# A New Orbiting Deployable System for Small Satellite Observations for Ecology and Earth Observation
## 5 Radiometric Model as Tool for DORA Feasibility Study

Table 3: _Cont._  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**0** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ \hline \multirow{2}{*}{**ID**} & \multirow{2}{*}{**Scientific Area**} & \multirow{2}{*}{**Albedo**} & \multirow{2}{*}{**Measure**} & **Spectral Range** & **Minimum** & **Maximum** & **Reguested** & **Model** & **Optimal** \\  & & & **Kind** & **Explicitly** & **Resolution** & **Time** & **SNR** & **SNR** & **SNR** & **Resolution** \\  & & & & **Written** & **(m/pix)** & **(ms)** & & **(m/pix)** & **(m/pix)** \({}^{\rm b}\) \\ \hline \multirow{2}{*}{_A1_} & \multirow{2}{*}{_Composition of the atmosphere: SO\({}_{2}\) and NO\({}_{2}\)_} & \multirow{2}{*}{0.43} & spectral measures in UV-VIS-IR & \multirow{2}{*}{100} & \multirow{2}{*}{10.13} & \multirow{2}{*}{50–100} & \multirow{2}{*}{50–100} & 47 & 200 \\ \cline{1-1} \cline{5-10}  & & & & & & & \(>\)few & hundreds & 20 \\ \hline \multirow{2}{*}{_A2_} & \multirow{2}{*}{_Polynas_} & \multirow{2}{*}{0.75} & 2 spectral & \multirow{2}{*}{1.075–1.125} & \multirow{2}{*}{<10–150 * } & \multirow{2}{*}{50.65} & \multirow{2}{*}{100} & \multirow{2}{*}{\ \begin{tabular}{c} \(>\)few \\ hundreds \\ \end{tabular}  } & \multirow{2}{*}{25} \\  & & & bands & & & & & \\ \cline{1-1} \cline{5-10}  & & & & & & & & 50 \\ \hline \multirow{9}{*}{_A1_} & \multirow{9}{*}{0.10} & \multirow{9}{*}{12 spectral bands in V-VIS-IR} & \multirow{9}{*}{0.450–0.550} & \multirow{9}{*}{30–100 * } & \multirow{9}{*}{3.04} & \multirow{9}{*}{3.04} & \multirow{9}{*}{ \begin{tabular}{c} \(>\)few \\ hundreds \\ \end{tabular}  } & \multirow{9}{*}{25} \\  & & & & & & & & \\ \cline{1-1}  
The radiometric model is developed from the solar radiation flux at the terrestrial upper atmosphere, which was shaped as the Plank function, assuming the sun as a black body at a temperature of 5800 K (BB model), and decreased in intensity to consider the radiation travel to the Earth's orbit. The characteristics of the telescope and platform were assumed on the basis of the most recent optical design. The deployable telescope is assumed with an aperture of 300 m, with an obstruction of 60 mm due to the presence of a secondary mirror. This is coupled with panchromatic and multispectral filters, ranging from about 0.3 to 2.5 \(\upmu\)m, with a bandwidth from about 0.05 to 0.2 \(\upmu\)m, depending on the considered application. In order to derive the final flux, we considered the optical efficiency (varying between 0.65 and 0.85 in the 350 to 1100 nm wavelength range, and 0.001 otherwise) and the detector quantum efficiency (set to 0.6). The reflected solar flux was obtained by assuming the albedo (which was different for each application, cf. Table 4), whereas no corrective factor was included to account for the terrestrial atmosphere effects, assuming to avoid the stronger absorption bands. The total radiation was derived using the maximum integration time, set to 70% of the dwell time. The SNR was estimated assuming as the main error source the shot noise, and was therefore computed as a square root of the signal. In Table 4, column 8, the results of the radiometric analysis are provided. We draw attention to the fact that these SNR values are functions of the _maximum integration time_, which is in turn computed from the ground resolutions (depending on the requirements requested by each applications), and the ground track speed (depending on the spacecraft speed and the altitude). We found that the DORA system is capable of resolving the majority of the targets and features described by the various applications. One of the most problematic observations is given by the _P. oceanica_. We therefore performed a parametric study to evaluate the downgrading of the ground resolution (Table 4, column 9) to have an SNR sufficient for observations. In this case, we obtained that _P. oceanica_ colonies can be observed and monitored by the DORA system with a ground resolution three times larger than requested.