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

Abstract

<i>Context. <i/>Modern radio interferometers sensitive to low frequencies will make use of wide-band detectors (with bandwidths of the order of the observing frequency) and correlators with high data processing rates. It will be possible to simultaneously correlate data from many sub-bands spread through the whole bandwidth of the detectors. For such wide bandwidths, dispersive effects from the atmosphere introduce variations in the fringe delay which change through the whole band of the receivers. These undesired dispersive effects must be estimated and calibrated with the highest precision.<i>Aims. <i/>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).<i>Methods. <i/>We computed the formal statistical uncertainty of the ionospheric delay, the delay ambiguity and the dynamic range of the correlated fringes using four different kinds of distributions of the sub-bands: constant spacing between sub-bands, random spacings, spacings based on a power-law distribution, and spacings based on Golomb rulers (sets of integers, <i>n<i/><sub><i>i<i/><sub/>, whose sets of differences, <i>n<i/><sub><i>j<i/><sub/> – <i>n<i/><sub><i>i<i/><sub/>, have non-repeated elements).<i>Results. <i/>We compare the formal uncertainties in the estimate of ionospheric effects in the data, the ambiguity of the delays, and the dynamic range of the correlated fringes for the four different kinds of sub-band distributions.<i>Conclusions. <i/>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 dynamic ranges of the fringes. Spacings based on the power-law distribution give similar (but slightly worse) results, although the results are better than those from the Golomb rulers for a smaller numbers of sub-bands. Random distributions of sub-bands result in relatively large dynamic ranges of the fringes, but the estimate of dispersive effects through the band is worse. A constant spacing of sub-bands results in very bad dynamic ranges of the fringes, but the estimates of dispersive effects have a precision similar to that obtained with the power-law distribution. Combining all the results, the power-law distribution gives the best compromise between homogeneity in the sampling of the bandwidth, precision in the estimate of the ionospheric dispersive effects, dynamic range of the correlated fringes, and ambiguity of the group delay.