Systematic Errors in Cosmic Microwave Background Interferometry

Cosmic microwave background (CMB) polarization observations will require superb control of systematic errors in order to achieve their full scientific potential, particularly in the case of attempts to detect the $B$ modes that may provide a window on inflation. Interferometry may be a promising way to achieve these goals. This paper presents a formalism for characterizing the effects of a variety of systematic errors on interferometric CMB polarization observations, with particular emphasis on estimates of the $B$-mode power spectrum. The most severe errors are those that couple the temperature anisotropy signal to polarization; such errors include cross talk within detectors, misalignment of polarizers, and cross polarization. In a $B$ mode experiment, the next most serious category of errors are those that mix $E$ and $B$ modes, such as gain fluctuations, pointing errors, and beam shape errors. The paper also indicates which sources of error may cause circular polarization (e.g., from foregrounds) to contaminate the cosmologically interesting linear polarization channels, and conversely whether monitoring of the circular-polarization channels may yield useful information about the errors themselves. For all the sources of error considered, estimates of the level of control that will be required for both $E$ and $B$ mode experiments are provided. Simulations of a mock experiment are presented to illustrate the results. Both experiments that interfere linear polarizations and those that interfere circular polarizations are considered. The fact that circular experiments simultaneously measure both linear polarization Stokes parameters in each baseline mitigates some sources of error.