Air-sky convolution for polarimetry experiments - art. no. 123002

We discuss all-sky convolution of the instrument beam with the sky signal i n polarimetry experiments, such as the Planck mission which will map the te mperature anisotropy and polarization of the cosmic microwave background (C MB). To account properly for stray light (from e.g. the galaxy, sun, and pl anets) in the far side-lobes of such an experiment, it is necessary to perf orm the beam convolution over the full sky. We discuss this process in mult ipole space for an arbitrary beam response, fully including the effects of beam asymmetry and cross polarization. The form of the convolution in multi pole space is such that the Wandelt-Gorski fast technique for all-sky convo lution of scalar signals (e.g. temperature) can be applied with little modi fication. We further show that for the special case of a pure co-polarized, axisymmetric beam the effect of the convolution can be described by spin-w eighted window functions. In the limits of a small angle beam and large Leg endre multipoles, the spin-weight 2 window function for the linear polariza tion reduces to the usual scalar window function used in previous analyses of beam effects in CMB polarimetry experiments. While we focus on the examp le of polarimetry experiments in the context of CR IB studies, we emphasize that the formalism we develop is applicable to anisotropic filtering of ar bitrary tensor fields on the sphere.