# HYPSO-1 CubeSat: First Images and In-Orbit Characterization
## 3 In-Orbit Payload Performance
### Spectral Resolution  
Spectral resolution of an HSI is typically measured in the laboratory prior to launch, as carried out for HYPSO-1 in [24]. A method to estimate spectral resolution in orbit is to compare the recorded spectrum with a reference spectrum [41]. The high-resolution reference spectrum is convolved with a simulated instrument response at different spectral resolutions to produce a simulated spectrum for each spectral resolution. These spectra are further compared to the recorded spectrum by HYPSO-1, and the most similar one gives an indication of which spectral resolution HYPSO-1 achieves. Here, the Solar spectrum (1985 Wehrli Standard Extraterrestrial Solar Irradiance Spectrum) with known Fraunhofer lines is used as the reference spectrum, while the recorded spectrum is reflected light off the Moon. The spectral range from 430 nm to 780 nm is investigated due to low amounts of recorded signal below 430 nm, and to avoid second order effects appearing above 780 nm. The instrument response is simulated as a perfect instrument response, represented by a triangular function of different half-widths to represent different spectral resolutions. The solar spectrum convolved with a set of instrument responses is shown in Figure 8. For wider triangular functions, the peaks that are close together get merged. This is observed in the 10 nm resolution response (red line). HYPSO-1 can capture data with and without binning. For nominal operations, only a subset of the available pixels stored, namely the center 1080 pixels in the spectral range and the center 684 pixels in the spatial range of the spectrogram. During nominal operations, binning of nine spectral pixels by summation is applied. Binning data reduce noise and data size. However, binning spectral pixels can also affect the spectral resolution. The spectral resolution is therefore estimated for both full resolution data, and data where binning is applied. Another method to reduce noise when imaging uniform areas is to average the signal from consecutive frames. Ten frames are therefore averaged and compared to the original and binned data in Figure 9. Only the center of the slit image is used to avoid smile effects. It can be seen that one full resolution frame has more noise fluctuations than both the 10 frames average and the binned data, and that the binned data are slightly worse at resolving the curves in the spectrum due to less datapoints. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Capture** & **Off-Nadir Angle** & **GSD along** & **GSD across** & **GRD 565 nm** & **Covered Area** \\ \hline
1 & 1.63\({}^{\circ}\) & 353.6 m & 64.57 m & 141.5 m & ca. 14,900 km\({}^{2}\) \\
2 & 48.7\({}^{\circ}\) & 350.9 m & 179.0 m & 392.4 m & ca. 40,900 km\({}^{2}\) \\
3 & 59.2\({}^{\circ}\) & 347.2 m & 406.3 m & 890.6 m & ca. 91,700 km\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Off-nadir angle, mean GSD’s in the along and across track directions and estimated GRD in terms of meters on ground across track for the three captures in Figure 7. The across track GRD is found using the LSF FWHM of 2.192 pixels for band 565 nm. Variation in along track GSD can due to noise in the ADCS telemetry. Figure 7: Ground sampling (“pixel-to-pixel”) distances of three captures with different off-nadir angles, determined using direct geo-referencing. No slewing maneuver was performed [5]. The left plot shows along track, and the right plot shows across track GSD. HYPSO-1 was holding a constant orientation during capture with respect to a reference frame co-moving with satellite and aligned with its orbital track. The \(y\)-axis range is equal for along- and across track for easier comparison between them. For further analysis, a low-pass filter is applied to smooth the full resolution data to reduce noise, and a high-pass filter applied to both the HYPSO-1 data and the reference data to remove slow intensity changes. The datasets are then normalized by scaling with their maximum values.