or neighbouring filters in both filter sets. We nevertheless introduced transformations to the ($U-V$) index in order to get colour transformations for colour indices that avoid the $b$ filter, which is the one for which the XMM-OM detector could be the most easily affected by saturation (XMM Users’ Handbook, eds. Dahlem & Shartel 1999). We also established various transformations in which the $uvw1$ filter supplants the $u$ filter. Indeed, contrary to the $u$ and $U$ filters, the $uvw1$ filter is defined on the short wavelength side of the Balmer jump. This property renders the transformations based on $uvw1$ far better than those based on the neighbouring $u$ filter, i.e. they are more linear and essentially possible on a wider temperature range. As expected (Sect. 2.1), the $uvw1$ band can be used to correct the ($U-u$) index in the critical domain where the Balmer jump is important (see Sect. 3.1.2).

The colour transformations presented below being established on synthetic spectra, it is obvious that they should be refined through actual observations of suitable standard fields with the satellite and from the ground. The main interest in the transformations given here is that they inform us about the kind of relations that 