 Radio interferometry

Radio interferometry measures the spatial coherence of received radio waves. At two antennas, a receiver preserves the relative wave phase, compensates the geometric delay for a chosen phase centre, and averages a product of one signal with the complex conjugate of the other. In a complex-signal description this correlation is $⟨E_1{E}_2^{\ast }⟩$. Its real and imaginary parts carry two complementary components of the complex visibility; measuring only the received powers discards the relative wave phase needed for general imaging.

A finite frequency band makes delay compensation essential. If the residual delay is $\Delta \tau$, the residual wave phase varies by $2\pi \Delta \nu \Delta \tau$ across a band of width $\Delta \nu$. Averaging these differently oriented complex contributions reduces the correlation. For an ideal rectangular band the multiplicative factor is $\sin (\pi \Delta \nu \Delta \tau )/(\pi \Delta \nu \Delta \tau )$. A phase correction at just the central frequency cannot remove this variation across the band. Long time averages can likewise smear a changing signal.