Revisiting a flux recovery systematic error arising from common deconvolution methods used in aperture-synthesis imaging

The point-spread function (PSF) is a fundamental property of any astronomical instrument. In interferometers, differing array configurations combined with their $uv$ coverage, and various weighting schemes can produce an irregular but deterministic PSF. As a result, the PSF is often deconvolved using CLEAN-style algorithms to improve image fidelity. In this paper, we revisit a significant effect that causes the flux densities measured with any interferometer to be systematically offset from the true values. Using a suite of carefully controlled simulations, we show that the systematic offset originates from a mismatch in the units of the image produced by these CLEAN-style algorithms. We illustrate that this systematic error can be significant, ranging from a few to tens of per cent. Accounting for this effect is important for current and future interferometric arrays, such as MeerKAT, LOFAR and the SKA, whose core-dominated configuration naturally causes an irregular PSF. We show that this offset is independent of other systematics, and can worsen due to some factors such as the goodness of the fit to the PSF, the deconvolution depth, and the signal-to-noise of the source. Finally, we present several methods that can reduce this effect to just a few per cent.