Estimation of the B-mode angular power spectrum of polarized anisotropies of the cosmic microwave background (CMB) is a key step towards a full exploitation of the scientific potential of this probe. In the context of pseudo-spectrum methods the majo
r challenge is related to a contamination of the B-mode spectrum estimate with residual power of much larger E-mode. This so-called E-to-B leakage is unavoidably present whenever an incomplete sky map is only available, as is the case for any realistic observation. The leakage has to be then minimized or removed and ideally in such a way that neither a bias nor extra variance is introduced. In this paper, we compare from these two perspectives three different methods proposed recently in this context Refs. Smith 2006, Zhao & Baskaran 2010, Kim & Naselsky 2010, which we first introduce within a common algebraic framework of the so-called chi-fields and then study their performance on two different experimental configurations - one corresponding to a small-scale experiment covering 1% of the sky motivated by current ground-based or balloon-borne experiments and another - to a nearly full-sky experiment, e.g., a possible CMB B-mode satellite mission. We find that though all these methods allow to reduce significantly the level of the E-to-B leakage, it is the method of Smith 2006, which at the same time ensures the smallest error bars in all experimental configurations studied here, owing to the fact that it permits straightforwardly for an optimization of the sky apodization of the polarization maps used for the estimation. For a satellite-like experiment, this method enables a detection of B-mode power spectrum at large angular scales but only after appropriate binning. The method of Zhao & Baskaran 2010 is a close runner-up in the case of a nearly full sky coverage.
We present an iterative scheme designed to recover calibrated I, Q, and U maps from Planck-HFI data using the orbital dipole due to the satellite motion with respect to the Solar System frame. It combines a map reconstruction, based on a destriping t
echnique, juxtaposed with an absolute calibration algorithm. We evaluate systematic and statistical uncertainties incurred during both these steps with the help of realistic, Planck-like simulations containing CMB, foreground components and instrumental noise, and assess the accuracy of the sky map reconstruction by considering the maps of the residuals and their spectra. In particular, we discuss destriping residuals for polarization sensitive detectors similar to those of Planck-HFI under different noise hypotheses and show that these residuals are negligible (for intensity maps) or smaller than the white noise level (for Q and U Stokes maps), for l > 50. We also demonstrate that the combined level of residuals of this scheme remains comparable to those of the destriping-only case except at very low l where residuals from the calibration appear. For all the considered noise hypotheses, the relative calibration precision is on the order of a few 10e-4, with a systematic bias of the same order of magnitude.
