= 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 $\langle E_1E_2^*\rangle$. 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.
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