Deconvolving the beam in small angular scale CMB experiments

This paper is concerned with experiments which measure CMB anisotropies on small angular scales. A certain coverage, a beam structure and a level of u ncorrelated noise define each experiment. We focus our attention on the rev ersion of the beam average. In each experiment, we look for the best pixeli zation for reversion, namely, for the pixelization that - after reversion - leads to good maps containing right spectra for the most wide range of ang ular scales. Squared pixels having different sizes "smaller" than the beam radius (theta(FWHM)) are considered. For a given size, the following questi on arises: How well can we assign a temperature to each pixel? Various math ematical methods are used to show that, in practice, this assignation - bea m reversion or deconvolution - only leads to right spectra for pixel sizes greater than a certain lower limit close to theta(FWHM)/2. This limit is es timated for negligible and relevant levels of noise and also for sphericall y symmetric and asymmetric beams. After this general study, we focus our at tention on two feasible detectors (which have been proposed to be on board of PLANCK satellite). For each of them, we estimate the size of the most ap propriate pixelization compatible with beam reversion, diffraction, observa tional strategy et cetera and, then, we answer the following question: Whic h is the part of the angular power spectrum which can be extracted from app ropriately pixelized maps after deconvolution? (C) 2000 Elsevier Science B. V. All rights reserved.