It has been shown in Chapter 2 that the visibility measured by the interferometer, ignoring the phase rotation, is given by
Eq. 14.1.1 is not a Fourier transform relation. For a small field of view () the above equation however can be approximated well by a 2D Fourier transform relation. The other case in which this is an exact 2D relation is when the antennas are arranged in a perfect East-West line. However often array configurations are designed to maximize the -coverage and the antennas are arranged in a `' shaped configuration. Hence, Eq. 14.1.1 needs to be used to map full primary beam of the antennas, particularly at low frequencies. Eq. 14.1.1 reduces to a 2D relation also for non-EW arrays if the time of observations is sufficiently small (snapshot observations).
In the first part of this chapter we will discuss the implications of approximating Eq. 14.1.1 by a 2D Fourier transform relation and techniques to recover the 2D sky brightness distribution.
The field of view of a telescope is limited by the primary beams of the antennas. To map a region of sky where the emission is at a scale larger than the angular width of the primary beams, mosaicing needs to be done. This is discussed in the second part of this lecture.