Results from the full forward-model fit of a simulated spectrogram of the CALSPEC star HD111980 with a Moffat PSF kernel. A second diffraction order was simulated. Top left: spectrum output from the full forward-model process (orange) compared with the true spectrum injected in the simulation (blue) and the intermediate 1D transverse fit used as the prior vector A₀ (green). Bottom left: residuals between the true spectrum and the 1D and 2D fits normalised by their estimated uncertainties. Top right: FWHM of the true PSF (blue, right below the green curve) compared with the fitted PSF during the full forward-model procedure (green) or the 1D transverse fit (orange). Bottom right: difference between the true PSF FWHM injected in the spectrogram simulation and the 1D and 2D fits. All blue curves are covered by the orange curves.