Software Correlator-III

In case of two-antenna interference, the cosine of cosine function for the fringe pattern was generated due to the geometric path delay between the two antennas. If we compensate for the phase difference electronically, or in software as we will, the fringes will disappear. This is called 'fringe stopping'.

Let us imagine, that for one source in the sky, fringes removed by the electronic circuits. Now, if there is another fainter point source anywhere in the sky, fringes due that source will be left behind. One can, thus, reason, that the observed fringes are due to superposition of fringes created by multiple point sources.

In synthesis imaging, we measure the cross-correlation coefficient of voltages V1V2* (note the complex conjugation) at two antennas. According to van-Cittert Zernicke theorem, the complex fringe visibility (cross-correlation coefficient) is the Fourier Transform of the normalised sky brightness.

For details of equations, and the transformation to l,m and u,v co-ordinates, see the paper by Thompson and Clark (Synthesis Imaging school at NRAO).


The diagram for synthesis imaging is as below.




we can express the complex cross-correlation coefficient between antennas as below.