Baseline-dependent sampling and windowing for radio interferometry: data compression, field-of-interest shaping and outer field suppression

Traditional radio interferometric correlators produce regular-gridded samples of the true $uv$-distribution by averaging the signal over constant, discrete time-frequency intervals. This regular sampling and averaging then translate to be irregular-gridded samples in the $uv$-space, and results in a baseline-length-dependent loss of amplitude and phase coherence, which is dependent on the distance from the image phase centre. The effect is often referred to as "decorrelation" in the $uv$-space, which is equivalent in the source domain to "smearing". This work discusses and implements a regular-gridded sampling scheme in the $uv$-space (baseline-dependent sampling) and windowing that allow for data compression, field-of-interest shaping and source suppression. The baseline-dependent sampling requires irregular-gridded sampling in the time-frequency space i.e. the time-frequency interval becomes baseline-dependent. Analytic models and simulations are used to show that decorrelation remains constant across all the baselines when applying baseline-dependent sampling and windowing. Simulations using MeerKAT telescope and the European Very Long Baseline Interferometry Network show that both data compression, field-of-interest shaping and outer field-of-interest suppression are achieved.