Radio Interferometry: Building a Telescope the Size of a Continent

The diffraction limit of a single dish

Any telescope's ability to separate two close points on the sky is limited by diffraction: light or radio waves of wavelength lambda passing through an aperture of diameter D spread out by an angle proportional to lambda / D. Radio waves are enormously longer than visible light, from centimetres to metres rather than hundreds of nanometres, so a radio dish needs to be proportionally larger than an optical telescope just to match its resolution. The 100-metre Green Bank Telescope observing at 21 cm still resolves details only about as fine as the human eye - roughly an arcminute. Matching the resolving power of a modest backyard optical telescope at radio wavelengths would require a single dish kilometres across, which is not something you can build, let alone steer.

Two dishes, one interference pattern

Interferometry sidesteps the size problem. Point two separate dishes, separated by a distance B called the baseline, at the same source. Because the source is not directly overhead both dishes, the wavefront reaches one dish slightly before the other, and a correlator combines the two signals to measure that tiny path-length difference as a phase shift. As the source appears to move across the sky, that phase shift cycles, producing interference fringes whose spacing depends only on the baseline length and the wavelength, not on the size of either individual dish.

theta ~ lambda / B     // angular resolution set by the baseline B, not the dish size
theta ~ lambda / D     // a single dish's resolution, set by its diameter D

Because B can be thousands of times larger than any single dish D, an interferometer's resolution can be thousands of times finer than any of its individual antennas could achieve alone - the pair behaves, for resolution purposes, like one dish as wide as their separation.

Aperture synthesis: many pairs, one picture

A real array like the Karl G. Jansky Very Large Array (VLA) in New Mexico has 27 dishes, which gives 27 x 26 / 2 = 351 simultaneous baseline pairs, each one sampling a different spacing and orientation. Each pair's measurement, called a visibility, corresponds to one point in a spatial-frequency map of the sky called the UV plane. Fourier-transforming the full set of visibilities back into an image is aperture synthesis: the array never physically fills in a giant dish, but its many baselines sample enough of the equivalent aperture's spatial frequencies to reconstruct an image as if it had.

Letting the Earth do the work

A fixed array of antennas only samples a limited set of baseline orientations at any instant. But as the Earth rotates beneath the sky, the projected geometry of every baseline, as seen from the direction of the source, sweeps around in a smooth ellipse over several hours. This Earth-rotation aperture synthesis means a modest number of physical antennas can, over the course of a night, sample a UV plane as densely as a much larger array observing for an instant - trading time for hardware.

VLBI: baselines the size of a planet

Push the same idea to its extreme and you get Very Long Baseline Interferometry (VLBI): radio telescopes on different continents, each recording its signal with an independent atomic clock rather than a shared cable, later correlated together in software. Baselines of thousands of kilometres give microarcsecond resolution - fine enough that the Event Horizon Telescope, a VLBI array spanning the globe, could image the shadow of the supermassive black hole at the centre of galaxy M87, a target whose apparent size on the sky is comparable to a doughnut on the Moon as seen from Earth.

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