Systematic errors in cosmic microwave background polarization measurements

We investigate the impact of instrumental systematic errors on the potential of cosmic microwave background polarization experiments targeting primordial B-modes. To do so, we introduce spin-weighted Muller matrix-valued fields describing the linear response of the imperfect optical system and receiver, and give a careful discussion of the behaviour of the induced systematic effects under rotation of the instrument. We give the correspondence between the matrix components and known optical and receiver imperfections, and compare the likely performance of pseudo-correlation receivers and those that modulate the polarization with a half-wave plate. The latter is shown to have the significant advantage of not coupling the total intensity into polarization for perfect optics, but potential effects like optical distortions that may be introduced by the quasi-optical wave plate warrant further investigation. A fast method for tolerancing time-invariant systematic effects is presented, which propagates errors through to power spectra and cosmological parameters. The method extends previous studies to an arbitrary scan strategy, and eliminates the need for time-consuming Monte-Carlo simulations in the early phases of instrument and survey design. We illustrate the method with both simple parametrized forms for the systematics and with beams based on physical-optics simulations. Example results are given in the context of next-generation experiments targeting tensor-to-scalar ratios r ~ 0.01.