# Using a Pair of Different-Sized Spheres to Calibrate Radar Data in the Microwave Anechoic Chamber
## 3 Results  
The RCS values of the two spheres in radar bands ranging from 2 GHz to 18 GHz follow the scattering region theory. The simulated values are shown in Figure 3. These results were calculated with the Phased Array System Toolbox in MATLAB 2009b [10]. We found that the curves in the colored frames corresponded to the analysis in Table 2. Only in the Ku-band (14-18 GHz) are the RCS values of the two spheres constant. The scattering data of the small sphere was only in the Mie region in the S-band. Other situations also occurred between the Mie region and the optic region. It should be noted that the term \"constant\" indicates that the fluctuation of the RCS values and the increasing radar frequency is continuous, and the change is small enough to be considered a statistical error. However, the RCS values of the spheres vibrated with the radar frequency when scattering occurred in the Mie region. The peak values were much larger than those in the optic region. If we calculate the mean amplitude within three radar bandwidths, which is equal to the quotient, when dividing the sampling number of frequency points in one radar bandwidth by the total number of all sampling amplitudes within the bandwidth (e.g., 2 GHz within S-band, 4 GHz within X-band, 4 GHz within Ku-band), the ratio values of that large sphere to the small sphere are 0.5589, 0.5468, and 0.5461, respectively. Furthermore, one of the resonance effects in the Mie region can be described as that a small frequency deviation can result in large changes in the RCS of a target. For example, it is reported that the scattering resonance effects in echoes from migrating birds are so strong that a 10% frequency deviation within the S-band can result in more than 10 dB changes in the reflectivity values [11]. Thereby, the standard deviation numbers of these data within the S-band, X-band, and Ku-band are 1.823, 0.423, and 0.200 for the small sphere, but 0.520, 0.066, and 0.0223 for the large sphere. In brief, the resonance effect in the Mie region could be the primary explanation for why the RCS values of the two spheres differ from their physical cross-sections. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Radar Band**} & \multicolumn{2}{c}{**Scattering Region**} \\ \cline{2-3}  & **Large Sphere (Radius: 0.15 m)** & **Small Sphere (Radius: 0.05 m)** \\ \hline S-band & Mie and optic region & Mie region \\ X-band & Optic region & Mie and optic region \\ Ku-band & Optic region & Optic region \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Radar bands and sphere sizes. The results of the two spheres in the anechoic chamber also support the above conclusions. Figure 4a-c shows the measured HRRPs of the two spheres in the three radar bands. Since the spheres are isotropic scattering targets, their signal envelopes appeared as a single peak at approximately 11.5 m in the range profile. These ranges represent the \"detection range\" of the spheres, which includes the length of the wires connecting the antennas to the network analyzer ports and the distance between the antennas and the target; thus, the ranges were longer than the size of the inside room (i.e., 7.9 m). The turntable center was located in the center of the receiving and transmitting antennas, but the signal peaks of both spheres did not remain in the same position at the 12 angles. Three possible reasons may cause this kind of position shift. (1) The turntable center is not exactly in the center line of the two antennas. (2) The directional diagrams of the two antennas may not be the same. (3) The spheres are not perfect because of machining errors. The width of the signal envelopes of the large sphere was much greater than that of the small sphere. The former was approximately 30 cm, while the latter was 10 cm. These values are equal to the diameters of two spheres. The large sphere had higher signal amplitudes in the three radar bands than the small sphere, and the differences are about 10 dB, as shown in Figure 4a-c.