Full-sky correlation functions for CMB experiments with asymmetric window functions

Abstract

We discuss full-sky convolution of the instrumental beam with the CMB sky signal in CMB single-dish and interferometry experiments using the method [A. Challinor et al., Phys. Rev. D 62, 123002 (2000); B. D. Wandelt and K. M. G\'orski, Phys. Rev. D 63, 123002 (2001).] that the measured temperature and polarization anisotropies are defined globally on the group manifold of the three-dimensional rotation by means of Wigner $D$ functions. We rederive the anisotropy and polarization correlation functions incorporated with asymmetric window functions, which are then explicitly calculated for a single-dish elliptical Gaussian beam and an interferometric Gaussian beam.