## 3 Results
### Mission Analysis
#### 3.1.1 Payload Analysis  
It was decided that the \({}^{3}\)Cat-3/MOTS mission would carry on-board two payloads: a multispectral optical sensor [27] in the VNIR (Visible and Near-InfraRed) [28; 29] and a GNSS-Reflectometer. The final product will consist of data fusion from both payloads merging the multispectral image obtained from the optical sensor and the data collected by the geolocated reflectometer. This section details the performance of the optical sensor and the GNSS-Reflectometer from the point of view of the physical constraints and technical requirements to fulfill the mission statement. Figure 5: Conceptual diagram on the dependency of the activity of the different subsystems with the budgets that reflect the results of the simulation. UHF: ultra-high frequency; SD: secure digital. The selected COTS (Commercial off the Shelf) optical sensor and telephoto lens (Table 3) fulfill the mission statement described in Section 2 in terms of the Ground Sampling Distance (GSD) and swath. The study has thoroughly considered several COTS candidates for the optical sensor and lenses, but the decisive criterion was the solution adopted to provide multispectrality to the optical system with reliable technology. The standard solution of a filter wheel presents a problem for both the size of the wheel and the filter switch delay introduced into the acquisition of the multispectral image. The selected camera [29] has a set of up to two charge-coupled device (CCD) optical sensors with its own filters, solving the multispectrality issue. The size of the camera allows for a 75 mm optical focal length lens. The resulting GSD at nadir is calculated from the sensor's pixel size (p), the focal length of the assembly (f), and the platform height (h) given the specifications of the manufacturer:  
\[\text{GSD}=\frac{\text{P}\cdot\text{h}}{\text{f}}. \tag{1}\]  
The predicted GSD values are only correct if the aperture of the optical system is large enough so as to satisfy the [PERSON]'s diffraction criterion. As the wavelength increases, the condition of the minimum aperture diameter (AP) of the optical system becomes more stringent:  
\[\text{AP}_{\text{min}}=\frac{\lambda_{\text{max}}\cdot\text{h}}{\text{GSD}}, \tag{2}\]  
where \(\lambda_{\text{max}}\) is the longest wavelength among all bands. Assuming a narrow swath, it is directly calculated from the GSD obtained as:  
\[\text{Swath}\cong\text{\#pixels-GSD}, \tag{3}\]  
where #pixels is the number of pixels in the cross-track direction. Another key parameter calculated after the swath is the Field of View (\(FOV\)). The lens manufacturer provides the \(FOV\) defined in the horizontal, vertical, and diagonal directions, which has to be larger than:  
\[FOV=2\cdot\arctan\left(\frac{\text{swath}}{2\cdot\text{h}}\right), \tag{4}\]  
so that the whole image is projected on the sensor. In order to measure the feasibility of the optical system in terms of image quality from the orbital configuration described, the signal-to-noise ratio (SNR) must also be calculated. The solar radiation spectrum at the top of the atmosphere (TOA) is not \begin{table}
\begin{tabular}{l c} \hline \hline
**Optical Sensor** & \\ \hline Sensor tech & CCD \\ \# pixels & 1296 \(\times\) 966 \\ Pixel size (m) & 3.75 \\ Digitalization (bits) & 8/12 \\ Power consumption & 12 VDC/8W \\ Shutter exposure (ms) & min. 6.5 \\ LENS & \\ Focal length (mm) & 75 \\ Aperture (f/\#) & f/2.8 \\ Angle of view & D 12 \\ Weight (g) & 765 \\ Diameter \(\times\) length (mm) & 36 \(\times\) 64.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Manufacturer’s specifications of both the optical sensor and the telephoto lens. constant in all bands of interest; thus, the reflected electromagnetic (EM) wave received by the optical sensor has different signal power values for each band studied [5], (pp. 17-20).