# Galactic stray light removal

The pickup of Galactic emission through the sidelobes of the beams causes two kinds of systematic errors:

1. it introduces a bias in the calibration process;

2. it leaves a spurious signal in the calibrated map.

The first error is corrected by including an estimate of the Galactic sidelobe pickup alongside the convolved dipole in the fit with the measured voltages. The beam pattern is decomposed into

- [math]B=B_{\rm main}+B_{\rm sl}[/math],

and our estimate of the gain *G* is given through a linear least-squares fit between the voltages *V(t)* and *T*_{model}, defined as

- [math]T_{\rm model}=B\ast D+B_{\rm sl}\ast T_{\rm sky}[/math].

The term *B*_{main}**T*_{sky} is neglected in the fit because during the calibration we mask the Galactic plane, and we assume that the contribution to the fit given by the terms with *T*_{CMBCosmic Microwave background} is negligible.

The second error is corrected by subtracting the residual signal caused by Galactic pickup through the sidelobes from the timelines immediately after the voltages have been calibrated into temperatures.

*T*_{sky} was estimated using temperature and polarization maps from the seventh Full Focal Plane simulation set (FFP7).

The included components were:

1. synchrotron diffuse emission;

2. thermal and anomalous diffuse emission from dust;

3. Thomson scattering diffuse emission;

4. faint and strong radio sources;

5. thermal and kinetic SZSunyaev-Zel'dovich sources.

The polarized signal from synchrotron and thermal emission from dust was included in the computation.

The convolution was performed by transforming the maps into spherical harmonics using the HEALPix([http://healpix.sourceforge.net Hierarchical Equal Area isoLatitude Pixelation of a sphere], {{BibCite|gorski2005}}) pixelation used to produce Planck sky maps (and HFI HPR). routine Anafast ^{[1]} with ℓ=2048, and combining the spherical harmonic coefficients *a*_{ℓm}. For each sample in the timeline, the stray light was computed with a linear
interpolation on the stray light ringset, given the corresponding pointing coordinates (θ,φ) and the orientation ψ of the beam.

## References

- ↑
**HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere**, K. M. Górski, E. Hivon, A. J. Banday, B. D. Wandelt, F. K. Hansen, M. Reinecke, M. Bartelmann, ApJ,**622**, 759-771, (2005).