Image-Plane Self-Calibration in Interferometry

TL;DR

This paper introduces a novel image-plane self-calibration method for interferometric imaging that uses shape-orientation-size conservation principles to correct phase errors, enabling high-resolution source imaging.

Contribution

The paper presents a new iterative calibration technique based on SOS conservation for small interferometric arrays, providing geometric insights and broad applicability.

Findings

Converges for simple models in high SNR scenarios

Most effective for small-element arrays

Provides geometric understanding of closure phase

Abstract

We develop a new process of image plane self-calibration for interferometric imaging data. The process is based on Shape-Orientation-Size (SOS) conservation for the principal triangle in an image generated from the three fringes made from a triad of receiving elements, in situations where interferometric phase errors can be factorized into element-based terms. The basis of the SOS conservation principle is that, for a 3-element array, the only possible image corruption due to an element-based phase screen is a tilt of the aperture plane, leading to a shift in the image plane. Thus, an image made from any 3-element interferometer represents a true image of the source brightness, modulo an unknown translation. Image plane self-calibration entails deriving the unknown translations for each triad image via cross-correlation of the observed triad image with a model image of the source brightness. After correcting for these independent shifts, and summing the aligned triad images, a good image of the source brightness is generated from the full array, recovering source structure at diffraction-limited resolution. The process is iterative, using improved source models based on previous iterations. We demonstrate the technique in the high signal-to-noise context, and include a configuration based on radio astronomical facilities, and simple models of double sources. We show that the process converges for the simple models considered, although convergence is slower than for aperture-plane self-calibration for large-$N$ arrays. As currently implemented, the process is most relevant for arrays with a small number of elements. More generally, the technique provides geometric insight into closure phase and the self-calibration process. The technique is generalizable to non-astronomical interferometric imaging applications across the electromagnetic spectrum.