## 2 Materials and Methods
### HyPlant Processing Chain
#### 2.2.3 HyPlant FLUO: From Raw Signals to Calibrated Radiances--Processing Cluster III  
The third cluster of the HyPlant processing chain describes the procedure of converting FLUO raw data to non-deconvolved/deconvolved at-sensor radiance (Figure 4). For this purpose, the CaliGeoPro software is used again, to perform the same processing steps already described for the DUAL data. This includes the dark frame subtraction and the radiometric correction of the image cube, as well as the boresight correction and the generation of the GLT file for the geometric correction. As the result of this process, the user receives the at-sensor radiance and the GLT file similar to the DUAL processing. In contrast to the DUAL module, the radiometric correction of the FLUO module can optionally be extended by the application of the PSF deconvolution. Ideally, an imaging spectrometer looking at a monochromatic point source should produce a single pixel response. In real systems like the HyPlant FLUO module, this is not the case, and the resulting signal spreads in the sensor matrix around this pixel. This distribution of light across the sensor (spatial cross-talk) is called \"point-spread function\" (PSF). For imaging spectrometers, the dimension of the sensor array corresponds to the spatial domain and the second dimension to the spectral domain. Smooth spectral signals are not significantly affected by (although not immune to) the PSF. However, when a spectrum presents neighboring bands with contrasting values (e.g., when absorption features or narrow emission peaks are resolved), the result is a transfer of energy between them, which causes the high signal to decrease and the low signal to increase. This leads to a distinct distortion of the shape and values of the spectrum. The same occurs in the spatial dimension at edges between contrasting targets. Furthermore, the effect can show diagonal contributions between the spectral and spatial signals. Given this, the number of diagonal elements contributing to the effect can be very large. This is especially important for discriminating a weak signal over a bright background, such as in the retrieval of SIF from HyPlant FLUO data. To correct for the above-mentioned effect, PSFs of the FLUO module were characterized in a laboratory by the sensor manufacturer at six wavelengths across the range of the sensor (680, 700, 720, 740, 760 and 775 nm) and at five positions within its field of view (spatial pixel 10, 96, 192, 288 and 374). Figure 5 illustrates two PSFs located in the center of the sensor array in the spatial domain (spatial pixel 192), and close to the oxygen absorption features at 680 and 760 nm in the spectral domain. Since the 30 determined PSFs show very similar shapes and values, it is possible to apply the same deconvolution algorithm to the entire image cube. The deconvolution follows the van-Cittert approach, which is explained in [35]. This iterative process results in an image with less stray light at each step, although, if the iteration is not stopped at a proper level, the stray light might not be completely removed or might even result in overcorrection, depending on the radiometric resolution and noise level of the acquired image cube. After processing numerous image cubes, however, it became clear that only one iteration within the deconvolution process tended to yield the best results. Figure 1c shows the at-sensor radiance spectra of selected surfaces after the deconvolution algorithm was applied, whereas Figure 6a focuses on the at-sensor radiance of vegetation zoomed in on the O\({}_{2}\)-A and O\({}_{2}\)-B absorption features that are used to retrieve SIF. Moreover, the FWHM and signal-to-noise ratio (SNR) of HyPlant in the two oxygen absorption features are displayed in Figure 6b,c, respectively. Figure 4: Flow chart of the third cluster of the HyPlant processing chain, presenting the entire workflow involved in processing HyPlant FLUO data, from raw images to non-deconvolved/deconvolved at-sensor radiance.