# Using a Pair of Different-Sized Spheres to Calibrate Radar Data in the Microwave Anechoic Chamber
## 3 Results
The difference between the maximum and the minimum within the S-band, X-band, and Ku-band are 2.159 dB, 1.475 dB, and 2.034 dB for the large sphere, but they are about 5.112 dB, 10.077 dB, and 2.368 dB for the small sphere, respectively. The data of the large sphere are more stable than those of the small sphere, and the position shifts of the small sphere are more likely to be affected by the radar bands than those of the large sphere. We used the peaks of envelopes to calibrate the RCS values of the spheres. At each angle, we measured the radar data of each object 20 times. The difference between the maximum and minimum of the 20 samplings differed in the radar bands. The difference in the S-band was the smallest, the difference in the X-band was larger, and the difference in the Ku-band was the largest. However, none of these differences were larger than 0.5 dB. Then, we calculated each peak of the signals in each radar band at each angle and drew the polar diagrams, as shown in Figure 4d. We found that the distribution of the RCS values and grades of the large sphere in the three bands was more uniform than that of the small sphere. The signal amplitude of the small sphere fluctuated in the X-band due to scattering between the Mie and optic regions. Compared with the radar bands, the attitude change has little effect on the signal amplitudes of both the large and small spheres. In Figure 4d, the mean difference between the small sphere and the large sphere was 10.3093 dB within the S-band, 8.5487 dB within the X-band, and 9.6803 dB within the Ku-band. As listed in Table 2, scattering regions are responsible for the difference between the measured values (i.e., 10.3093 dB, 8.5487 dB, and 9.6803 dB) within the three radar bands and the theoretical one (i.e., 9.5424 dB, calculated using Equation (8)). First, both the large sphere and the small sphere are in the optic region (i.e., Ku-band), and their measured difference (i.e., 9.6803 dB)  
Figure 3: Theoretic RCS values of the two spheres in the radar bands (2-18 GHz). was closest to the theoretical value of 9.5424 dB among the three bands. Second, when the test was in the X-band, the radar data of the small sphere was amplified due to the resonant effect in the Mie region, but that of the big sphere was not amplified because it stayed in the optic region. Thus, the difference of 8.5487 dB within the X-band was smaller than that of 9.6803 dB in the Ku-band, and is also farther from the theoretical value of 9.5424 dB. Finally, since the S-band radar data of the large sphere and small sphere were in the Mie region, they were both amplified to some degree. As a result, the value of 10.3093 dB was greater than 9.5424 dB. In this case, the resonant effect contributed more to the scattering power of the large sphere than that of the small one. However, in other cases, the value may be closer to 9.5424 dB. In conclusion, when the data of any sphere is in the Mie region, the difference in the RCS values of the two spheres differs from the difference of theoretical geometrical cross-sections. The rules of scattering regions must be considered in radar calibration. Thus, the relationship between the calibration object and the calibrated target, such as the size and material compositions, must be considered. Table 3 shows the differences in the data between the other objects and the small sphere in other tests. The data of the small sphere were set as 0 dB, and the data of the other objects were relative values to those of the small sphere. The drone was a quad-rotor drone, the DJI Phantom 3, with a general size of about 40 cm. The bird was a seagull with a size of approximately 40 cm. It presents the different data for the drone, the seagull, and the big sphere over that of the small sphere. Based on the ratio of the targets to the spheres, the scattering regions differed for the different targets. According to the scattering region theory, the data in the Ku-band are in the optic region for each object, while all data in the S-band are in the Mie region.