For this paper: postscript 4 Results of beam ... Abstract... Acknowledgements...

5 Discussion: implications of beam tests  

In the previous section we have shown that the typical difference between the temperature by symmetric and distorted beams is about few , depending on the eccentricity of the beam response shape and on the beam FWHM. Although the value of this effect is not very high, for some ``pixels'' the effect may be significantly higher than the average. In addition it can be not significantly reduced by repeating the observation with different spin axis directions, because a given sky region is typically observed (for scanning strategy similar to that proposed for the PLANCK mission) with similar orientation of the plane ; therefore this kind of distortion produces systematic and not statistic errors in the temperature measurements of any given pixel. Deconvolution techniques are generally developed for symmetric beams and it is presently not clear how deconvolving an observed map in the case of asymmetric beams, particularly when the orientation in the sky of plane may change with time. On the other hand, by averaging maps deconvolved with standard methods and obtained from different channels at the same frequency, this effect may be reduced, provided that detectors at the same frequency observe the same sky region with different beam orientations. Then, we can hope that the final product will be less sensitive to beam distortions.

The present analysis shows that, for the same beam distortion parameter , the effect is more important for the low frequency beams than for high frequency ones, due to the different beam widths. This fact indicates that a good solution may be to arrange low frequency feedhorns near to the optical axis and high frequency ones in the outer regions of the focal plane, because beam distortions typically increase with its distance from the optical axis. On the contrary, when this distance is fixed, the distortion parameter is typically larger for high frequency detectors than for low frequency ones (Nielsen & Pontoppidan (1996)) as recently studied by Villa (1997) for the case of the coma distortion; this fact suggests a focal plane arrangement that goes in a direction opposite to that delined above. Given the present knowledge of beam distortion as function of the distance from optical axis and of the frequency and the numerical estimates quoted in Table 1, this second choice seems to be more advantageous. On the other hand, the goodness of the focal plane arrangement must be checked by evaluating the average global temperature effect, , and by minimising the resulting potential errors introduced by all the distortion effects.

Finally, an other crucial point is the comparison between the value of due to beam distortion and the sensitivity of different receivers. For PLANCK LSI, low frequency channels are more sensitive (Bersanelli et al. (1996)); on the other hand, high frequency channels are more efficient for the primary cosmological goal.

We intend to complete the present analysis in the next future, to examine other CMB anisotropy maps, different extrapolation laws for the Galaxy contamination and the effect of discrete sources and to explore a more complete set of distortion parameters, FWHM's and map resolutions.