## 2 Methods
### Image Processing
#### 2.6.2 Vignetting Correction  
The effect of radial fall-off of light intensity from the center towards the periphery in photographed images is known as vignetting. Different sources of vignetting contribute to a progressive reduction of irradiation across the image plane and may cumulate up to 60% at the periphery of an image. Although lens manufacturers go the limit to what is technically feasible, the geometry of the sensor optics contributes most to this effect [6; 28]. In order to minimize the vignetting, an image based correction method was applied to each of the 12 bands of every single image captured during the mission. The method basically uses a look-up table (LUT) for each band, composed of correction factors for each pixel derived from flat field imagery. The proper generation of flat field imagery requires an evenly illuminated white surface with Lambertian properties and constant spectral characteristics. However, for practical considerations, a white surface with near Lambertian properties may serve to generate acceptable flat field imagery. Figure 5: (a) Dark offset image of b471 showing periodic noise and progressive shutter band noise; (b) Dark offset image of b899 showing a global checkered pattern and progressive shutter band noise. Numerous artificial white and black materials (various types of paper, rubber and plastic) were examined regarding their spectral properties. A halogen lamp was used for an even illumination of the targets and an ASD FieldSpec 4 Wide-Resolution spectrometer (ASD Inc., Boulder, CO, USA) was used to collect spectral reflectance data. The instrument measures the spectral radiance (W\(\cdot\) m\({}^{-2}\cdot\) sr\({}^{-1}\cdot\) nm\({}^{-1}\)) over the wavelength range of 350-2500 nm with a spectral resolution of 3 nm at 700 nm and 30 nm at 1400 nm and 2100 nm, respectively. In order to yield the relative reflectance of a target (vegetation, calibration panels, soil), the measurement of the spectral radiance from a reference panel with Lambertian characteristic and constant spectral properties over VIS and NIR wavelengths was required. Therefore, a Spectralon(r) reference panel was mounted on a tripod for collecting reference spectra prior to every single measurement of a target. Without fore optics, the bare fiber has a 25\({}^{\circ}\) field of view. A matt white Bristol Cardboard with a density of 625 g\(\cdot\) m\({}^{-2}\) was found to show the highest and most uniform reflectance over the same wavelength range from 466 nm to 978 nm that is covered by the filter configuration of the MCA. Vignetting imagery was created under diffuse illumination conditions using the matt white Bristol Cardboard. The camera was operated manually at a distance of approximately 1 m with the sensors pointing downwards to the Cardboard. Between each triggering the orientation of the camera has been changed slightly to minimize possible heterogeneities on the surface of the cardboard. During image acquisition we ensured that the cardboard completely covered the field of view of all 12 bands. In a first step, the per-pixel average was calculated from a total of 10 images for each of the 12 sensors at different exposure levels, followed by a subtraction of the respective dark offset imagery. To account for the horizontal band noise induced by the progressive shutter of the camera, a shutter correction factor has been calculated in a second step. Each flat field image has been averaged along the y-axis (row-wise). While most profiles showed a behavior that could be approximated by a 3-grade polynomial function, satisfying approximation for b\({}_{761}\), b\({}_{899}\) and b\({}_{953}\) could only be achieved by a 5-grade polynomial function. For the sake of consistency, we used a 5-grade polynomial for the approximation in all 12 bands. Figure 6 shows the y-axis average and its approximation for two examples, b\({}_{831}\) and b\({}_{899}\), respectively. For each row, the shutter correction factor has then been calculated by dividing the row-wise average by the approximation.