The input template map (see Fig. \[figure\_dustmap\]) is derived from an observation at a wavelength of $\lambda=100~\umu\mathrm{m}$, i.e. $\nu_0=3~\mathrm{THz}$. Its amplitudes $A_\mathrm{dust}$ are given in MJy/sr, which are extrapolated to the actual frequency channels of [[*Planck*]{}]{} using a two-component model suggested by C. Baccigalupi (personal communication). Despite the fact that the dust is expected to spread over a large range of temperatures, the model reproduces the thermal emission remarkably well. This model yields for the flux $S_\mathrm{dust}(\nu)$:

$$S_\mathrm{dust}(\nu) = 
\frac{f_1 q\cdot\left(\frac{\nu}{\nu_0}\right)^{\alpha_1} B(\nu,T_1) + 
f_2\cdot\left(\frac{\nu}{\nu_0}\right)^{\alpha_2} B(\nu,T_2)}{f_1 q B(\nu_0,T_1) + f_2 B(\nu_0,T_2)}\cdot 
A_\mathrm{dust}\mbox{.}$$

The choice of parameters used is: $f_1 = 0.0363$, $f_2 = 1-f_1$, $\alpha_1=1.67$, $\alpha_2=2.70$, $q=13.0$. The two dust temperatures are $T_1 = 9.4$ K and $T_2 = 16.2$ K. The function $B(\nu,T)$ denotes the Planckian emission-law: $$B(\nu,T) = \frac{2h}{c^2}\cdot\frac{\nu^3}{\exp(h\nu/k_B T)-1}\mbox{.}$$

Galactic synchrotron emission {#foreground_synchro}
-----------------------------

Relativistic electrons of the interstellar medium produce synchrotron radiation by spiralling around magnetic field lines, which impedes CMB observations most strongly at frequencies below 100 GHz. The synchrotron emission reaches out to high Galactic latitude and is an important ingredient for modelling foreground emission in microwave observations. An all-sky survey at an observing frequency of 408 MHz has been compiled by and adopted for 