Scintillation

Figure 16.5: Scintillation due to the ionosphere

In the last section we dealt with an ionosphere which had random density fluctuations in it. In the model we assumed the density was assumed to vary randomly with position, but not with time. In the earth's ionosphere however, the density does vary with both position and time. Temporal variations arise both because of intrinsic variation as well as because of traveling disturbances in the ionosphere, because of which a given pattern of density fluctuations could travel across the line of sight.

This temporal variation of the density fluctuations means that the coherence function (even at some fixed separation on the surface of the earth) will vary with time. This phenomena is generically referred to as ``scintillation''. Depending on the typical scattering angle as well as the typical height of the scattering layer from the surface of the earth, the scintillation could be either ``weak'' or ``strong''.

As discussed in the previous section, rays on passing through an irregular ionosphere get scattered by a typical angle $\theta_{scat}$. If the scattering occurs at a height $h$ above the antennas, then as shown in Figure 16.5 these scattered rays have to traverse a further distance $h$ before being detected. The transverse distance traveled by a scattered ray is $\sim h \theta_{scat}$. If this length is much less than the coherence length $a$, then the rays scattered by different irregularities in the scattering medium do not intersect before reaching the ground. The corresponding condition is that $h\theta_{scat} < a$, i.e. $h\theta_{scat} < \lambda/\theta_{scat}$ or $h\theta_{scat}^2 < \lambda$.

If this condition holds, then, at any instant of time, (as discussed in the previous section), what the observer sees is an undistorted image of the source, which is shifted in position due to refraction. As time passes, the density fluctuations change^16.3 and so the image appears to wander in the sky and in a long exposure image which averages many such wanderings, the source appears to have a scattered broadened size $\theta_{scat}$. Provided that one can do self calibration on a time scale that is small compared to the time scale of the ``image wander'', this effect can be corrected for completely. On the other hand, when the $h\theta_{scat}^2 > \lambda$ the rays from different density fluctuations will intersect and interfere with one another. The observer sees more than one image, and because of the interference, the amplitude of the received signal fluctuates with time. This is called ``amplitude'' scintillation. Amplitude scintillation at low frequencies, particularly over the Indian subcontinent can be quite strong. The source flux could change be factors of 2 or more on very short timescales. This effect cannot be reliably modeled and removed from the data, and hence observations are effectively precluded during periods of strong amplitude scintillation.

Footnotes

... change^16.3

but we assume that their statistics remain exactly the same, i.e. that they continue to be realization of a Gaussian random process with variance $\phi_0$ and auto-correlation $\rho(r)$