A new map-making algorithm for CMB polarization experiments

With the temperature power spectrum of the cosmic microwave background (CMB) at least four orders of magnitude larger than the B-mode polarization power spectrum, any instrumental imperfections that couple temperature to polarization must be carefully controlled and/or removed. Here we present two new map-making algorithms that can create polarization maps that are clean of temperature-to-polarization leakage systematics due to differential gain and pointing between a detector pair. Where a half-wave plate is used, we show that the spin-2 systematic due to differential ellipticity can also be removed using our algorithms. The algorithms require no prior knowledge of the imperfections or temperature sky to remove the temperature leakage. Instead, they calculate the systematic and polarization maps in one step directly from the time-ordered data (TOD). The first algorithm is designed to work with scan strategies that have a good range of crossing angles for each map pixel and the second for scan strategies that have a limited range of crossing angles. The first algorithm can also be used to identify if systematic errors that have a particular spin are present in a TOD. We demonstrate the use of both algorithms and the ability to identify systematics with simulations of TOD with realistic scan strategies and instrumental noise.