Appendix

We give here a more detailed description of the differential correction algorithm discussed in Sect. 4.3.

For each model spectrum and given parameter values $(T,\log g,\chi)$in the grid, we proceed along the following steps:

1.

we compute the synthetic colors, $c_{ij}^{\circ}(T,\log g,\chi)$, from the original theoretical energy distribution, $S^{\circ}_{\lambda}(T,\log g,\chi)$, and the normalized response functions of the filters, $P^{i}_{\lambda}$, (Eq. 6) by

$$\begin{eqnarray} \lefteqn{c_{ij}^{\circ}(T,\log g,\chi) = }\nonumber \\ & & -2.... ...{\lambda}(T,\log g,\chi)P^{j}_{\lambda} {\rm d}\lambda} \right)\,;\end{eqnarray}$$ (13)

2.

as described in detail in LCB97, these theoretical colors, and hence the monochromatic fluxes within each wavelength band, are then used to calculate the theoretical pseudo-continuum, ${pc}^{\circ}_{\lambda}(T,\log g,\chi)$, as a black-body with smoothed color temperatures, $T_{\rm c}(\lambda)$, varying with wavelength:  

$${pc}^{\circ}_{\lambda}(T,\log g,\chi) \propto B_{\lambda}(T\rm _c(\lambda))\, ;$$ (14)

3.

from the theoretical colors, $c_{ij}^{\circ}(T,\log g,\chi)$, we compute the theoretical color differences,

$$\begin{eqnarray} \lefteqn{\Delta c_{ij}(T,\Delta \log g,\Delta \chi) = }\nonumbe... ...g,\chi) - c_{ij}^{\circ}(T,\log g_{\mathrm{seq}},\chi_{\odot})\, ,\end{eqnarray}$$ (15)

where $\Delta \log g$ and $\Delta \chi$ are respectively the surface gravity and the metallicity variations relative to the empirical sequences - for dwarfs and giants at solar metallicity - given in Table 1:

$$\Delta \log g = \log g - \log g_{\mathrm{seq}}\, ,$$ (16)

with

$$\log g_{\mathrm{seq}} = \left\{ \begin{array} {ll} \log g_{... ..., \mathrm{dwarf}} & \mbox{otherwise} \, , \end{array} \right.$$

and

$$\Delta \chi = \chi - \chi_{\odot} \nonumber \,;$$

4.

by adding these color differences to the empirical colors, $c_{ij}^{\rm emp}(T,\log g_{\mathrm{seq}},\chi_{\odot})$ given in Table 1, we then define the semi-empirical colors, $\stackrel{\sim}{c_{ij}} (T,\log g,\chi)$:

$$\begin{eqnarray} \stackrel{\sim}{c_{ij}} (T,\log g,\chi) & = & c_{ij}^{\rm emp}(... ...\nonumber \\ & + & \Delta c_{ij}(T,\Delta \log g,\Delta \chi)\,;\end{eqnarray}$$ (17)

5.

from Eq. (14), these semi-empirical colors allow us to calculate the semi-empirical pseudo-continuum, $\stackrel{\sim}{pc}_{\lambda} (T,\log g,\chi)$;

6.

a ``spectral function'', $\Gamma_{\lambda}(T,\log g,\chi)$, which contains the high-resolution information of the theoretical spectrum, is defined by the ratio of the original spectrum and the theoretical pseudo-continuum,

$$\Gamma_{\lambda} (T,\log g,\chi) = S^{\circ}_{\lambda} (T,\log g,\chi)\: / \: pc_{\lambda} (T,\log g,\chi) \,;$$ (18)

7.

the corrected spectrum is finally computed by multiplying the spectral function with the semi-empirical pseudo-continuum:

$$S^{\rm c}_{\lambda}(T,\log g,\chi) = \stackrel{\sim}{pc}_{\lambda} (T,\log g,\chi) * \Gamma_{\lambda}(T,\log g,\chi) \,.$$ (19)