# HYPSO-1 CubeSat: First Images and In-Orbit Characterization
## 3 In-Orbit Payload Performance
### Top-of-Atmosphere Radiometric Validation  
Radcalnet provides top-of-atmosphere reflectance data with uncertainties at a 10 nm resolution in the range of 400-1000 nm at intervals of 30 min. The data from RadCalNet are intended to be representative for a nadir-viewing perspective [42]. Data collected near RadCalNet sites are used in this section to evaluate the radiometric accuracy of HYPSO-1. The top of ToA reflectance is a measure of the amount of light that is reflected off the Earth and its atmosphere when illuminated by the sun. It is calculated using the following formulas [43]:  
\[\rho_{\rm P}=\frac{\pi\cdot\mathbf{L}_{\lambda}\cdot\mathbf{d}^{2}}{\text{ ESUN}_{\lambda}\cdot\cos\theta_{\mathbf{S}}} \tag{1}\]  
where \(\rho_{\rm P}\) is the ToA reflectance, \(\mathbf{L}\lambda\) is the radiance, \(\mathbf{d}\) is the distance between the Earth and the sun, ESUN\({}_{\lambda}\) is the mean solar exo-atmospheric irradiance, and \(\theta_{\mathbf{S}}\) is the Solar zenith angle. This formula is used to compare the ToA reflectance of data from the HYPSO-1 instrument with data from selected RadCalNet sites [42; 44]. These sites provide inferred ToA reflectance. As a result, it is possible to compare the measurements from HYPSO-1 using the calibration coefficients acquired on ground with the data provided by RadCalNet without further processing. Each line in a HYPSO-1 capture has its solar zenith angle, and each band has its mean solar exo-atmospheric irradiance. The analysis of the radiometric sensitivity of HYPSO-1 considers the ToA reflectance. This section gives a comparison between the ToA reflectance from HYPSO-1 with selected RadCalNet [42; 44] sites. The instrumented RadCalNet sites provide inferred ToA Reflectance. No compensation of atmospheric effects is needed by comparing the HYPSO-1 data with the inferred ToA reflectance. To calibrate the measured radiometric intensity of the HSI payload, the ToA reflectance values measured by HYPSO-1 are compared to Sentinel-2 data [45] and RadCalNet test sites [22; 44], which have hyperspectral cameras that measure the bottom-of-atmosphere reflectance and, in turn, compute the ToA reflectance. The meta information from the different data sources are given in Tables 6 and 7. Figure 11 show the estimated HYPSO-1 ToA reflectance compared to the RadCalNet ToA reflectance and Sentinel-2 ToA reflectance. Figure 12 shows the estimated HYPSO-1 ToA reflectance compared to the RadCalNet ToA reflectance from the Railroad Valley playa test site. The calculation of ToA reflectance in Figures 11 and 12 was performed using two different solar spectra. The first solar spectrum is the ChKur solar spectrum [46], which is \begin{table}
\begin{tabular}{l l l l} \hline \hline
**RadCalNet site** & **HYPSO-1** & **Sentinel-2** & **RadCalNet** \\ \hline Railroad Valley Playa & & & \\ lat: 38.50, Ion: \(-\)115.69 & 2022-10-05T17:49Z & 2022-10-05T18:32Z & 2022-10-05T18:00Z \\ Gobabeb & & & \\ lat: \(-\)23.60, Ion: 15.12 & 2022-09-03T08:39Z & 2022-09-01T08:46Z & 2022-09-02T08:30Z \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Shows when the captures/data, which were used in Figure 11 were taken for each RadCalNet site. also used for the Landsat missions [43]. The second solar spectrum used is the Thuillier solar spectrum [22; 47]. Both solar spectra were used to calculate the TOA reflectance in Figures 11 and 12, and the latter has a higher spectral resolution. HYPSO-1, at wavelengths beyond 650 nm, frequently reads higher ToA reflectance than RadCalNet, causing a relative error for wavelengths above 700 nm to occasionally reach 20%. When using the Thuillier solar spectrum, which has a finer spectral resolution, the relative error between 700 nm and 750 nm is lower than when using the ChKur solar spectrum. In this region, there are oxygen bands that will be heavily affected by the spectral resolution of the measured signal. At wavelengths between 761 nm and 765 nm, the ToA reflectance HYPSO-1 reads are lower than RadCalNet.