Maximum Likelihood Analysis of Systematic Errors in Interferometric Observations of the Cosmic Microwave Background

We investigate the impact of instrumental systematic errors in interferometric measurements of the cosmic microwave background (CMB) temperature and polarization power spectra. We simulate interferometric CMB observations to generate mock visibilities and estimate power spectra using the statistically optimal maximum likelihood technique. We define a quadratic error measure to determine allowable levels of systematic error that does not induce power spectrum errors beyond a given tolerance. As an example, in this study we focus on differential pointing errors. The effects of other systematics can be simulated by this pipeline in a straightforward manner. We find that, in order to accurately recover the underlying B-modes for r = 0.01 at 28 < l < 384, Gaussian-distributed pointing errors must be controlled to 0.°7 root mean square for an interferometer with an antenna configuration similar to QUBIC, in agreement with analytical estimates. Only the statistical uncertainty for 28 < l < 88 would be changed at ~10% level. With the same instrumental configuration, we find that the pointing errors would slightly bias the 2σ upper limit of the tensor-to-scalar ratio r by ~10%. We also show that the impact of pointing errors on the TB and EB measurements is negligibly small.