Image Domain Gridding: a fast method for convolutional resampling of visibilities

Abstract

In radio astronomy obtaining a high dynamic range in synthesis imaging of wide fields requires a correction for time and directiondependent effects. Applying direction-dependent correction can be done by either partitioning the image in facets and applying a direction-independent correction per facet, or by including the correction in the gridding kernel (AW-projection). An advantage of AW-projection over faceting is that the effectively applied beam is a sinc interpolation of the sampled beam, where the correction applied in the faceting approach is a discontinuous piece wise constant beam. However, AW-projection quickly becomes prohibitively expensive when the corrections vary over short time scales. This occurs for example when ionospheric effects are included in the correction. The cost of the frequent recomputation of the oversampled convolution kernels then dominates the total cost of gridding. Image domain gridding is a new approach that avoids the costly step of computing oversampled convolution kernels. Instead lowresolution images are made directly for small groups of visibilities which are then transformed and added to the large uv grid. The computations have a simple, highly parallel structure that maps very well onto massively parallel hardware such as graphical processing units (GPUs). Despite being more expensive in pure computation count, the throughput is comparable to classical Wprojection. The accuracy is close to classical gridding with a continuous convolution kernel. Compared to gridding methods that use a sampled convolution function, the new method is more accurate. Hence the new method is at least as fast and accurate as classical W-projection, while allowing for the correction for quickly varying direction-dependent effects.

The first power spectrum limit on the 21-cm signal of neutral hydrogen during the Cosmic Dawn at z = 20–25 from LOFAR

“…In the case of two pointings, the bandwidth is reduced to 48 MHz per pointing. Readers may refer to van Haarlem et al (2013) for more information about the observation capabilities of LOFAR.…”

“…(ii) Deconvolve (clean) and image the calibrated visibilities using the WSClean package (Offringa et al 2014) with the following settings: cleaning threshold = 0.5σ, weighting scheme = uniform, imaging baseline range = 0 − 5000λ, 4th order linear polynomial 15 for fitting the source spectrum over 15 points which correspond to averaged flux over 2.2 MHz bands spread within 33 MHz bandwidth. The cleaning parameters are chosen such that the modelled sources with lowest flux values are still a factor of few above the confusion limit at 60 MHz (σ c ∼ 10mJy/beam −1 , see van Haarlem et al 2013 for calculation of σ c ). Since we do not apply the primary beam correction during imaging, the source fluxes are apparent and their spectra also possess the primary beam variations which are less smooth compared to the intrinsic source spectra.…”

“…The redshifted 21-cm signal corresponding to the hyperfine transition of HI has been identified as an excellent probe of the HI distribution in the IGM during the CD and the EoR (Madau et al 1997;Shaver et al 1999;Furlanetto et al 2006;Pritchard & Loeb 2012;Zaroubi 2013). A number of ongoing and upcoming experiments, such as the LOw Frequency ARray 1 (LOFAR; van Haarlem et al 2013), the Giant Meterwave Radio Telescope 2 (GMRT; Paciga et al 2011), the Murchison Widefield Array 3 (MWA; Tingay et al 2013;Bowman et al 2013), the Precision Array for Probing the Epoch of Reionization 4 (PAPER; Parsons et al 2010), the Hydrogen Epoch of Reionization Array 5 (HERA; DeBoer et al 2017), NenuFAR 6 (New extension in Nançay Upgrading loFAR; Zarka et al 2012), and the Square Kilometre Array 7 (SKA; Mellema et al 2013;Koopmans et al 2015) are seeking to detect the brightness temperature fluctuations in the cosmological 21-cm signal using statistical methods e.g. the power spectrum.…”

w-Stackingw-projection hybrid algorithm for wide-field interferometric imaging: implementation details and improvements

“…The advent of wide-field interferometers such as the Murchison Widefield Array (MWA; Tingay et al 2013;Wayth et al 2018), Long Wavelength Array (Ellingson et al 2009) and the Low-Frequency Array (van Haarlem et al 2013) has created a number of imaging challenges. These challenges include the large number of measurements in each observation, the instrumental effects that are measurement dependent, and the large image sizes due to high resolution and wide-field of view.…”

Science with the Murchison Widefield Array: Phase I results and Phase II opportunities

“…;Hughes et al, 2007;Wong et al, 2012Wong et al, , 2011b Crawford et al, 2011;Wong et al, 2011a) in addition to forthcoming A region of sky centred on RA 17 h 22 m , Dec -36 • at 139-170 MHz is shown using three different datasets and imaging techniques. Left: A single two-minute snapshot from the original Phase I configuration, imaged with multiscale W S C L e a n and a Briggs weighting of -1 (Hurley-Walker et al 2019a, accepted); Middle: A single two-minute snapshot from the extended array, imaged with multiscale W S C l e a n and a Briggs weighting of 0; Right: The two observations imaged together using image-domain-gridding(van der Tol et al, 2018) in W S C l e a n and a Briggs weighting of 0. Known SNRs are shown with solid lines, while SNRs detected byHurley-Walker et al (2019b, accepted) are shown with dotted lines.…”