Optimum estimate of delays and dispersive effects in low-frequency interferometric observations

Modern radio interferometers sensitive to low frequencies will make use of wide-band detectors. For such wide bandwidths, dispersive atmospheric effects introduce variations in the fringe delay which change through the band of the receivers. These undesired dispersive effects must be estimated and calibrated with the highest precision. We studied the achievable precision in the estimate of the ionospheric dispersion and the dynamic range of the correlated fringes for different distributions of sub-bands in low-frequency and wide-band interferometric observations. Our study is focused on the case of sub-bands with a bandwidth much narrower than that of the total covered spectrum (case of LOFAR). We computed the uncertainty of the ionospheric delay, the delay ambiguity, and the dynamic range of the fringes using four different kinds of sub-band distributions: constant spacing between sub-bands, random spacings, spacings based on a power-law distribution, and spacings based on Golomb rulers (sets of integers whose sets of differences have non-repeated elements). For a large number of sub-bands ($> 20$, depending on the delay window) spacings based on Golomb rulers give the most precise estimates of dispersive effects and the highest fringe dynamic ranges. Spacings based on the power-law distribution give similar results, although better than those with the Golomb rulers for smaller number of sub-bands. Random distributions result in large fringe dynamic ranges, but the estimate of dispersive effects is worse. A constant spacing of sub-bands results in very bad fringe dynamic ranges, but good estimates of ionospheric dispersion. Combining all the results, the power-law distribution gives the best compromise between homogeneity in the bandwidth sampling, precision in the estimate of ionospheric effects, dynamic range of the correlated fringes, and group-delay ambiguity.Comment: 8 pages, 7 figures. Accepted for publication in A&