## 4 Damage Detection Results by TD-BOCDA Sensor System
These two points had insufficient damage area in the two-dimensional view, but could be confirmed in the one-dimensional frequency graph. These 5 J measurement results indicate that the system's signal-to-noise ratio needs to be further improved if it is required to detect residual strain of less than 5 J. An important topic in future research will be to increase the accuracy of measurement of the residual strain for impact energy of less than 5 J and obtain its high-resolution damage image. Almost all impact points lie on one horizontal axis, but two impact locations for the 15 and 20 J impacts in groups 2 are off the axis in the cylinder photo. The randomness of these positions is clearly measured in the damage map. For comparison, Figure 6c shows the damage map with 5 Gbps modulation. In this figure, all the impact points are well measured, so the two maps look broadly similar. Figure 6: (**a**) Photo of the cylinder marked with white circles for impact points, and the damage maps with (**b**) 16 Gbps measurement and (**c**) 5 Gbps measurement. Figure 7 compares the damage maps for the 10 and 20 J impacts in detail, according to the modulation rate. In these six maps, the resolution on the vertical axis for the circular position is varied by the modulation rate, while the resolution on the horizontal axis for the longitudinal position is independent of the rate. The maps all have the same unit scale for both axes. For the 10 J impact in group 2, map (a) of 5 Gbps does not show a sufficient two-dimensionally symmetric damage image, but as the resolution increases to 16 Gbps, a circularly symmetrical damage map is clearly evident. Considering the hemispherical tip of the impactor, point symmetric damage is expected, and the map of 16 Gbps, which has the highest resolution, shows this well. The same trend is also seen for maps (d)-(f) of the 20 J impact. The definite difference between the 10 and 20 J maps (comparison between (a)-(c) and (d)-(f)) is in the size of the damaged image, which means that the large impact left a larger deformation. The multi-circle structure shown in the 16 Gbps maps suggests that the expansion deformation did not occur linearly with respect to the center of the circle. Figure 7: Damage map comparison for (**a–c**) 10 and (**d–f**) 20 J impacts according to the modulation rates of 5, 10, and 16 Gbps. To confirm this, Figure 8 analyzes the 20 J impact map of group 2 with 16 Gbps. The vertical axis for the circular position is about twice the resolution of the horizontal axis for the longitudinal position in the graph of Figure 8b. Figure 8c shows the one-dimensional deformation graph of residual strain along the horizontal axis with respect to the center of the circle. This shows that the expansion deformation due to impact is rather decreased at the center point of the circle. This phenomenon is more evident in another one-dimensional deformation graph of Figure 8a for the vertical axis with high resolution. Both the up- and down-shifts of the Brillouin frequency in Figure 8a mean that material expansion and compression alternated with respect to the impact point. It is highly interesting that this is very similar to the deformation of the surface of a liquid shaped by a thrown object. Our previous experiment also observed results similar to this phenomenon [11]. However, in that case, the optical fiber was installed on the composite surface, whereas in this experiment, it was embedded inside the composite. Considering the two experimental results together confirms that the residual strain pattern shown in Figure 8 extends from the surface to the inside of the composite material. To calculate the total representative amount of residual strain on the impact point, the overall amount of the Brillouin frequency shifts was integrated from the one-dimensional plot on the horizontal axis, and then these values were all added along the vertical axis in Figure 8b.