## Directivity  
The directivity of the rotation-symmetric Pickett-horn antenna described in Section 2.3 is derived from polarization averaged brightness temperatures \(T_{\rm B}=(T_{\rm B}{}^{\rm H}+T_{\rm B}{}^{\rm V})\)/2, measured with the radiometer looking towards the sky. Brightness temperatures \(T_{\rm B}{}^{p}=T_{\rm RM\,inf}{}^{p}\) - \(\Delta T_{\rm B,\,FC}\) entering the antenna aperture are deduced from \(T^{p}{}_{\rm RM\,in}\) (\(p=\rm H\), V) at the two radiometer input ports, corrected for the noise contribution \(\Delta T_{\rm B,\,FC}\) of the FC computed with (6) (\(t_{\rm FC}=0.98\) corresponding to \(L_{\rm FC}\approx 0.1\) dB):  
\[T_{\rm B}^{p}=\frac{T_{\rm RM,in}^{p}-\left(1-t_{\rm FC}\right)T_{\rm FC}}{t_ {\rm FC}} \tag{15}\]  
Data records, \(U_{\rm RS}\), \(U_{\rm ACS}\), \(U^{\rm H}\), \(U^{N}\), with duration \(\tau_{\rm rec}=5\) s acquired with \(f_{\rm ADC}=800\) Hz and the set point \(T_{0}=305\) K are measured every 10 minutes. The actual temperatures, \(T_{0}\) and \(T_{\rm FC}\) (FC temperature \(\approx\) air temperature), are measured for each record. Furthermore, \(T_{\rm RS}=T_{0}=32\)\({}^{\circ}\)C (305 K) is assumed,and \(T_{\rm ACS}(T_{0})\) is determined with (9). Based on these data records, the noise temperatures \(T^{p}_{\rm RM\,in}\) at the two radiometer input ports are derived as:  
\[T^{p}_{\rm RM,in}=\frac{\left<T_{\rm RS}\right>-\left<T_{\rm ACS}\right>}{ \left<U_{\rm RS}\right>-\left<U_{\rm ACS}\right>}\left(U^{\,p}-\left<U_{\rm ACS }\right>\right)+\left<T_{\rm ACS}\right> \tag{16}\]  
Measurements \(T_{\rm B}=(T_{\rm B}^{\rm\,H}+T_{\rm B}^{\rm\,V})/2\) were taken every 10 minutes between 11 a.m. and 4 p.m. on 30 April 2009. The antenna was oriented towards the South at the zenith angle \(\theta\approx 58^{\circ}\), such that the sun was in the main observation direction at 1:25 p.m. At that time, the maximum brightness measured was \(T_{\rm sun}\approx 180.8\) K. To relate the times from the sky measurements, the polar angles \(\Theta\) between the main direction of the antenna and the sun's position at that time was also computed using [32]. This provides a relation \(T_{\rm B}(\Theta)\), which is used to derive the normalized antenna directivity \(D(\Theta)\) shown in Figure 9.  
This is obtained by first subtracting the base line value \(T_{\rm B}(\Theta>30^{\circ})\approx T_{\rm sky}\approx 5\) K from \(T_{\rm B}(\Theta)\), and then normalizing the resulting values to unity for \(\Theta=0^{\circ}\). The normalized directivity (red circles) measured and the fitted Gaussian bell-shaped model \(D(\Theta)\) with \(\Theta\) in units of degrees (solid black line) are shown.  
\[D\left(\Theta\right)=\exp\left(-0.01781\cdot\Theta^{2}\right) \tag{17}\]  
The sensitivity of the measured \(D(\Theta)\) is limited by the contrast \(T_{\rm sky}\,/\,T_{\rm sun}\approx\) -14.3 dB. Therefore, the measurements are considered to be reliable for \(\Theta\leq 15^{\circ}\), implying that side lobes with \(D<\) -14.3 dB are not identified by the chosen measurement approach.  
The beam widths at \(D=\) -3 dB, -6 dB, and -10 dB derived with (17) are at \(\theta\approx 6.2^{\circ}\), \(8.8^{\circ}\), and 11.3\({}^{\circ}\). Strictly speaking the solar disc is not a point source but exhibits a full angle of \(\approx 0.5^{\circ}\) at L-band frequencies. This implies that the measured \(D(\Theta)\) is the convolution of the antenna directivity with the solar disc. Nevertheless, the measured characteristic angles agree very well with the numerical simulations [30], yielding \(\approx 6^{\circ}\) at -3 dB, 9\({}^{\circ}\) at -6 dB, and 12\({}^{\circ}\) at -10 dB.  
Figure 8: **(a)** Return losses \(RL^{p}\) of the antenna feed measured after fine-tuning the receiving \(\lambda/4\)-elements for horizontal (red solid) and vertical (green dashed) polarization. **(b)** Measured isolation between the H- and the V port of the antenna. The radiometer center frequency at 1,413.5 MHz is indicated.