Ionosphere

So far we have been dealing with an ionosphere, which, while not homogeneous, is still fairly simple in that the density fluctuations are smooth, slowly varying functions. Further, the ionospheric density was assumed to not vary with time. In reality, the earth's ionosphere shows density fluctuations on a large range of length and time scales. A density fluctuation of length scale at a height above the earth's surface corresponds to a fluctuation on an angular scale of . For a typical length scale of 10 km, at a height of 200 km, the corresponding angular scale is . This means that the phase difference introduced by the ionosphere changes on an angular scale of . If this phase is to be calibrated out, then one would need to pick a calibrator that is within of the target source -- for most sources it turns out that there is no suitable calibrator this close by. This problem gets increasingly worse as one goes to lower frequencies since the excess ionospheric phase increases as . As discussed in Chapter 5 therefore, as long as the excess ionospheric phase is constant over the field of view, this phase can be lumped in with the electronic phase of receiver chain, and can be solved for using self-calibration.

However, for a given antenna, as one observes at lower and lower frequencies, the field of view increases as . Since the excess ionospheric phase is also increasing rapidly with decreasing frequency, one will soon hit a point where the assumption that the excess phase is constant over the field of view is a poor one. At this point the self-calibration algorithm is no longer applicable. Variations of the ionospheric phase over the field of view are referred to as ``non isoplanaticity''. As illustrated in Figure 16.3, when the baseline length is small compared to the typical length scale of ionospheric density fluctuations, even though the ionospheric phase is different for different sources in the field of view, the excess phase is nearly identical at both ends of the baseline. Since interferometers are sensitive only to phase differences between the two antennas, the isoplanatic assumption still holds. The non isoplanaticity problem hence arises only when the baselines as well as the field of view are sufficiently large. For the GMRT, isoplanaticity is often a poor assumption at frequencies of 325 MHz and lower.