yet seen an example in which the size of the microstructure is inserted as an analysis condition in the finite element method (or two-dimensional analysis). Therefore, in order to analyze the shape and size of the microstructure, it is necessary to express the shape of the grain in three dimensions. On the other hand, the size and shape of the grains affect the analysis results of non-destructive tests [16; 17; 18; 19], such as ultrasonic testing, magnetic particle testing, and eddy current testing. For instance, in the case of ultrasonic examination, research results have been reported that the size and shape of the microstructure influence the scattering of the sound [20]. However, analysis or qualitative matters considering only the average size of the microstructure are reported in [21], and it is difficult to find previous studies on ultrasound wave scattering targeting the size and shape of the actual microstructure. In the magnetic particle inspection method, the sample is magnetized, and the adsorption of magnetic particles by the magnetic flux leakage generated around the defect is observed. At this point, if a strong external magnetic field is applied and then removed, residual magnetization occurs. A similar fault signal is generated, in which magnetic particles are adsorbed even in non-defective areas due to residual magnetization [22; 23; 24]. Even though the deformation caused by an external force causes the magnetic moment inside the magnetic domain to be anisotropic in a specific direction and, therefore, residual magnetization occurs even if an external magnetic field is not applied [25; 26; 27]. In addition, residual magnetization is frequently generated in welds where heat and residual stress are generated by an external force. In the eddy current method of inspection, an induced current is applied to an object to be measured, and the distortion of the induced current occurring around a fault, that is, a change in impedance and a different phase due to eddy currents is measured [28; 29].