Geometric delay (${\tau }_g=\mathbf{b}\cdot \mathbf{s}/c$)

The difference in plane-wave propagation time between two antennas is the projected baseline along the source direction divided by the speed of light. Its sign depends on the ordering of the receivers. A monochromatic signal acquires relative phase $2\pi \nu {\tau }_g$; its change with Earth rotation is compensated by fringe stopping for the chosen reference direction.

For an east-west baseline $b$ and phase-centre zenith angle $\theta$ in its vertical plane, path compensation subtracts $b\sin \theta$. An offset $\alpha$ leaves $\delta \ell =b[\sin (\theta +\alpha )-\sin \theta ]\simeq b\alpha \cos \theta$. The complex correlation therefore has phase $2\pi b\alpha \cos \theta /\lambda$, up to receiver-order convention. Equal cable lengths do not remove this sky-dependent path difference.