# Evaluation of Ultrasonic Bonding Strength with Optoacoustic Methods
## 4 Results and Discussions
### Evaluation of Bonding Strength with ESPI  
The ESPI arrangement in this study visualizes the out-of-plane displacement distribution of the specimen surface (the out-of-plane component of the bending displacement). Since the frame rate of the CCD camera (30 fps) is much lower than the driving frequency of the vibration test, the ESPI image shows the averaged displacement during a given frame. Figure 14 shows interference fringes observed at four driving frequencies. Here, the left and right ends of the image are the clamped and oscillating (driven by the transducer) ends of the specimen, respectively. In the fringe patterns (a)-(c), it is seen that in going from the clamped to the oscillating end, the fringe interval decreases. This indicates that the out-of-plane displacement increases nonlinearly from the clamped to the oscillating end. In other words, the specimen underwent a bending motion. As the driving frequency increases from 160 Hz to 170.5 Hz (Figure 14a-c), the fringe interval becomes smaller, indicating that in this frequency range the vibration amplitude increases with the driving frequency. At the driving frequency of 173 Hz (Figure 14d), the type of fringe pattern observed in Figure 14a-c that represents a monotonic increase in the out-of-plane displacement from the clamped to oscillating end disappears. Instead, a bright region appears in the middle of the specimen. This pattern is considered to indicate an eigen mode (resonance) oscillation, and is called the characteristic pattern hereafter. In a characteristic pattern, the bright region is interpreted as representing a node of the oscillation. Since dark fringes generally represent null displacement and at a node of eigen mode oscillation the oscillation is null, this interpretation may sound counterintuitive. However, we believe this is a correct interpretation. The ground for this argument is as follows. When the specimen is oscillated at resonance, the vibration is close to null in the vicinity of nodal points and much larger in the other areas. In the present experimental arrangement, it is expected that the oscillation in non-nodal areas is so large that the speckle pattern loses correlation between the subtracted (after deformation) frame and the subtracted-from (before deformation) frame. (See Section 3.3. Electronic Speckle Pattern Interferometry (ESPI) for the image subtraction.) Consequently, the gray scale level of the captured image tends to be saturated in both the after-deformation and before-deformation frames, converging to the maximum level of 255 (in the 8-bit format). Therefore, when the image subtraction is made, the gray-scale values of the before and after deformation images are close to each other in the vicinity of 255. This makes these areas appear to be dark. On the other hand, the gray-scale value in the area near a nodal point  
Figure 14: Increase in number of fringes as resonance is reached. (**a–c**) show fringe patterns at the driving frequency near the resonance, and (**d**) 173 Hz shows a fringe pattern at the resonance. tends to be a low value that fluctuates from subtraction to subtraction. Consequently, in the subtracted image the nodal area appears to be whiter. Figure 15 shows the frequency response of the bonded specimen detected by ESPI. The total intensity of the specimen was plotted against the driving frequency. Original data was smoothed with the 10-point moving average method. The averaged total intensity shows a rapid decrease at certain frequencies, which appears as sharp minima in Figure 15. Based on the above argument, we interpret that these minima represent resonant frequencies. Characteristic patterns were observed at other frequencies as shown in Figure 16. Figure 16a,b,e-g show the similar bending motion to Figure 14d. The nodes appeared bright. The number of nodes increased with the increase in driving frequency, as expected. In Figure 16c,d,h, the fringes appear in the transverse direction. These patterns can be interpreted as representing torsional vibration modes.