## 5 Identification of Surface Crack Depth  
In the present work, the surface crack of the metal material is equivalent to a filter: the laser ultrasonic signals with a wavelength less than the crack depth interact with the edge of the crack to transform into scattered waves, and the laser ultrasonic signals with a wavelength larger than the depth of the crack cross the crack and form transmission waves that continue to propagate. Therefore, the depth of the surface crack affects the signal enhancement, which can be induced by the superposition of scattered waves and incident waves. In this section, a method for determining the depth of the surface crack by using the SLLS peaks of signal enhancement is investigated. Studies were made using rectangular cracks with a range of depths. The depths of the cracks on the cylinder with diameters of 10 and 20 mm range from 0.2 to 2.0 mm with a step of 0.2 mm. In order to obtain the SLLS peaks, the position of the crack in the SLLS method is at \(\alpha=85^{\circ}\), while the positions of detection are at \(\theta=30^{\circ}\), \(60^{\circ}\), \(90^{\circ}\), \(120^{\circ}\), and \(150^{\circ}\). Figure 14 shows the main results of this study. It can be observed from Figure 14a that, with each increment of the crack depth, the SLLS peaks for different detection positions rise monotonically until the crack depth is 1.2 mm. It then remains almost unchanged. The trend of the SLLS peaks variation with the depth of the crack is independent of the position of detection. The same trend can be observed in Figure 14b. The trends of the SLLS peaks for each position of detection for a diameter of 10 mm are much more complex than those for a diameter of 20 mm. This is due to the reduction of the diameter, which results in the susceptibility of the propagation of the surface waves on the cylindrical surface to interference from other types of waves. From the discussion in Section 3, we know that the enhancement of the signal in the SLLS method is mainly due to the superposition of LTR with the surface wave that propagates clockwise. The LTR is generated by the interaction of longitudinal waves propagating inside the material with the edge of the crack. From the perspective of the spatial distribution of the wave propagation, as the crack depth increases, more longitudinal waves are affected by the edge of the cracks and more converted surface waves are generated, resulting in an increased SLLS peaks. However, the longitudinal waves propagating inside the material demonstrate a directivity pattern, as shown in Figure 15a. The directivity pattern of the longitudinal waves excited by the laser line source is obtained according  
Figure 13: Phase shift rate (PSR) as a function of cylinder diameters. to the calculation method in the cited literature [54]. It is observed from Figure 15a that the amplitude directivity of longitudinal waves in aluminum is 30\(\sim\)60\({}^{\circ}\)and 120\(\sim\)180\({}^{\circ}\). The geometric relationship between the crack and the laser source is shown in Figure 15b, where \(d=20\) mm, \(\beta=30^{\circ}\), and \(\alpha=85^{\circ}\). According to the geometric relation, we obtain \(h=1.3\) mm, which indicates that, if the crack depth exceeds 1.3 mm, the range of the amplitude directivity pattern is 90\(\sim\)120\({}^{\circ}\). Hence, the energy of the longitudinal waves is very small, resulting in very little energy in the LTR. Therefore, the SLLS peaks no longer continue to increase, as shown in Figure 14a. To verify the results, we obtained \(h=0.6\) mm for the cylinder with a diameter of 10 mm, based on the same calculation method. Figure 15b shows that, when the depth of the crack exceeds 0.6 mm, the SLLS peaks no longer increase, and oscillations occur. In light of the above discussion, the SLLS peaks are proposed to characterize the depth of the crack on a cylinder within the amplitude patterns of longitudinal waves. In other words, the SLLS peaks of signal enhancement only respond to the depth of the surface crack within a limited range.