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

Abstract

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.

Simulations and performance of the QUBIC optical beam combiner

“…Unlike other ground-based experiments, all the QUBIC mirrors are inside the cryostat (4 K) and after the polariser in the optical chain, reducing the effect of any instrumental polarisation due to them. An autocalibration technique, making use of redundant baselines, has been developed 6,7 so that QUBIC will achieve unprecedented control of systematics along with a sensitivity comparable to that of more traditional imaging polarimeters. Simulations have shown that this first module could constrain the tensor-to-scalar ratio down to ( ) = 0.01 after a two-year survey 4 .…”

“…Waveguide switches placed between the horns in each back-to-back pair will allow signals from individual horns or baselines to be turned on and off. The switches will be opened and closed regularly while QUBIC observes a calibration source to allow self-calibration of the system 6,7 . QUBIC will be used as a synthetic imager, observing the fringes from all baselines simultaneously.…”

“…The advantage of using QUBIC as an interferometer rather than an imager (i.e. with just a clear aperture rather than the array of input horns) is that the redundancy of baselines can be exploited in a self-calibration procedure 6,7 to correct for systematic effects due to different horn gains and cross-polarization, for example.…”

QUBIC: the Q&U Bolometric Interferometer for Cosmology. A novel way to look at the polarized Cosmic Microwave Background.

“…Even with 1 s per baseline (corresponding to a full day dedicated to self-calibration) we can reduce significantly the E → B leakage. This leakage can be further reduced by spending more time in self-calibration (adapted from [3]). The parameter r represents the ratio between the amplitudes of the tensor and scalar fluctuations during inflation.…”

QUBIC: A Fizeau Interferometer Targeting Primordial B-Modes

“…1, left panel): thanks to this feature, a given baseline can be characterised independently, and a set of baselines realising the same Fourier mode (equivalent baselines) can be used to obtain a largely redundant number of measurements of an artificial far-field source to recover the systematics of the instrument, encoded in a certain number of unknown parameters describing horn cross-polarisation, transmission unbalancing, etc. (see [6] for a comprehensive discussion). In this way, the instrument can be self-calibrated, and a novel way of handling systematics can be exploited.…”