All Figures

$\begin{figure} \par\mbox{\includegraphics[width=7.5cm]{2230fi01.eps} (a)} \par\mbox{\includegraphics[width=7.5cm]{2230fi02.eps} (b)} \end{figure}$ Figure 1: a) The scanning of the polarized detectors provides the measurements of intensity of the CMB field components along four directions at each point on the scan path. b) Definition of axis specifying the Stokes parameters reference frame as seen from the sky. The detector pair on the left (e.g. 143-4) measures the Q Stokes parameter, while the pair on the right (e.g. 143-2) measures U when Q and U are defined with respect to the $(x_\alpha ,y_\alpha )$ frame (see Appendix A for further detail on reference axis).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8cm]{2230fi03.eps}\end{figure}$ Figure 2: Planck focal plane unit (FPU) with polarization sensitive bolometers as seen from the sky. Complementary pairs of PSB detectors are arranged in two horns following each other while scanning the sky so that four detectors are in an optimized configuration for polarization measurement.
Open with DEXTER

In the text

$\begin{figure} \par\mbox{\includegraphics[width=7.3cm]{2230fi04.eps} (a)} \par\mbox{\includegraphics[width=7.3cm]{2230fi05.eps} (b)} \end{figure}$ Figure 3: Broad-band power patterns ( $\protect\widetilde I$ responses) of the telescope beams to be superimposed on the sky for polarization measurements, a) HFI-143-2a and b) HFI-143-4a, in SC spherical frame on the sky, with the spin axis of telescope as a pole (isolevels are shown from the maximum down to -60 dB with a step of -3 dB).
Open with DEXTER

In the text

$\begin{figure} \par\mbox{\includegraphics[angle=90,width=6.5cm]{2230fi06.ps} (a)... ...m] \mbox{\includegraphics[angle=90,width=6.5cm]{2230fi07.ps} (b)} \end{figure}$ Figure 4: a) Input and recovered B mode power spectrum with an ideal instrument, i.e. when four identical and axially symmetric Gaussian beams are used for both the readout generation and the C_l reconstruction. The small peak at $l\sim 100$ is produced by the gravitational waves (the tensor to scalar ratio is r=0.1), while the main pattern peaking at $l\sim 1000$ is due to the lensing effect. The error bars are smaller than the thickness of the black solid line showing the input model. b) The relative error between the recovered and the initial power spectrum; the recovered power spectrum is the average of 450 simultations: the statistical error is less than 2%, thus allowing the detection, in non ideal cases, of biases higher than 2%. Identical figures are obtained for T, E and T-E correlation power spectra.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[angle=90,width=7cm]{2230fi08.ps}\end{figure}$ Figure 5: Histogram of the biases divided by the statistical dispersion for all multipole bins shown in Fig. 4. As expected, the histogram is well fitted by a Gaussian of unit variance, showing that the dispersion on 450 simulations gives a good estimate of the errors.
Open with DEXTER

In the text

$\begin{figure} \par\mbox{\includegraphics[angle=90,width=7.3cm]{2230fi09.ps} (a)} \par\mbox{\includegraphics[angle=90,width=7.3cm]{2230fi10.ps} (b)} \end{figure}$ Figure 6: Input and recovered power spectra of a) temperature and b) T-E correlation signals, using the simulated beams of Sect. 2 for the readout simulation and the C_l reconstruction. The recovered power spectra are corrected for an average symmetric beam effect by multiplying them by the power spectrum of the average beam map.
Open with DEXTER

In the text

$\begin{figure} \par\mbox{\includegraphics[angle=90,width=7.3cm]{2230fi11.ps} (a)} \mbox{\includegraphics[angle=90,width=7.3cm]{2230fi12.ps} (b)} \end{figure}$ Figure 7: Input and recovered power spectra of a) E mode and b) B mode signals, using the simulated beams of Sect. 2 for the readout simulation and the C_l reconstruction. The recovered power spectra are corrected for an average symmetric beam effect by multiplying them by the power spectrum of the average beam map.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8.5cm]{2230fi13.ps} \end{figure}$ Figure 8: Recovered B mode power spectrum in a simulation with no initial B mode. The theoretical B mode power spectra due to primordial gravitational waves are also shown for different values of the tensor-to-scalar ratio: 0.1, 10^-3, 10^-5 and 10^-6from top to bottom.
Open with DEXTER

In the text

$\begin{figure} \par\mbox{ \includegraphics[angle=90,width=8cm]{2230fi14.ps} (a)}... ...par\mbox{\includegraphics[angle=90,width=8cm]{2230fi16.ps} (c)} \par\end{figure}$ Figure 9: Spurious generation of E and B modes from temperature signals using simulated beams of Sect. 2 for the readout simulation and the C_l reconstruction, but with no initial E mode.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[angle=90,width=8cm]{2230fi17.ps} \includegraphics[angle=90,width=8cm]{2230fi18.ps} \end{figure}$ Figure 10: Recovered B mode power spectrum before (red, dashed line) and after (green, dot-and-dashed line) correction. The power spectrum is corrected by subtracting the estimated leakage (blue dotted line) assuming knowledge of the exact beams (see text). Bottom: difference between corrected and initial power spectra.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[angle=90,width=8cm]{2230fi19.ps}\par\includegraphics[angle=90,width=8cm]{2230fi20.ps}\end{figure}$ Figure 11: Recovered B mode power spectrum before (red, dashed line) and after (green, dot-and-dashed line) correction. The power spectrum is corrected by subtracting the estimated leakage (blue dotted line) using beams averaged within one horn (0.5% error, see text). Bottom: difference between corrected and initial power spectra.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[angle=90,width=8cm]{2230fi21.ps}\par\includegraphics[angle=90,width=8cm]{2230fi22.ps}\end{figure}$ Figure 12: Recovered B mode power spectrum before (red, dashed line) and after (green, dot-and-dashed line) correction. The power spectrum is corrected by subtracting the estimated leakage (blue dotted line) using elliptic Gaussian beams fitted on the exact beams (2% error, see text). Bottom: difference between corrected and initial power spectra.
Open with DEXTER

In the text

$\begin{figure} \par\mbox{\includegraphics[width=8.2cm]{2230fi23.eps} (a)} \par\mbox{\includegraphics[width=8.2cm]{2230fi24.eps} (b)} \end{figure}$ Figure A.1: Relative difference of power patterns a) $\widetilde I_{4a} - \widetilde I_{4b}$ of two orthogonal channels of the same beam HFI-143-4 ( $\psi =0^{\circ }$ and $\psi =90^{\circ }$ , respectively) and b) $\widetilde I_{4a} - \widetilde I_{2a}$ of the channels HFI-143-4a and HFI-143-2a ( $\psi =0^{\circ }$ and $\psi =45^{\circ }$ , respectively) when superimposed by spinning the telescope about the geometrical spin axis.

In the text

$\begin{figure} \par\mbox{\includegraphics[width=8.2cm]{2230fi25.eps} (a)} \par\mbox{\includegraphics[width=8.2cm]{2230fi26.eps} (b)} \end{figure}$ Figure A.2: The $\protect\widetilde Q$ and $\widetilde U$ Stokes parameters responses: a) $\protect\widetilde Q$ of the beam HFI-143-2a and b) $\widetilde U$ of the beam HFI-143-4a (ideally, both $\protect\widetilde Q$ and $\widetilde U$ should be zero in the beams of these polarizations for the selected reference axes).

In the text

$\begin{figure} \par\includegraphics[width=8cm]{2230fi03.eps}\end{figure}$	Figure 2: Planck focal plane unit (FPU) with polarization sensitive bolometers as seen from the sky. Complementary pairs of PSB detectors are arranged in two horns following each other while scanning the sky so that four detectors are in an optimized configuration for polarization measurement.
Open with DEXTER

$\begin{figure} \par\mbox{\includegraphics[width=7.3cm]{2230fi04.eps} (a)} \par\mbox{\includegraphics[width=7.3cm]{2230fi05.eps} (b)} \end{figure}$	Figure 3: Broad-band power patterns ( $\protect\widetilde I$ responses) of the telescope beams to be superimposed on the sky for polarization measurements, a) HFI-143-2a and b) HFI-143-4a, in SC spherical frame on the sky, with the spin axis of telescope as a pole (isolevels are shown from the maximum down to -60 dB with a step of -3 dB).
Open with DEXTER

$\begin{figure} \par\includegraphics[angle=90,width=7cm]{2230fi08.ps}\end{figure}$	Figure 5: Histogram of the biases divided by the statistical dispersion for all multipole bins shown in Fig. 4. As expected, the histogram is well fitted by a Gaussian of unit variance, showing that the dispersion on 450 simulations gives a good estimate of the errors.
Open with DEXTER

$\begin{figure} \par\mbox{\includegraphics[angle=90,width=7.3cm]{2230fi09.ps} (a)} \par\mbox{\includegraphics[angle=90,width=7.3cm]{2230fi10.ps} (b)} \end{figure}$	Figure 6: Input and recovered power spectra of a) temperature and b) T-E correlation signals, using the simulated beams of Sect. 2 for the readout simulation and the C_l reconstruction. The recovered power spectra are corrected for an average symmetric beam effect by multiplying them by the power spectrum of the average beam map.
Open with DEXTER

$\begin{figure} \par\mbox{\includegraphics[angle=90,width=7.3cm]{2230fi11.ps} (a)} \mbox{\includegraphics[angle=90,width=7.3cm]{2230fi12.ps} (b)} \end{figure}$	Figure 7: Input and recovered power spectra of a) E mode and b) B mode signals, using the simulated beams of Sect. 2 for the readout simulation and the C_l reconstruction. The recovered power spectra are corrected for an average symmetric beam effect by multiplying them by the power spectrum of the average beam map.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=8.5cm]{2230fi13.ps} \end{figure}$	Figure 8: Recovered B mode power spectrum in a simulation with no initial B mode. The theoretical B mode power spectra due to primordial gravitational waves are also shown for different values of the tensor-to-scalar ratio: 0.1, 10^-3, 10^-5 and 10^-6from top to bottom.
Open with DEXTER

$\begin{figure} \par\mbox{ \includegraphics[angle=90,width=8cm]{2230fi14.ps} (a)}... ...par\mbox{\includegraphics[angle=90,width=8cm]{2230fi16.ps} (c)} \par\end{figure}$	Figure 9: Spurious generation of E and B modes from temperature signals using simulated beams of Sect. 2 for the readout simulation and the C_l reconstruction, but with no initial E mode.
Open with DEXTER

$\begin{figure} \par\includegraphics[angle=90,width=8cm]{2230fi17.ps} \includegraphics[angle=90,width=8cm]{2230fi18.ps} \end{figure}$	Figure 10: Recovered B mode power spectrum before (red, dashed line) and after (green, dot-and-dashed line) correction. The power spectrum is corrected by subtracting the estimated leakage (blue dotted line) assuming knowledge of the exact beams (see text). Bottom: difference between corrected and initial power spectra.
Open with DEXTER

$\begin{figure} \par\includegraphics[angle=90,width=8cm]{2230fi19.ps}\par\includegraphics[angle=90,width=8cm]{2230fi20.ps}\end{figure}$	Figure 11: Recovered B mode power spectrum before (red, dashed line) and after (green, dot-and-dashed line) correction. The power spectrum is corrected by subtracting the estimated leakage (blue dotted line) using beams averaged within one horn (0.5% error, see text). Bottom: difference between corrected and initial power spectra.
Open with DEXTER

$\begin{figure} \par\includegraphics[angle=90,width=8cm]{2230fi21.ps}\par\includegraphics[angle=90,width=8cm]{2230fi22.ps}\end{figure}$	Figure 12: Recovered B mode power spectrum before (red, dashed line) and after (green, dot-and-dashed line) correction. The power spectrum is corrected by subtracting the estimated leakage (blue dotted line) using elliptic Gaussian beams fitted on the exact beams (2% error, see text). Bottom: difference between corrected and initial power spectra.
Open with DEXTER