Correlator - II: Implementation

D. Anish Roshi

The visibility measured by an interferometer is characterized by the amplitude and phase of the fringe at different instants. For simplicity first consider the output of a two element interferometer. In the quasi monochromatic approximation the multiplier output can be written as (see Chapter 4)

$$r_R(\tau_g) = \mbox{Re}[v_1(\nu,t)v^*_2(\nu,t)] = \vert{\cal V}\vert \cos (2\pi\nu\tau_g + \Phi_{\cal V}),$$ (9.0.1)

where $v_1(\nu,t)$ and $v^*_2(\nu,t)$ are the voltages at the outputs of the receiver systems of the two antennas, $\vert\cal V\vert$ and $\Phi_{\cal V}$ are the amplitude and the phase of the visibility and $\tau_g$ is the geometric delay. The quantities required for mapping a source are $\vert{\cal V}\vert$ and $\Phi_{\cal V}$ for all pairs of antennas of the interferometer. These quantities are measured by first canceling the $2\pi\nu\tau_g$ term in Eq. 9.0.1 by delay tracking and fringe stopping. In general, one needs to know the amplitude and phase of the visibility as a function of frequency. This chapter covers the implementation of a spectral correlator to measure the visibility amplitude and phase. Further since the delay tracking (and fringe stopping for some cases) is usually also done by the correlator, these issues are also discussed.