All-sky convolution for polarimetry experiments

Abstract

We discuss all-sky convolution of the instrument beam with the sky signal in polarimetry experiments, such as the Planck mission which will map the temperature anisotropy and polarization of the cosmic microwave background (CMB). To account properly for stray light (from e.g. the galaxy, sun, and planets) in the far side-lobes of such an experiment, it is necessary to perform the beam convolution over the full sky. We discuss this process in multipole space for an arbitrary beam response, fully including the effects of beam asymmetry and cross-polarization. The form of the convolution in multipole space is such that the Wandelt-Górski fast technique for all-sky convolution of scalar signals (e.g. temperature) can be applied with little modification. 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-weighted window functions. In the limits of a small angle beam and large Legendre multipoles, the spin-weight 2 window function for the linear polarization reduces to the usual scalar window function used in previous analyses of beam effects in CMB polarimetry experiments. While we focus on the example of polarimetry experiments in the context of CMB studies, we emphasise that the formalism we develop is applicable to anisotropic filtering of arbitrary tensor fields on the sphere. 98.70.Vc,

Elliptical beams in CMB temperature and polarization anisotropy experiments: An analytic approach

“…(B10), is obtained by parallel-transporting the local cartesian basis defined at the north pole, σ x and σ y , along great circles through the poles of the sphere (see e.g. [7] for a discussion). Replacing Eq.…”

“…In this formalism the "scanning strategy" of a given experiment is obtained by specifying the Euler angles as a function of time t, (φ(t), θ(t), ω(t)), where n = n(θ(t), φ(t)) gives the pointing direction of the beam and ω(t) is the rotation angle around the pointing direction n which specifies the orientation of an asymmetric beam (eg, the major axis orientation for an elliptical Gaussian beam) with respect to a fix reference orientation (eg, ω(t = 0)). Accordingly, the rotation operator D(φ, θ, ω) acts on the beam so that it takes all possible orientations with respect to a fix reference frame in the sky [31], [7]. Simple scanning strategies allow a convenient decomposition of the rotation matrix D(φ(t), θ(t), ω(t)) for the implementation of fast methods to compute the full-sky convolution [31], [7].…”

“…Accordingly, the rotation operator D(φ, θ, ω) acts on the beam so that it takes all possible orientations with respect to a fix reference frame in the sky [31], [7]. Simple scanning strategies allow a convenient decomposition of the rotation matrix D(φ(t), θ(t), ω(t)) for the implementation of fast methods to compute the full-sky convolution [31], [7]. In what follows we shall suppress the time dependence of the Euler angles to simplify notation.…”

“…Following standard notation (see e.g [25], [23], [14], [7]), the Stokes parameters of the beam are decomposed in the spin-2 spherical harmonics basis ±2 Y m as,…”

A multifrequency angular power spectrum analysis of the Leiden polarization surveys

“…Beside this obvious application, they can be used as input to construct templates for simulation activities in the context of current and future microwave polarization anisotropy experiments. For example they can be utilized to build templates for straylight evaluation (see, e.g., Challinor et al 2000;Burigana et al 2001;Barnes et al 2003) and for component separation analyses.…”