Calibration of the spectral projection for the HR 8799 dataset (square root stretch, colour bar: adu). a: averaged wavelength calibration acquisition y^w. b: averaged spectral flat-field calibration acquisition y^s. c: zoom of (a). The found positions for the calibration wavelengths are highlighted by coloured dots. The black circles are proportional to the size of the Gaussian patterns. d: simulation of the wavelength calibration by the projection model. e: zoom of (b). The positions of the wavelengths simulated in the forward model are highlighted by coloured dots. f: simulation of the spectral flat by the projection model. g: residuals of the first estimation of the wavelength calibration. h: final residuals of the wavelength calibration. i: residuals of the first estimation of the spectral flat calibration. j: final residuals of the spectral flat calibration. k: histogram of the residuals of the spectral flat calibration along the iterations. For comparison purposes, a Gaussian profile of standard deviation σ = 175 adu is plotted.