## 1 Introduction
### Experimental Result  
Static measurements were taken under the positional conditions of generation and detection, as shown in Figure 4a. The generation gap \(\Delta x\) was 0.1 mm, and the generation range was set to \(-\)3\(-\)3 mm. As a result, the number of generation points was 61. The measurement result for a defect-free cross-section (\"Reference\" in Figure 3) is shown in Figure 4b, and that for a defective cross-section (\"Defect\" in Figure 3) is shown in Figure 4c. The red boxes in the figure include the longitudinal reflected wave on the back surface and conversion from longitudinal to transverse wave. The comparison of the area indicated by the yellow circle shows that attenuation was observed in the presence of defects. This generation and detection points arrangement allows the affected waves transmitted through the defect to arrive after the surface lateral waves and before the Rayleigh waves, making it possible to evaluate the signal attenuation.  
The area containing the focused wave was extracted, and the root mean square (\"RMS\") within the extraction area was calculated for each generation position as a measure of signal intensity. Figure 5 shows the RMS distribution. The slope values of those plots were used to determine the presence or absence of a defect in the \(x>0\) region, where the attenuation could be observed. In practice, a slope calculation was performed on the distribution normalized by the RMS distribution obtained for the defect-free section. Therefore, if the slope value was negative, it was judged that attenuation had occurred (i.e., that a defect was present).  
Figure 4: B-scope result for the specimen in Figure 3. (**a**) Irradiation points of the lasers. (**b**) Without defect. (**c**) With defect.  
Figure 3: Appearance of the specimen and the RT result.  
Next, the traveling measurement was performed to measure the cross-section continuously while moving the specimen in the y direction. Continuous inspection for defects while moving in the direction of the weld line is possible because laser ultrasonics is a non-contact measurement. The measurement range was within the dotted line shown in Figure 3. The traveling speed was set to 0.5 m/min, and the generation point gap \(\Delta\)x was increased to 0.5 mm to reduce the number of generation points per cross-section and to improve the spatial resolution in the y direction. With the number of generation points per cross-section reduced to 13, the y-movement distance required to acquire a single B-scope (i.e., the spatial resolution in the y-direction) was determined to be 1.08 mm. Figure 6 shows the correspondence between RT and the defect detection indicator value calculated by applying the previous judgment method to the traveling measurement. It can be seen that there was a correspondence between the portion of the slope value, which is the detection indicator for each cross-section, above a certain value, and the location of the defect in the RT image. On the other hand, it could be observed that the magnitude of the detection indicator for defects varied. The reason for the variation in the detection indicator is that the slope of the underlying signal distribution, in other words, the attenuation, is different. This variation can lead to a difference in the detection of defects depending on the setting of the threshold value.  
Therefore, in the next section, we clarify the reason for the variation in the detection indicator when traveling of the laser ultrasonic method is accompanied, and the relationship between spatial resolution and detection probability with a finite element simulation.  
Figure 5: RMS of the extracted signal and its slope at each cross-section with or without defects.  
Figure 6: Variation of the normalized RMS slope as a detection indicator in the dynamic measurement range.