## 3 Signal Enhancement of Cylindrical Surface Waves
It is observed that, when the crack position \(\alpha\) is \(80^{\circ}\), a new wave appears at the time of LTR, and the amplitude is significantly larger than that of the other waves except for the surface wave, as shown in Figure 6b. However, when the crack position is \(85^{\circ}\), where it is closer to the excitation source position, the new wave dominates the out-of-plane displacement and superimposes with the surface wave, resulting in an increase of peak-to-peak, as shown in Figure 6c. According to the propagation time of the wave, this new wave can only be a converted wave of the longitudinal wave that is generated by the interaction between the longitudinal propagation inside of the material and the edge of the crack. Figure 5b shows the out-of-plane displacement for \(\alpha=80^{\circ}\) when the detection position \(\theta\) is \(5^{\circ}\), \(10^{\circ}\), \(15^{\circ}\), \(20^{\circ}\), \(25^{\circ}\), and \(30^{\circ}\). This shows that, as the detection distance increases, the time interval between the superposition waves of LTR and the new wave with Rr remains unchanged. It also reveals that the new wave has the same velocity as the Rayleigh waves, so we can deduce that the new wave is the LTR, and the mode can be explained by the pulse laser impinging on the top surface of the cylinder and propagating into the cylinder. Some components of longitudinal waves with limited directions impact on the edge of the notch so that the longitudinal waves are converted into the Rayleigh waves, which in turn propagate back into the surface of the cylinder and superimpose with the surface waves. When the crack is closer to the excitation source, more longitudinal waves are converted into surface waves, resulting in the enhancement of the surface waves. In the plate, the laser scanning method can be divided into SLLS and scanning laser detection (SLD) techniques [40]. The SLD method is mainly performed by scanning the detector. When the detection position is close to the edge of the crack, the peak-to-peak amplitudes of the surface waves in the near field of the crack are enhanced due to the superposition of the reflected wave, RTL, and the incident wave. Meanwhile, the enhancement of the surface waves can be used as a fingerprint of the presence of the surface crack. The SLLS method is realized by scanning the pulse laser beam. When the pulsed laser beam approaches the edge of the crack, the peak-to-peak amplitudes of the surface waves also increase. In light of the above discussion, during the laser ultrasonic scanning detection of a cylinder, the crack approaching the laser source can be recognized as SLLS, and the crack passing the detection point can be considered as SLD. Figure 7 shows the peak-to-peak amplitudes of the SLLS and SLD when the cylinder is rotated counterclockwise from the position \(\alpha=0\). This indicates that the peak-to-peak amplitudes of surface waves rapidly increase in the range of \(\alpha=60\)-\(90^{\circ}\), and rapidly decrease after the crack has passed the laser source. Comparing the peak-to-peak amplitudes of the SLLS and SLD, it can be seen that the SLLS peak is obviously higher than that of the SLD peak. This is mainly due to the different modes of superposition waves in these two cases, which has been discussed above. Moreover, the span of the peak-to-peak variation of the SLLS method is much larger than that of the SLD method, as shown in Figure 1:6 This is because the RTL, which plays a decisive role in the signal enhancement of the SLD method, attenuates rapidly as the distance increases. On the other hand, the attenuation of the LTR, which makes a relatively large contribution to the signal enhancement of the SLLS, is very small in comparison. In light of the above discussion, it is obvious that the signal enhancement of the SLLS method is more sensitive in the identification of the surface crack on a cylinder than that of the SLD method.