Amplitude and phase

The visibilities are complex numbers, whose real and imaginary parts are measured in the correlator. However, since amplitude and phase distortions have different physical origin, and that amplitude and phase errors have quite distincts consequences in the image plane, one often decomposes the visibilities in amplitude and phase following:

$$V_{ij}(t) = a_{ij} (t) e^{i\varphi_{ij}(t)}$$ (13)