# ATLAS: Latest Advancements and First Observations
## 2 Materials and Methods
### Calibration Procedure  
Calibration of both the radar performance and the pointing system requires well-characterized and stable sources of electromagnetic energy, preferably located in the far-field region of the antenna. The far field of an antenna is the distance from the source necessary to approximate the electromagnetic wavefronts as approximately planar [23] (Chapter 1). This condition is met if the distance from the source to the aperture is at least \(\frac{2D^{2}}{\lambda}\). This approximation is typically used as a condition in the radar equation, so we need to ensure that targets are in this region. The far-field distance of ATLAS is approximately 3 km, so we consider all satellites in orbit and celestial bodies (including the Sun) to meet this criterion. The use of EM energy from the Sun is a well-established method for checking antenna alignment and receiver sensitivity, and it is quite common for manufacturers to provide Sun calibration tools as part of their software packages. In [24], the authors presented a method for locating the Sun's coordinates and determining the pointing offsets. A method for determining the true elevation of a target using observations of the Sun was introduced in [25]. In [26], the authors presented an improved method for pointing calibration with the Sun using operational weather radar scans made at very low elevation angles. When calibrating radar using the Sun, the radar is, in fact, used as a radiometer. The transmitter is not used since we expect no echo from the Sun due to its distance from the Earth [27]. Because of this, only the receiving chain can be calibrated using the Sun, and to calibrate the whole system, other techniques have to be used, such as the ones explained in Section 2.3. The Sun is one of the preferred candidates for calibration because of the following:  
* It can be regularly observed from any point on Earth;
* Its position in the sky can be precisely calculated at any time and location [26; 28];
* It radiates at all wavelengths, and the radiation is generally unpolarized [29];
* The solar flux incident on the Earth's surface varies between 100 and 300 solar flux units. The solar flux is measured constantly by many stations worldwide, and these measurements are public;  
The diameter of the Sun in the visible wavelengths is approximately 695,700 km, as defined by the International Astronomical Union (IAU) [30], which results in an apparent arc of approximately 0.53\({}^{\circ}\). At centimeter wavelengths, this value is different, and an effective RF diameter can be obtained [31]. For ATLAS's operating frequency, the Sun can be considered a homogeneous disc with a diameter of approximately 0.57\({}^{\circ}\)[27] (and the references therein). It is common to use the horizontal coordinate system [32] when working on a radar ground station. This system uses the station's (observer's) local horizon as the plane to define two angles: azimuth and elevation. Azimuth is the angle around the horizon; it starts at 0\({}^{\circ}\) at true north and increases eastward. Elevation is the angle above the horizon starting at 0\({}^{\circ}\) at the horizon and increasing until 90\({}^{\circ}\) at the zenith, for visible objects. The horizontal coordinate system is always referenced to the station position, which is the origin, so to obtain the position of the object referenced to the Earth, the location of the station on the Earth is necessary. The equations for the elevation and azimuth calculations of the Sun are:  
\[E_{l}=\sin^{-1}(\sin\theta_{lat}\sin\delta+\cos\theta_{lat}\cos\delta\cos T_{ 0}),T_{0}=(t_{s}-12)\times 15^{\circ}, \tag{1}\]  
\[A_{z}=\cos^{-1}\frac{\sin E_{l}\sin\theta_{lat}-\sin\delta}{\cos E_{l}\cos \theta_{lat}}, \tag{2}\]  
where \(E_{l}\) and \(A_{z}\) are the elevation and azimuth of the Sun, respectively. \(\delta\) is the declination of the Sun, \(\theta_{lat}\) is the latitude of the ground station, and \(t_{s}\) is the hour angle of the Sun. The up-to-date declination and hour angle of the Sun are made public by many observatories.