respectively: $$\begin{aligned}
\mathcal{Y} & = & \int{\mathrm{d}}\Omega\: y(\bmath{\theta}) = 
d_A^{-2}(z)\cdot\frac{\sigma_\mathrm{T} k_B}{m_e c^2}\:\int{\mathrm{d}}V\:n_e T_e\\
\mathcal{W} & = & \int{\mathrm{d}}\Omega\: w(\bmath{\theta}) = 
d_A^{-2}(z)\cdot\frac{\sigma_\mathrm{T}}{c}\:\int{\mathrm{d}}V\:n_e \upsilon_r\end{aligned}$$ Here, $d_A(z)$ denotes the angular diameter distance of a cluster situated at redshift $z$.

Submillimetric observations with [[*Planck*]{}]{} {#sect_planck}
=================================================

The [[*Planck*]{}]{}-mission[^2]$^{,}$[^3] will perform a polarisation sensitive survey of the complete microwave sky in nine observing frequencies from the Lagrange point $L_2$ in the Sun-Earth system. It will observe at angular resolutions of up to $5\farcm0$ in the best channels and will achieve micro-Kelvin sensitivity relying on bolometric receivers [high frequency instrument [[*HFI*]{}]{}, described in @lit_hfi] and on high electron mobility transistors . The main characteristics are summarised in Table \[table\_planck\_channel\]. [[*Planck*]{}’s ]{}beam characteristics are given Sect. \[planck\_beamshape\] and the scanning strategy and the simulation of spatially non-uniform detector noise is outlined in Sect. \[planck\_scannoise\].

  [[*Planck*]{}]{}  channel                                             1                   2                   3                   4                   5                   6                   7                   8                   9
  --------------------------------------------------- ------------------- ------------------- ------------------- ------------------- ------------------- ------------------- ------------------- ------------------- -------------------
  centre frequency $\nu_0$                                         30 GHz              44 GHz              70 GHz             100 GHz             143 GHz             217 GHz             353 GHz             545 GHz             857 GHz
  frequency window $\Delta\nu$                                    3.0 GHz             4.4 GHz             7.0 GHz            16.7 GHz            23.8 GHz            36.2 GHz            58.8 GHz            90.7 GHz           142.8 GHz
  