Precise polarisation measurements of the cosmic microwave background ( CMB ) require accurate knowledge of the instrument orientation relative to the sky frame used to define the cosmological Stokes parameters .
Suitable celestial calibration sources that could be used to measure the polarimeter orientation angle are limited , so current experiments commonly ‘ self-calibrate. ’ The self-calibration method exploits the theoretical fact that the EB and TB cross-spectra of the CMB vanish in the standard cosmological model , so any detected EB and TB signals must be due to systematic errors .
However , this assumption neglects the fact that polarized Galactic foregrounds in a given portion of the sky may have non-zero EB and TB cross-spectra .
If these foreground signals remain in the observations , then they will bias the self-calibrated telescope polarisation angle and produce a spurious B -mode signal .
In this paper we estimate the foreground-induced bias for various instrument configurations and then expand the self-calibration formalism to account for polarized foreground signals .
Assuming the EB correlation signal for dust is in the range constrained by angular power spectrum measurements from Planck at 353 GHz ( scaled down to 150 GHz ) , then the bias is negligible for high angular resolution experiments , which have access to CMB-dominated high \ell modes with which to self-calibrate .
Low-resolution experiments observing particularly dusty sky patches can have a bias as large as 0.5 ^ { \circ } .
A miscalibration of this magnitude generates a spurious BB signal corresponding to a tensor-to-scalar ratio of approximately r \sim 2 \times 10 ^ { -3 } , within the targeted range of planned experiments .