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 reionisation (EoR) using interferometric low-frequency 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. We do this ultimately to determine the suitability of different imaging algorithms and gridding settings for an analysis of a 21 cm power spectrum. Methods. We simulated realistic Low-Frequency Array (LOFAR) data and constructed power spectra with convolutional gridding and w stacking, w projection, image-domain gridding, and without w correction. These were compared against data that were directly Fourier transformed. The influence of oversampling, kernel size, w-quantization, kernel windowing function, and image padding were quantified. The gridding excess power was measured with a foreground subtraction strategy, for which foregrounds were subtracted using Gaussian progress regression, as well as with a foreground avoidance strategy. Results. Constructing a power spectrum with a significantly lower bias than the expected EoR signals is possible with the methods we tested, but requires a kernel oversampling factor of at least 4000, and when w-correction is used, at least 500 w-quantization levels. These values are higher than typically used values for imaging, but they are computationally feasible. The kernel size and padding factor parameters are less crucial. Of 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 EoR power spectrum experiments, including for future analyses of data from the Square Kilometre Array (SKA) EoR. Nevertheless, convolutional gridding with tuned parameters results in sufficient accuracy for interferometric 21 cm EoR experiments. This also holds for w stacking for wide-field imaging. The w-projection algorithm is less suitable because of the requirements for kernel oversampling, and a faceting approach is unsuitable because it causes spatial discontinuities.