An Efficient Feedback Calibration Algorithm for Direct Imaging Radio Telescopes

We present the E-field Parallel Imaging Calibration (EPICal) algorithm, which addresses the need for a fast calibration method for direct imaging radio astronomy correlators. Direct imaging involves a spatial fast Fourier transform of antenna signals, alleviating an $\mathcal{O}(N_{\mathrm{ant}}^2)$ computational bottleneck typical in radio correlators, and yielding a more gentle $\mathcal{O}(N_g \log_2 N_g)$ scaling, where $N_{\mathrm{ant}}$ is the number of antennas in the array and $N_g$ is the number of grid points in the imaging analysis. This can save orders of magnitude in computation cost for next generation arrays consisting of hundreds or thousands of antennas. However, because antenna signals are mixed in the imaging correlator without creating visibilities, gain correction must be applied prior to imaging, rather than on visibilities post-correlation. We develop the EPICal algorithm to form gain solutions quickly and without ever forming visibilities. This method scales as the number of antennas, and produces results comparable to those from visibilities. We use simulations to demonstrate the EPICal technique and study the noise properties of our gain solutions, showing they are similar to visibility based solutions in realistic situations. By applying EPICal to two seconds of Long Wavelength Array data we achieve a 65% dynamic range improvement compared to uncalibrated images, showing this algorithm is a promising solution for next generation instruments.