maps are a current research topic (for example, the [Mirage]{}-algorithm proposed by @2004astro.ph..1505Y, [MAPCUMBA]{} by and the max-likelihood algorithm by ), but it can be expected that the destriping can be done very efficiently such that the remaining noise largely consists of uncorrelated pixel noise.

In order to incorporate uncorrelated pixel noise into the simulation, a set of maps has been construced, where at each pixel a number from a Gaussian distribution with width $\sigma_\mathrm{N}$ has been drawn. For [[*Planck*]{}’s ]{}[[*HFI*]{}]{}-receivers, the rms-fluctuations $\sigma_\mathrm{N}$ in antenna temperature can be calculated from the noise equivalent power NEP and the sampling frequency $\nu_\mathrm{sampling}=200$ Hz via: $$\sigma_\mathrm{N} = \frac{2~\mathrm{NEP}\sqrt{\nu_\mathrm{sampling}}}{k_B \Delta\nu}
\quad\mbox{({{\em HFI}})}
\label{eqn_hfi_noise}$$

Alternatively, for [[*Planck*]{}’s ]{}[[*LFI*]{}]{}-receivers, the rms-fluctuations $\sigma_\mathrm{N}$ in antenna temperature are given by: $$\sigma_\mathrm{N} = \sqrt{2}\frac{T_\mathrm{noise} + T_\mathrm{CMB}}{\sqrt{\Delta\nu/\nu_\mathrm{sampling}}}
\quad\mbox{({{\em LFI}})}
\label{eqn_lfi_noise}$$ Values for $T_\mathrm{noise}$ and NEP can be obtained from [[*Planck*]{}’s ]{}simulation pipeline manual. The resulting effective noise level for all [[*Planck*]{}]{} channels for a single observation of a pixel is given in Table \[table\_planck\_channel\]. The formulae and respective parameters are taken from the-planck simulation manual, available via [[*Planck*]{}’s ]{}[LiveLink]{}.

The rms-fluctuations $\sigma_\mathrm{N}$ in antenna temperature have to be scaled by $\sqrt{n_\mathrm{det}}$ (assuming Poissonian statistics), where $n_\mathrm{det}$ denotes the number 