= Interferometric baseline
{title2=$\mathbf b,\ \mathbf b_\perp/\lambda$}
An interferometric baseline is the displacement $\mathbf b=\mathbf r_2-\mathbf r_1$ between two <antennas>. For a unit <line of sight> $\mathbf s_0$ toward the <phase centre>, its projection onto the <plane of the sky> is
$$
\mathbf b_\perp=\mathbf b-(\mathbf b\cdot\mathbf s_0)\mathbf s_0,\qquad
|\tau_g|=\frac{|\mathbf b\cdot\mathbf s_0|}{c}.
$$
Here $c$ is the <speed of light>. The signed delay depends on which receiver is delayed; the geometric path difference's magnitude does not. If $\mathbf e_\theta$ is a unit tangent in the direction being imaged, the dimensionless coordinate $u=\mathbf b\cdot\mathbf e_\theta/\lambda$ is a <spatial frequency>, measured in cycles per <radian> of small sky offset. A single pair gives fringes of angular period $1/|u|$ along that tangent. This period specifies one measured oscillation; it does not specify a whole image's <angular resolution> or eliminate ambiguous source arrangements.
\Image[/radio-interferometer-projected-baseline.png]
{title=Geometric delay, projected baseline, and a schematic Earth-rotation track; original geometry, not telescope data}
The left panel separates the component producing the reference delay from the component measuring angular structure. The right panel shows a possible <Earth-rotation aperture synthesis> track, with its opposite <complex conjugate> track. Those opposite samples provide the symmetry required by a real brightness distribution; they are not independent extra observations.
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