Direction-dependent calibration with image-domain gridding

TL;DR

Wide-field radio interferometric imaging suffers from direction-dependent errors. The authors propose image-domain gridding (IDG) as a forward model for calibration, representing direction-dependent effects with a sub-grid basis in Fourier space to yield continuous corrections across the field. They derive per-sub-grid derivatives and implement a stochastic LBFGS optimization to estimate A-terms, demonstrating on LOFAR data that IDG-CAL produces fewer artifacts and lower background noise than traditional facet-based calibration, while enabling imaging over larger fields. The approach offers scalable, GPU-friendly calibration suitable for next-generation wide-field instruments, with future work focusing on basis refinement and spectral regularization.

Abstract

Wide-field images made by radio interferometers are invariably affected by direction-dependent systematic effects such as the ionosphere or the beam pattern. Calibration along a set of discrete directions in the sky is the default technique to estimate and correct these systematic errors. However, additional processing such as smoothing and mosaicing are required to reconcile the step wise variation of the estimated systematic errors at the edges of the discrete directions (facets). We overcome the discrete nature of direction-dependent calibration by using image-domain gridding as the model for the calibration. Instead of discrete directions in the sky, calibration is performed using a basis that represents a set of sub-grids in the Fourier space. This automatically removes the need for extra operations to recover the wide-field systematics error model without any discontinuity. We provide results based on LOFAR data where we compare the traditional facet-based (discrete directional gains) calibration with the proposed approach. The comparison shows improved image quality, mainly because of the physical plausibility of the proposed approach as opposed to using a piecewise constant model for direction-dependent systematic errors.

Figures (4)

• Figure 1: Total time and final error variation with the number of mini-batches. A large number of mini-batches implies a small mini-batch size, which, hence, reduces the computational cost. The error is normalized by the error reached with the full-batch mode of solving.
• Figure 2: Full field-of-view image produced by standard facet-based calibration after four major cycles. The image size is 19k$\times$19k pixels of $1.25^{\prime\prime}\times 1.25^{\prime\prime}$ covering a field of view of about 7$\times$7 square degrees. The color-scale is linear within the range of [-0.1, 3] mJy/PSF.
• Figure 3: Full field-of-view image produced by IDG-CAL after three major cycles. The image size is 30k$\times$30k pixels of $1.2^{\prime\prime}\times 1.2^{\prime\prime}$ covering a field of view of about 10$\times$10 square degrees. The color-scale is linear within the range of [-0.1, 3] mJy/PSF (the same as in Fig. \ref{['rapthor_full_fov']}).
• Figure 4: Closeup view of a small part (1$\times$1.3 square degrees) of the images from facet calibration using Rapthor (left) and that from IDG-CAL (right). The color-scale is in Jy/PSF and is shown on the right hand side and is the same for both panels.