# Using a Pair of Different-Sized Spheres to Calibrate Radar Data in the Microwave Anechoic Chamber
## 1 Introduction  
Researchers need to collect and calibrate the radar data of targets to analyze radar signatures. The radar cross-section (RCS) value of a target is the first of many radar signatures that need to be measured. There are several approaches to calibrating the RCS value [1, 2]. The most practical method for calibrating the RCS value of a measured target is to use a standard object with a known RCS. This is known as the ratio method [3, 4], in which the signal amplitude of the target is compared to that of the calibration object. The process is described by [5]  
\[\sigma_{m}=\frac{P_{m}}{P_{r}}\sigma_{r} \tag{1}\]  
where \(\sigma_{m}\) is the RCS value of the measured target, \(\sigma_{r}\) is the known RCS value of the standard object, \(P_{r}\) is the received power of the standard object, and \(P_{m}\) is the received power of the measured target. The isotropic conducting sphere is the most commonly used calibration object because its RCS value within different scattering regions can be calculated theoretically using different scattering rules [6]. For example, its RCS in the Rayleigh region and Mie region can be calculated using complex equations with the Rayleigh scattering principle and Mie scattering rules, respectively. However, in the optic region, the RCS value (\(\sigma_{s}\)) of an isotropic sphere with a diameter of \(r\) can be determined based on its geometric cross-section [6, 7], which is  
\[\sigma_{s}=\pi r^{2} \tag{2}\]Note that Equation (2) is only effective in the optic region. However, many available measurements seldom consider this condition, and researchers use incorrectly sized spheres to calibrate the radar data within different scattering regions. For example, [PERSON] et al. noted that the RCS value of a stainless-steel sphere with a diameter of 20.3 cm as 0.0321 m\({}^{2}\) should be calculated by the Mie series solution, but they still used this value to calibrate an X-band radar to detect birds, whose radar data were in the optic region [5]. They seemed to ignore the scattering mechanism within the Mie region, as well as the material of the sphere and its influence on calibrating radar echoes from birds [5]. Some previous work used two different standard spheres with known RCS values [4]; however, they did not discuss the relationship between the radar calibration and the scattering region.  
In this paper, we propose a method to calibrate the standard method of one standard sphere using a pair of different-sized spheres, and we emphasize that radar calibration should consider the scattering regions when selecting the calibration sphere. The method provides references for answering questions concerning how big the standard sphere is, the material of the standard sphere, and what the proper distance between the standard sphere and the antenna should be. In Section 2, we present the method using two spheres with radii of 0.05 m and 0.15 m. In Section 3, we analyze the results using the radar data of the two spheres in various radar bands, including the S-band (2\(\sim\)4 GHz), X-band (8\(\sim\)12 GHz), and Ku-band (14-18 GHz), in an anechoic chamber to support our claim. In Section 4, we discuss the results, describe the procedure of the method using a pair of different-sized spheres, and present the potential applications. Finally, in Section 5, after summarizing the method, the results, and the applications, we conclude that our method can be a practical approach to validate the standard radar calibration method using one sphere.