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.
