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 wide range of instrumental systematic errors in polarization-sensitive instruments.
Methods: This procedure takes advantage of the need for measurements on redundant baselines to match each other exactly in the absence of systematic effects. For a given systematic error model, measuring each baseline independently therefore allows writing 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.