Relaxing the isoplanatism assumption in self-calibration; applications to low-frequency radio interferometry

A fundamental assumption of the self-calibration/hybrid mapping techniques, which are in widespread use in aperture synthesis data reduction, is one of isoplanatism: that over any given element of the array, all incident wave fronts, regardless of their directions of arrival, are subject to the same tropospheric/ionospheric path delays. This a poor assumption in the case of a low-frequency array (operating at frequencies lower than approximately 300 MHz), because of the large field of view of such an instrument and because of the wavelength dependence of wave-front perturbation by the ionosphere. The isoplanatism assumption may be relaxed by incorporating an interpolation formula in the solution for antenna/IF phases, and the usual mapping/deconvolution techniques then must be modified in order to cope with space-variant effects. Because of the consequent increase in the number of solution parameters, a better source model, higher signal-to-noise ratio, and a larger number of array elements (than are ordinarily required in order to self-calibrate) become desirable.