## 4 Results  
Figure 9 shows the ultrasonic image acquired in the absence of the specimen and the position coordinate values for three axes, which were measured using the laser tracker during transport of the bogie axis to identify axis misalignment. As shown in Figure 9, the ultrasonic image acquired during the transport of the bogie axis was observed to include dark and bright sections, which appear to have occurred because of the change in sound pressure caused by axis misalignment.  
In the case of the \(y\)-axis, the intensity of the ultrasound sharply decreased at positions where there were rapid changes on the coordinate axis, resulting in the formation of dark images. The misalignment of the \(y\)-axis had the greatest effect on the ultrasonic image. The \(x\)-axis, which represents the distance between the robots, had a lower effect on the change in sound pressure.  
To correct the axis misalignment, the roll, pitch, and yaw values were calculated at each point. This calculation was achieved by using the coordinate values that were measured using the laser tracker and Equations (3)-(5). Subsequently, these roll, pitch, and yaw values were applied in the rotation matrices to calculate the misaligned coordinate values on all \(yy\)-axes and the derived correction values. Based on this procedure, the developed software performed automatic correction during scanning.  
Figure 10 shows the ultrasonic image that was acquired after performing yaw correction, in which the deleterious effects appearing in the ultrasonic image before correction are significantly diminished. Although the misalignment of the \(y\)-axis had the greatest effect among the three axes, pitch correction was also performed and data were re-acquired.  
Figure 11 shows the image acquired after performing pitch correction in addition to the yaw correction. The change in the sound pressure was observed to be constant at almost all points; this confirms that the developed algorithm can perform accurate axis compensations.  
Figure 10: Image after yaw correction.  
Figure 9: Image of \(x\)-, \(y\)-, and \(z\)-axis misalignment for the R1 and R2 robots.  
Figure 12 shows C-scan images of the reference specimen that were captured before and after implementing the corrections; the specimen was fabricated to verify the validity of the correction algorithm. C-scan is a method of taking plane images using a signal measured by the TTU method. Here, only pitch and yaw corrections were performed, as in the previous case. As shown in Figure 12, a relatively dark image appeared within the red box before correction because the received sound pressure was reduced by axis misalignment. This characteristic can be mistaken for delamination or the presence of voids during actual composite material inspection. To address this problem, axis misalignment was corrected by applying the developed algorithm, then an image was acquired from the same specimen. Figure 12 shows that the changes in contrast that appeared before the correction were almost completely removed. This confirmed that the developed algorithm could accurately correct the axis misalignment.  
Figure 11: Image after pitch and yaw correction.  
Figure 12: C-scan images of the specimen with simulated defects.  
The same experiment was performed with the actual composite material specimen; the results are shown in Figure 13. As with the results of the reference specimen, the majority of the changes in image contrast caused by axis misalignment were removed after correction.