## 4 Application examples
### Fire ant antenna vibration in near-field sound  
Another experiment was conducted with a live fire ant in a sound field, to verify the capability of the described image pattern tracking algorithm. The purpose of the test is to determine the possibility for fire ants to detect sound waves. During this experiment, a pipe guided a sound wave of 700 Hz from a loudspeaker to a nozzle of 3-mm diameter. The ant was made unconscious with CO\({}_{2}\) and then put within 10 mm to the nozzle with head directed to the nozzle. The camera view was centered at one of the two antennas of the fire ant and the focus was put on some tiny hairs on the antenna. Shadow images were taken with a back lighting at a frame rate of 4000 fps. Totally 4000 successive frames of size of 512\(\times\)256 pixels were recorded in one second at a scale of 2.58 \(\upmu\)m/pixel. The first frame of this  
Figure 11: Time histories of the termite head velocity in a 33-ms head-banging period.  
Figure 12: Time histories of the termite head acceleration in a 33-ms head-banging period.  
image group is given on the left in Fig. 13. As marked in picture \"A\" on the left with a yellow box, an image pattern of size of 16\(\times\)16 pixels (i.e. 41\(\times\)41 \(\upmu\)m\({}^{2}\)) is selected at a hair tip on the fire ant antenna, an enlarged picture of which is shown in picture \"B\" on the top right.  
Figure 14: Position time histories of a fire ant antenna hair tip.  
Figure 15: Tracking bias distribution on the freedom limit for the fire ant case at the 805 th frame.  
Figure 13: Image pattern of a vibrating hair tip on a fire ant antenna: (A) first frame of 4000 consecutive images, (B) selected image pattern in the 1 st frame, (C) tracked image pattern in the 805 th frame.  
Test run results shown in Fig. 14 indicate that the investigated hair tip drifts away from the original position after 200 ms, possibly because the ant was not completely unconscious, and it moved the antenna slowly. In order to determine the optimal tracking freedom limit, the accumulated tracking bias is tested at the 805 th frames for t=201.25 ms, at which the tracked image pattern goes almost back to the original position so that the image pattern deformation is small between the first and last frame in the test period, see picture B and C in Fig. 13. The accumulated tracking biases at the 805 th frame are given in Fig. 15 for the freedom limit up to 8. Fig. 15 shows that the accumulated image tracking bias reduces from _L_=1 to _L_=5, and it begins to increase at _L_=6, so that the optimal tracking freedom limit is determined as _L_=5 for this test case.  
A Fourier analysis is conducted on time histories of the fire ant antenna hair tip position given in Fig. 14, and the frequency responses are given in Fig. 16. The figure shows that low frequency responses to different sources are limited in the region of 0-350 Hz. The first and second harmonic responses to the exciting sound wave of 700 Hz have peak amplitudes of 1.82 and 0.25 \(\upmu\)m, respectively. The third harmonic response is very weak but can be identified as an amplitude peak of 90 nm at 2100 Hz. Because of the periodicity assumption of the Fourier transformation, a peak can be seen at 1900 Hz, which has the same height as that at 2100 Hz. The test results illuminates that the hairs on the fire ant antenna may be able to detect the near-field sound. However, whether or not the detected mechanical signal can be interpreted biologically and used to influence the behavior of the fire ant is under study and out of the scope of this paper.