Beams LFI

Overview

LFI is observing the sky with 11 pairs of beams associated with the 22 pseudo-correlation radiometers. Each beam of the radiometer pair (Radiometer Chain Assembly - RCA) is named as LFIXXM or LFIXXS. XX is the RCA number ranging from 18 to 28; M and S are the two polarization namely main-arm and side-arm of the Orthomode transducers #darcangelo2009b (see also LFI naming convention).

Figure 1. A sketch of the Planck LFI field of view in the (u,v) plane is shown. The polarization direction on the sky are highlighted by the colored arrows. The M-polarization is shown in green and the S-polarization in red. Main beam shapes are shown for completness and they are not representative of flight beams.

Main Beams and Focal Plane calibration

As the focal plane calibration we refer to the determination of the beam pointing parameters in the nominal Line of Sight (LOS) frame through main beam measurments using Jupiter transits. the parametes that characterise the beam pointing are the following:

• THETA_UV ($\theta_{uv}$)
• PHI_UV ($\phi_{uv}$)

They are calculated starting from u,v coordinates derived form the beam reconstruction algorithm as

$\theta_{uv} = \arcsin(u^2+v^2)$

$\phi_{uv} = \arctan(v/u)$

Two additional angles are used to characterize the beams in the RIMO:

• PSI_UV ($\psi_{uv}$)
• PSI_POL ($\psi_{pol}$)

$\psi_{uv}$ and $\psi_{pol}$ are not derived from measurements but they are extimated form optical simulations. They are the quantities that represent the polarization direction of each beam, in the following approximation: the M- and S- beams of the same RCA point at the same direction on the sky.

The main beams are characterised by 2 method:

• elliptical (or bivariate) gaussian fit as in #[planck2011-1-6] with modification explained in #[planck2013-p02d]. This method is used to determine
  • the beam centre
  • the average full width half maximum defined as $\sqrt{FWHM_{max}\cdot FWHM_{min}}$
  • the beam ellipticity defined as $FWHM_{max}\over{FWHM_{min}}$
  • the beam tilting, $\psi_{ell}$, with respect the u-axis.

• Electromagnetic simulation (using GRASP Physical Optics code) by appropriately tuning the Radio Frequency Flight Model (RFFM) #tauber2010b. The Radio Frequency Tuned Model, called RFTM, was implemented to fit the beam data with electromagnetic model. It is derived as follow:
  • The Focal plane unit electromagnetic model has shifted by 3.5mm toward the secondary mirror;
  • each feed horn phase centre has been moved alogn horn axis to optimize the match between simulations and data;
  • center frequency of the simulated monochromatic beams have been chosen at 30 GHz according to the centre frequency of the RIMO;

Effective beams

TBW

Window Functions

TBW

Sidelobes

There is no direct measurements of sidelobes for LFI. The sidelobe pattern is estimated by simulations taking into account the geometry of the telescope and the satellite structure. In figure

References

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1. References

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