# Portable L-Band Radiometer (PoLRa): Design and Characterization
## 3 Radiometer Characterization
### Radiometer Stability  
For nominal use of the radiometer, the antenna temperatures at horizontal and vertical polarization are calibrated using a two-point calibration with internal matched resistive source (RS) and active cold source (ACS) as references. Similar to Equations (3) and (4), the radiometer gain \(G\) and offset \(T_{\text{off}}\) are calculated by:  
\[G~{}=~{}\frac{T_{\text{RS}}-T_{\text{ACS}}(\overline{T}_{\text{ACS}})}{u_{\text{ RS}}-u_{\text{ACS}}}, \tag{8}\]  
\[T_{\text{off}}~{}=~{}-G\cdot u_{\text{RS}}+T_{\text{RS}}, \tag{9}\]  
and the noise temperature \(T_{\text{in}}^{p}\) (at the input reference plane of the switch), for switch positions \(p~{}=~{}\{\text{V},\text{H}\}\) is given as:  
\[T_{\text{in}}^{p}~{}=~{}G\cdot u^{p}+T_{\text{off}} \tag{10}\]  
where \(u^{p}\) is the detector voltage measured for the switch at the horizontal and vertical polarization input ports while the antenna is pointing towards the target scene. The radiometer stability was characterized by attaching resistive matched sources to the end of the two antenna feed cables. The radiometer was constantly measuring, beginning from cold startup, for about 20 min, using the \(\tau~{}=~{}16\) ms integration time on each of the two external resistive sources. The corresponding total time to switch between the four switch positions, sample the detector for 16 ms at each position (ACS, RS, and the two external resistive sources), and sample the four temperature sensors is 69 ms. During the stability test, the radiometer was operated on battery power. The external matched resistive sources were passively maintained at ambient temperature during the stability test. The respective RF cables and the matched resistive sources are assumed to be at equal and uniform temperature. A thermocouple temperature sensor was attached to the matched resistive sources to monitor their physical temperature during the test. A slight heating (\(\sim\)0.6 K) of the matched resistive sources during the measurement period was detected, likely caused by heat generated by the radiometer electronics, which were in close proximity. The noise equivalent delta (\(\Delta\)) temperature (NEAT) was calculated experimentally from this matched resistive source stability test. The NEAT depends on integration time (\(\tau\)), which is, in our system, represented by a trailing rolling mean of the raw 16 ms samples. The NEAT values presented are calculated as the standard deviation of the calibrated antenna temperatures over 1000 raw samples. The integration times are implemented as a trailing rolling mean (rectangular window) of length corresponding to the integration time, hence the multiples of 16. Table 2 provides the experimental NEAT values for different integration times. An example of measured raw (sampled at \(\tau\) = 16 ms (blue)) and integrated antenna temperatures for the H polarization switch port, and a histogram and Gaussian fit of the respective raw data is provided in Figure 7. The kurtosis of the raw samples shown in Figure 7 is 3.018, indicating a nearly Gaussian distribution. \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline \(L^{\text{V}}\) & 3.849 dB \\ \(L^{\text{H}}\) & 3.838 dB \\ \(m~{}=~{}\left<m^{\text{H}},m^{\text{V}}\right>\) & 0.3047 K/K \\ \(b~{}=~{}\left<b^{\text{H}},b^{\text{V}}\right>\) & 66.54 K \\ RMSE of \(T_{\text{ACS}}^{p,i}(\overline{T}_{\text{ACS}})\) & 0.660 K \\ \hline \end{tabular}
\end{table} 
Table 1: Parameter values from ACS characterization. NEAT can also be calculated theoretically by the equation [29]:  
\[\text{NEAT}\equiv T_{\text{sys}}/\sqrt{B\cdot\tau}. \tag{11}\]  
where \(T_{\text{sys}}\) is the system noise temperature discussed in Section 2.1 (627 K), \(B\) is the RF bandwidth of the system, and \(\tau\) is the post-detection integration time. The RF bandwidth is determined by the FE filters, which have a 3 dB passband of 27 MHz from 1400-1427 MHz.