Self-calibration: an efficient method to control systematic effects in bolometric interferometry

Context. The QUBIC collaboration is building a bolometric interferometer dedicated to the detection of B-mode polarization fluctuations in the Cosmic Microwave Background. Aims. We introduce a self-calibration procedure related to those used in radio-interferometry to control a large range of instrumental systematic errors in polarization-sensitive instruments. Methods. This procedure takes advantage of the fact that in the absence of systematic effects, measurements on redundant baselines should exactly match each other. For a given systematic error model, measuring each baseline independently therefore allows to write a system of nonlinear equations whose unknowns are the systematic error model parameters (gains and couplings of Jones matrices for instance). Results. We give the mathematical basis of the self-calibration. We implement this method numerically in the context of bolometric interferometry. We show that, for large enough arrays of horns, the nonlinear system can be solved numerically using a standard nonlinear least-squares fitting and that the accuracy achievable on systematic effects is only limited by the time spent on the calibration mode for each baseline apart from the validity of the systematic error model.