“Slit decomposition” is the algorithm that we use in the new data-reduction system to extract 1D-spectra from the detector images. This works by approximating a cut-out from a spectral order (top-left panel) by two one-dimensional vectors (black lines), one being the spectrum (middle panel), the other the slit illumination (right panel). From these two one can reconstruct a 2D-model, which is shown in the lower left panel. The animation shows how we step in overlapping chunks along the spectral order. The red dots are the individual pixel values from the input image, collapsed along the respective direction.