Beam distortion effects on anisotropy measurementsof the cosmic microwave background

High resolution observations of CMB anisotropy requires the use of feed arrays at the focus of an optical system. Beam responses are typically not symmetric for array elements de-centred from the telescope focus, whereas theoretical predictions and standard deconvolution methods generally assume pure symmetric beams. For estimating the effect of main beam asymmetry on temperature fluctuations measurements we have generated high resolution sky maps by using standard spherical harmonics expansion for the CMB fluctuations and by extrapolating available full sky maps to predict Galaxy emission at frequencies and angular scales appropriate to future space missions, like Planck and MAP. We have then convolved simulated maps of the microwave sky with asymmetric beams by adopting the Planck configuration and scanning strategy. We find that the typical difference between temperature measurements performed by symmetric and asymmetric beams is of few $\mu {\rm K}$ and that it is an increasing function of the beam eccentricity and FWHM. Although this effect is not very large, it is of order of the ultimate sensitivity of the next generation of experiments, and must be reduced by optimizing the feedhorns locations on the focal plane.