The Baselines
A baseline is a line segment in three dimensions, defined by the vector between two antenna positions. In interferometry, the baseline is not just geometry — it is the fundamental unit of information. Every baseline measures one complex visibility, which is one point in the Fourier plane, and every Fourier point is one step toward an image.
The u-v plane is the projection of all baselines onto the plane perpendicular to the source direction. The coordinates u, v are measured in wavelengths. A baseline of one hundred meters at a wavelength of two centimeters gives u = v = 5000. That's a high spatial frequency, and it corresponds to fine angular structure in the sky. A baseline of ten meters at the same wavelength gives u = v = 500, which probes structure ten times coarser.
The relationship is inverse and precise: angular scale theta equals lambda divided by baseline length B. Long baseline, small angle. Short baseline, large angle. This is why interferometers need short baselines as well as long ones. The short baselines measure the large-scale structure — the diffuse emission, the extended halos, the things that fill in the image. The long baselines measure the compact structure — the cores, the jets, the sources that concentrate the flux. Remove the short baselines, and your image is missing its flux. Remove the long baselines, and your image is a blurry mess. You need both.
The Earth's rotation does the heavy lifting of u-v coverage. As the source moves across the sky, the projected baseline rotates. The same physical baseline, observed over several hours, traces out an ellipse in the u-v plane. Two telescopes, one source, one night — and you get an arc of u-v points. The arc's shape depends on the source's declination, the telescopes' latitude, and the baseline's orientation. If the source is at the celestial pole, the arc is a circle. If the source transits the zenith, the arc is straight. The geometry is fixed; the sampling is what you get.
A single baseline pair gives you one point. A thousand baselines in an array of forty-five telescopes give you nearly nine thousand. The array is not a collection of dishes; it is a sampling instrument. Each dish pair is a coordinate probe. The more pairs, the more densely you sample the Fourier plane, and the better your image.
But density is not the whole story. Coverage matters. A uniform distribution of baselines gives uniform weight to all spatial frequencies, which produces a point spread function with a clean main beam and low sidelobes. A clumped distribution — many short baselines, few long ones — produces an image with strong artifacts. The uv coverage determines the dirty beam, and the dirty beam determines what you can trust in the image.
Interferometric arrays are designed with this in mind. The VLA's Y configuration places telescopes along three arms, maximizing the number of independent baselines for any given number of dishes. The number of baselines in an N-element array is N(N-1)/2. Ten dishes give forty-five baselines. Twenty-seven dishes give three hundred fifty-one. The scaling is quadratic, which is why adding dishes to an existing array is so much more powerful than building a new one.
The Event Horizon Telescope pushed baseline geometry to its limit. Baselines ranged from a few hundred kilometers to twelve thousand, spanning the diameter of the Earth. The uv coverage was sparse — only a few hundred independent baselines — but the longest baselines were long enough to resolve the event horizon scale of a supermassive black hole. The resulting image was low resolution but unprecedented in angular scale. A trade-off, but a deliberate one.
Baselines are the skeleton of every interferometric observation. They determine resolution, sensitivity, image fidelity, and the kinds of sources you can detect. Understanding them is understanding interferometry itself. Every fringe pattern, every visibility, every image begins with a vector between two points on the ground.