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 sidelobes pickup alongside the convolved dipole in the fit with the measured voltages. The beam pattern is decomposed into

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

and our estimate the gain [math]G[/math] is given through a linear least-squares fit between the voltages [math]V(t)[/math] and [math]T_{model}[/math] , defined as

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

The term [math]B_{main}\ast T_{sky}[/math] 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 [math]T_{CMB}[/math] is negligible.

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

[math]T_{sky}[/math] was estimated using temperature and polarization maps from the Full Focal Plane simulation 7.

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 SZ sources

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

The convolution was performed transforming the maps into spherical harmonics using HEALPix Anafast with [math]\ell_{max}= 2048[/math], and combining the spherical harmonic coefficients [math]a_{\ell m}[/math]. For each sample in the timeline, the straylght was computed with a linear interpolation on the stray light ringset, given the corresponding pointing coordinates [math](θ, φ)[/math] and the orientation [math]ψ[/math] of the beam.