Beam Deconvolution Map-Making Charmaine Armitage Benjamin Wandelt UIUC

Deconvolution Map-Making Technique Allows for arbitrary beam shapes Main beam distortions Planck beam has elliptic contours with  up to 1.4 Far sidelobes Uses algorithm for fast, exact convolution on the sphere and works in spherical harmonic space (see Appendix) Speeds up the convolution by a factor of a million (versus pixel-based methods) for nearly symmetric beams and lmax of a few thousand Iterative scheme to solve for the maximum-likelihood estimate of the true sky ATN-1As=ATN-1d

Current Status of PREBEAM Have shown gain in map-reconstruction accuracy through deconvolution technique for temperature maps (Armitage & Wandelt, PRD70 2004) Currently generating polarization maps: Polarized REgularized BEAm deconvolution Map-making (PREBEAM) Uses M3 interface: allows for use of common LevelS CTP data

Preliminary Polarization Results INPUT SKY: Simulated, noise-free BEAM: LFI-27a, LFI-27b, LFI-28a, LFI-28b with FWHMmax/FWHMmin ~ 1.2 SCAN: Planck-like cycloidal scan (sampling frequency reduced) RESOLUTION: pixel-size ~ 0.25 degrees  FINDINGS: Standard map-making method (binning of TOD from elliptical beam into pixel map) results in polarization maps with large signal at high frequency Coupling of temperature to polarization Reconstruct accurate map with PREBEAM

LFI 27

LFI 28

Preliminary Polarization Results Input Q map Standard map (sym. beam) Standard map (ellip. beam) PREBEAM map (ellip. beam)

Preliminary Polarization Results Input Q map Standard map (sym. beam) Standard map (ellip. beam) PREBEAM map (ellip. beam) Beam-induced polarization systematic has RMS of the same order magnitude as the entire polarization signal

Deconvolution Goals We have begun to demonstrate the effectiveness of PREBEAM to remove systematic effects due to beam distortions, with a particular view to polarization anisotropies Future work will be motivated by the need to assess systematics due to beam asymmetries We aim to develop PREBEAM to run a full Planck simulation for the 30GHz channel for a worst case assessment of beam-induced systematics, including the full beam response pattern Near term impact: scanning strategy; assessment of polarization capabilities of Planck mission Post launch: recovery of faint polarization signal in the presence of beam-induced systematics

Appendix: Convolution General convolution on the sphere of two arbitrary functions b and s Fourier transform:

Appendix: Transpose convolution General transpose convolution on the sphere: Fourier transform: