# _remote sensing_
## 3. HORUS Multiangle and Multispectral Observation Module
### Signal-to-Noise Ratio  
The performed signal-to-noise ratio (SNR) analysis shows that the HORUS payload performances are compatible with the defined mission objectives. Generally, satellite's optical sensors aiming at similar applications within the EO field set a minimum SNR of 100 as requirement. Indeed, an SNR of 100 is particularly adequate for atmospheric aerosol optical depth (AOD) retrieval at 550 nm under typical remote sensing conditions and a surface reflectance of 10% or less [50]. Moreover, this minimum requirement ensures a good data quality to accurately differentiate among materials for multispectral applications and hyperspectral applications [19]. Finally, the most known reference off-nadir multispectral \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type of** & **HFOV** & **VFOV** & **Optical Axis** & **Filter’s Central** \\
**Camera** & **(degrees)** & **(degrees)** & **(degrees)** & **(degrees)** & **Wavelength (nm)** \\ \hline \hline \multirow{3}{*}{c} & & & & 5. b1: 443 (blue) \\  & & & & 6. b2: 555 (green) \\  & 33.4 & 33.4 & \(-\)16.7 & 7. b3: 670 (red) \\  & & & & 8. b4: 865 (NIR) \\  & & & & 1. c1: 4430 (blue) \\  & & & & 2. c2: 555 (green) \\  & & & & 3. c3: 670 (red) \\  & & & & 4. c4: 865 (NIR) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: _Cont._ \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**View-Angle** & **Type of Filter** & **Central** & & **Diffraction-** \\
**(degrees)** & **Type of Filter** & **Wavelength** & **GSD (m)** & **Limited** \\  & & & **(nm)** & **Resolution (m)** \\ \hline \hline \multirow{3}{*}{**0**} & Dark red & 443 & 147.1 & 62.1 \\  & Green & 555 & 147.1 & 50.7 \\  & Blue & 670 & 147.1 & 45.2 \\  & NIR & 865 & 147.1 & 79.0 \\ \hline \multirow{3}{*}{\(\pm\)**26.1**} & Dark red & 443 & 180.8 & 76.4 \\  & Green & 555 & 180.8 & 62.3 \\  & Blue & 670 & 180.8 & 55.6 \\  & NIR & 865 & 180.8 & 97.1 \\ \hline \multirow{3}{*}{\(\pm\)**45.6**} & Dark red & 443 & 289.8 & 122.4 \\  & Green & 555 & 289.8 & 99.9 \\  & Blue & 670 & 289.8 & 89.1 \\  & NIR & 865 & 289.8 & 155.7 \\ \hline \multirow{3}{*}{\(\pm\)**60**} & Dark red & 443 & 534.7 & 226.0 \\  & Green & 555 & 534.7 & 184.4 \\ \cline{1-1}  & Blue & 670 & 534.7 & 164.5 \\ \cline{1-1}  & NIR & 865 & 534.7 & 287.4 \\ \hline \multirow{3}{*}{\(\pm\)**70.5**} & Dark red & 443 & 1065.8 & 450.9 \\ \cline{1-1}  & Green & 555 & 1065.8 & 368.0 \\ \cline{1-1}  & Blue & 670 & 1065.8 & 328.2 \\ \cline{1-1}  & NIR & 865 & 1065.8 & 573.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Ground sample distance (GSD) and diffraction limited resolution at different wavelengths and view angles for 500 km orbital height. data currently available are the ones acquired by the TERRA's MISR since 1999, where the minimum requirement for the related SNR was set to 100 for a 2% reflectance [51]. To evaluate the SNR, the radiance at the sensor was calculated considering the exo-atmospheric solar irradiance in each selected bandwidth [51], the atmosphere transmittance on the downward path at the solar incident angle for a 10:30 am Sun-Synchronous Orbit (SSO) orbit [52], a worst case Earth's surface reflectance of 2% and the atmosphere transmittance upward path which varies with the off-nadir angle [52]. The radiative transfer equation was used to evaluate the light received by the sensor in all mission wavelengths and view angles. Only the portion of light reflected by the surface was considered, without including the part scattered or reflected by the atmosphere, with the assumption of a Lambertian surface. The optical field of view determines the number of photons collected, transformed into signal electrons according to the sensor quantum efficiency (QE), which is higher than 50% for all the selected wavelengths. The main noise source considered in this configuration is the shot noise due to the high photons' number. The other main sources of noise are dark current noise and read out noise. The expected number of shot noise electrons, at minimum illumination, is around 100.