Appendix B: Beam optical properties of the 30 GHz beams

As well known, for the same telescope and feed position, the beam optical distortions increase with the frequency. On the other hand, we know that for example for elliptical beams with the same eccentricity the difference of the observed temperature with respect to the case of symmetric beams increases with the beam size (Burigana et al. 1998). Whereas the HFI feeds are located close to the optical axis, particularly at the highest frequencies, the distance from the telescope optical axis of the LFI feeds increases with the wavelength. It is then crucial to analyze the optical performance of PLANCK telescope also at the lowest frequency, the 30 GHz channel.

In this case we have only two beams with identical optical properties, due to the symmetry of their positions in the FPU. By exploiting the Method 3, only considering the sky convolution with the simulated beam and with Gaussian beams of comparable width up to 3^ $^{\circ}\;$ from the beam centre (and using then a suitable larger number of grid points, namely 96 $\times$ 96 grid points) we estimated its equivalent FWHM for the PHASE A and ENLARGED telescope: we find 38.86' and 28.72' respectively. Also, the corresponding rms temperature difference between the distorted beams and the corresponding Gaussian beams is $\simeq 2~\mu$K and $\simeq 1.2~\mu$K respectively.

Again, also at low frequencies a larger telescope significantly reduces the impact of beam distortions and makes much more comfortable to reach a good compromise between the reduction of sidelobe contamination and a good resolution.