Precision Calibration of Radio Interferometers for 21 cm Cosmology with No Redundancy and Little Knowledge of Antenna Beams and the Radio Sky

We introduce CALibration AMITY (calamity), a precision bandpass calibration method for radio interferometry. calamity can solve for direction-independent gains with arbitrary frequency structure to the high precision required for 21 cm cosmology with minimal knowledge of foregrounds or antenna beams and does not require any degree of redundancy (repeated identical measurements of the same baseline). We have achieved this through two key innovations. First, we model the foregrounds on each baseline independently using a flexible and highly efficient set of basis functions that have minimal overlap with 21 cm modes and enforce spectral smoothness in the calibrated foregrounds. Second, we use an off-the-shelf GPU accelerated API (tensorflow) to solve for per-baseline foregrounds simultaneously with per-frequency antenna gains in a single optimization loop. GPU acceleration is critical for our technique to be able to solve for the large numbers of foreground and gain parameters simultaneously across all frequencies for an interferometer with ≳10 antennas in a reasonable amount of time. In this paper, we give an overview of our technique and, using realistic simulations, demonstrate its performance in solving for and removing pathological gain structures down to 4.5 orders of magnitude below the level of foregrounds and consistent with our simulated thermal noise limit. If readers want to start using calamity now, they can find a tutorial notebook online.