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 e ects, 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 e ects is only limited by the time spent on the calibration mode for each baseline apart from the validity of the systematic error model.