ISAAC spectra are strongly curved and tilted. Before the 2d spectra are shifted and combined, users should think about straightening them. It is useful to do the wavelength calibration at the same time, so that the horizontal axis is in wavelength units. Wavelength calibration in the LW is more complicated. The arc lines are fewer and they have to compete with the bright thermal background. In the M band, there are no arc lines at all, so the wavelength calibration with arcs can only be done with the grating in third order.
For L band MR spectroscopy we provide arcs with the grating in the first and third order. Users can choose which arc they wish to use. For reasons which are not clear, the measured wavelengths of the 3rd order lines are slightly different to what one gets by multiplying the wavelengths by 3. The difference has been measured in the L band, since it is possible to see both 3rd order and 1st order lines. For the medium resolution grating the difference is described by the formula.
The formula for the low resolution grating has still to be determined.
Alternatively, for bright targets, one can use the ubiquitous telluric absorption lines. This has been tested on 1-d spectra only and has proven to be as accurate as using the arcs. For faint targets or for the purpose of correcting the 2d slit curvature, one can use the telluric emission features.
It is perfectly reasonable to use the arc lines to correct for the slit curvature and the telluric features to do the wavelength calibration of the extracted spectra. For both arcs and telluric lines a 3rd order Legendre (4 terms) gives a good description of dispersion.