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Table A.1
Selected LFI beams analysis notation.
| Symbol | Description |
|
|
|
| M, S | Main and Side radiometer arm |
| LOS frame | Telescope’s Line of Sight reference frame |
| θ,φ | Polar coordinates in the LOS frame |
| θ MB , φ MB | Polar coordinates in the main beam frame |
| u, v | Cartesian dimensionless coordinates in the LOS frame |
| e | Beam ellipticity |
| FWHM | Full width half maximum |
| ψ ℓ | Beam orientation defined with respect to the x-axis of the MB frame |
| ψ | Polarization angle (angle between the detector’s polarization axis and the local meridian) |
|
Standard deviation of the elliptical Gaussian |
| η | Main beam efficiency |
| τ(ν) | Bandpass |
( ) |
Detector output in antenna temperature for the M (S) radiometer in the main beam frame |
( ) |
Co-polar electric field component of the beam in the M (S) radiometer |
( ) |
Cross-polar electric field component of the beam in the M (S) radiometer |
| χ omt | Cross-polarization of the orthomode transducer |
|
Pointing direction for time sample t |
|
i-pixel center direction |
| A ti | Pointing matrix for pixel i and time sample t |
| Bij ≡ B | Effective beam for pointing pixel i and beam pixel j |
|
Scanning beam at a direction
 with the pointing angles
 |
| bopt(θ) | Optical beam profile |
| γ | Polarization efficiency γ = (1 − ϵ) / (1 + ϵ), being ϵ the cross-polar leakage |
| w | Polarization weight factor |
| Ωscn | Solid angle of the scanning beam |
| Ωopt | Solid angle of the optical beam |
| Ωsim | Solid angle of the simulated beam |
| Ωeff | Solid angle of the effective beam |
| FWHMeff | Effective beam full width half maximum |
| W ℓ | Beam window function |
| Λk | Eigenvalues of the covariance matrix |
| V k | Eigenvectors of the covariance matrix |
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