ISAAC spectra are strongly curved and tilted. Before the 2d spectra are combined, they need to be straightened. It is useful to do the wavelength calibration at the same time, so that the horizontal axis is in wavelength units.
The wavelength scale can be calibrated with either arc frames or the OH lines that are imprinted on each spectrum. The advantage of the arcs is that there are lines covering the entire 0.9 to 2.5 micron range. The disadvantage is that the arcs are taken separately and, in most cases, this means that the grating has moved between the time the target was observed and the arcs were taken. One can use the OH lines to cross check and correct the zero point of the wavelength calibration, which will be a necessary step in most cases.
The advantage of the OH lines is that they are numerous and that they lead to a slightly more accurate wavelength calibration. The disadvantages are that: in some regions, particularly beyond 2.2 microns, there may be too few lines to do a good fit; in standard star observations, where exposure times are short, the OH lines may be too faint; and in LR observations, where the resolution is low, the OH lines may be heavily blended.
For both arcs and OH lines a 3rd order Legendre (4 terms) gives a good description of the dispersion.