An Efficient Feedback Calibration Algorithm for Direct Imaging Radio Telescopes

TL;DR

The paper introduces EPICal, a fast calibration algorithm for direct imaging radio telescopes that improves computational efficiency and image quality without forming visibilities, suitable for large arrays.

Contribution

EPICal is a novel calibration method that rapidly computes antenna gains directly from imaging data, reducing computational costs for large radio arrays.

Findings

EPICal achieves 65% dynamic range improvement in real data.

The algorithm scales linearly with the number of antennas.

Simulations show noise properties similar to traditional visibility-based solutions.

Abstract

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.