Interferometry: How Separate Antennas Act Like One Enormous Dish

A radio telescope's resolving power, its ability to tell two close objects apart, depends almost entirely on its diameter relative to the wavelength it is observing. Optical telescopes work in wavelengths measured in nanometres, so even a modest mirror delivers sharp images. Radio waves are millions of times longer. To match the angular resolution of a decent optical telescope at radio frequencies, you would need a dish several kilometres wide. The largest single steerable radio dish ever built, the 500-metre FAST telescope in China's Guizhou province, is already an extraordinary feat of engineering. But even FAST has a ceiling. You cannot keep building bigger dishes. At some point the structure collapses under its own weight, or the cost becomes impossible, or the Earth simply runs out of flat ground.

The solution is not a bigger dish. It is the realisation that you do not need one.





When two radio waves from the same source arrive at two separate antennas, they carry the same information, but they arrive at slightly different times, because the antennas are in different positions relative to the sky. That tiny time difference, called the delay, encodes the angle from which the signal came. If the waves arrive perfectly in step, they reinforce each other: constructive interference. If they arrive half a wavelength out of step, they cancel: destructive interference. By recording both signals simultaneously and then comparing them, a process called cross-correlation, engineers can extract the interference pattern between every pair of antennas in the array.


Each pair of antennas is called a baseline. A baseline oriented east-west is sensitive to structure in the east-west direction on the sky. A baseline oriented north-south reads structure in the other axis. A baseline 1,000 kilometres long resolves detail that a 1,000-kilometre dish would resolve. The array does not collect as much light as that dish, the gaps between antennas collect nothing, but its resolution is governed by the longest baseline, not by the total collecting area. Resolution and sensitivity are separate properties, and interferometry trades some of the latter to gain an almost unlimited amount of the former.

The raw output of an interferometer is not a picture. It is a set of complex numbers, amplitudes and phases, one for each baseline, each moment in time, each frequency channel. This dataset lives in what engineers call the uv-plane, a mathematical space where each measurement samples one spatial frequency of the sky's brightness distribution. The relationship between the uv-plane and the actual image is a Fourier transform: the image is the transform of the measurements, and the measurements are the transform of the image.

Because real arrays have gaps between their antennas, the uv-plane is sampled incompletely. Reconstructing an image from incomplete Fourier samples is an ill-posed problem, many possible skies are consistent with the same measurements. Astronomers solve this using algorithms that impose physical constraints: the sky cannot have negative brightness, and the true image should be as simple as possible given the data. The most widely used algorithm, CLEAN, was developed in the 1970s and is still running in some form inside every major radio observatory on Earth, including the Giant Metrewave Radio Telescope outside Pune, which ISRO and NCRA-TIFR have used for studies of the interstellar medium and pulsar timing.



Extend the baselines to intercontinental distances and you have Very Long Baseline Interferometry, or VLBI. In VLBI, the antennas cannot be connected by cable, the distances are too large. Instead, each antenna records its data to hard drives alongside a timestamp from a hydrogen maser atomic clock, accurate to better than a nanosecond. The drives are physically shipped to a correlator, where the recordings are aligned by their timestamps and cross-correlated in software. The speed-of-light delay between antennas thousands of kilometres apart is computed precisely from the known positions of each dish and the known direction of the source.

The Event Horizon Telescope is VLBI taken to its logical extreme. In April 2017, eight observatories on four continents, including the South Pole Telescope, the Atacama Large Millimeter Array in Chile, and the IRAM telescope in Spain, observed the galaxy M87 simultaneously at a wavelength of 1.3 millimetres. The effective baseline was close to Earth's diameter: roughly 10,000 kilometres. The angular resolution achieved was approximately 20 microarcseconds, sharp enough to read a newspaper in New York from a pavement in Mumbai. The image released in 2019, showing the bright ring of superheated gas around the shadow of M87's central black hole, was assembled from petabytes of hard drives flown to MIT Haystack Observatory and the Max Planck Institute for Radio Astronomy and correlated over two years.

Earth's diameter is a hard ceiling for ground-based VLBI. The next step is to put one antenna in orbit. The Japanese HALCA satellite, launched in 1997, formed baselines with ground stations up to 2.6 Earth diameters long as part of the VSOP mission. Its successor, RadioAstron, operated by Russia's Lebedev Physical Institute, flew to distances of 350,000 kilometres, nearly as far as the Moon, and formed baselines nearly 30 Earth diameters long before the mission ended in 2019. At those scales, interstellar scattering and the physical coherence of the radio source itself become the limiting factors, not the baseline length.

The principle that makes all of this possible has not changed since Martin Ryle and Antony Hewish received the 1974 Nobel Prize in Physics partly for developing aperture synthesis, the technique at interferometry's core. Separate dishes, separated by any distance for which you can synchronise the clocks and correlate the recordings, behave as a single instrument whose resolution is set by the gap between them. The dish in between does not need to exist. The mathematics fills it in.