2025MNRAS.541.3993B

Many astronomical questions require deep, wide-field observations at low radio frequencies. Phased arrays like LOFAR and SKA-Low (low band part of the Square Kilometre Array) are designed for this, but have inherently unstable element gains, leading to time, frequency, and direction-dependent gain errors. Precise direction-dependent calibration of observations is therefore key to reaching the highest possible dynamic range. Many tools for direction-dependent calibration utilize sky and beam models to infer gains.
However, these calibration tools struggle with precision calibration for relatively bright (e.g. A-team) sources far from the beam centre. Therefore, the point spread function of these sources can potentially obscure a faint signal of interest. We show that, and why, the assumption of a smooth gain solution per station fails for realistic radio interferometers, and how this affects gain-calibration results. Subsequently, we introduce an improvement for smooth spectral gain constraints for direction-dependent gain-calibration algorithms, in which the level of regularization is weighted by the expected station response to the sky model. We test this method using direction-dependent calibration method DDECAL and physically motivated beam-modelling errors for LOFAR-HBA (High-Band Antennas of the Low Frequency Array) stations. The new method outperforms the standard method for various calibration settings near nulls in the beam, and matches the standard inverse-variance-weighted method's performance for the remainder of the data. The proposed method is especially effective for short baselines, both in visibility and image space. Improved direction-dependent gain calibration is critical for future high-precision SKA-Low observations, where higher sensitivity, increased antenna beam complexity, and mutual coupling call for better off-axis source subtraction, which may not be achieved through improved beam models alone.