Precision requirements for interferometric gridding in the analysis of a 21 cm power spectrum

Abstract

Context. Experiments that try to observe the 21-cm redshifted signals from the Epoch of Reionization using interferometric lowfrequency instruments have stringent requirements on the processing accuracy. Aims. We analyse the accuracy of radio interferometric gridding of visibilities with the aim to quantify the power spectrum bias caused by gridding, ultimately to determine the suitability of different imaging algorithms and gridding settings for 21-cm power spectrum analysis. Methods. We simulate realistic Low-Frequency Array (LOFAR) data, and construct power spectra with convolutional gridding and w-stacking, w-projection, image domain gridding and without w-correction. These are compared against directly Fourier transformed data. The influence of oversampling, kernel size, w-quantization, kernel windowing function and image padding are quantified. The gridding excess power is measured with a foreground subtraction strategy, for which foregrounds have been subtracted using Gaussian progress regression, as well as with a foreground avoidance strategy. Results. Constructing a power spectrum that has a bias significantly lower compared to the expected EoR signals is possible with the tested methods, but requires a kernel oversampling factor of at least 4000 and, when using w-correction, at least 500 w-quantization levels. These values are higher than typical values used for imaging, but are computationally feasible. The kernel size and padding factor parameters are less crucial. Among the tested methods, image domain gridding shows the highest accuracy with the lowest imaging time.Conclusions. LOFAR 21-cm power spectrum results are not affected by gridding. Image domain gridding is overall the most suitable algorithm for 21-cm Epoch of Reionization power spectrum experiments, including for future Square Kilometre Array (SKA) EoR analyses. Nevertheless, convolutional gridding with tuned parameters results in sufficient accuracy for interferometric 21-cm Epoch of Reionization experiments. This holds also for w-stacking for wide-field imaging. The w-projection algorithm is less suitable because of the kernel oversampling requirements, and a faceting approach is unsuitable due to the resulting spatial discontinuities.

Improved upper limits on the 21 cm signal power spectrum of neutral hydrogen at z ≈ 9.1 from LOFAR

“…Offringa et al (2019a) assessed the impact of missing data due to RFI flagging and found that the combination of flagging and averaging causes tiny spectral fluctuations, resulting in 'flagging excess power' which can be mitigated to a sufficient level by sky-model subtraction before gridding and by using unitary weighted visibilities during gridding 14 . The impact of the gridding algorithm itself is also assessed in Offringa et al (2019b), and a minimum requirement on various gridding parameters is prescribed. In the present work we follow all these recommendations: (i) our sky-model is subtracted by Sagecal before gridding, (ii) we use unit weighting during gridding, (iii) we use a Kaiser-Bessel anti-aliasing filter with a kernel size of 15 pixels and an oversampling factor of 4095, along with 32 w-layers.…”

Reduced-Precision Acceleration of Radio-Astronomical Imaging on Reconfigurable Hardware

“…Image-Domain Gridding performs much better [28] than classical gridding/degridding algorithms, such as Wprojection [29] or AW-projection [30]. It also employs Wterms to solve artifacts around sources away from the phase center in wide-field imaging.…”

“…et al [100] implement an optimized prototype for the degridding algorithm on FPGA, outperforming both CPU and GPU by respectively 2.74x and 2.03x in terms of energydelay product (EDP). However, they employ an outdated version of the degridding algorithm called W-projection, which does not reach the performance of IDG and does not include DDE corrections [28].…”

A numerical study of 21-cm signal suppression and noise increase in direction-dependent calibration of LOFAR data

“…After calibration and sky model subtraction, the residual visibilities are imaged, using (Offringa et al 2014). Imaging is performed with settings that are sufficiently accurate for 21-cm power spectra (Offringa et al 2019). Each frequency channel is imaged individually, resulting in an image cube with dimensions 𝑙, 𝑚, 𝑓 , with 𝑙, 𝑚 the direction cosines and 𝑓 the frequency.…”