Array Radio Telescopes (ARTs) are powerful instruments that combine multiple antennas to act together as a single, enormous telescope. By measuring and correlating the signals received at different antennas, they achieve far higher angular resolution and sensitivity than any single dish could provide.

An array radio telescope collects radio waves from astronomical sources—galaxies, pulsars, or the cosmic background—and converts them into electrical voltages. Each antenna has two perpendicular dipoles that measure the X and Y components of the incoming electric field. These voltages are stored as complex numbers to capture both amplitude and phase, which together contain the full information of the electromagnetic wave.

The voltage outputs from two antennas are then cross-correlated to form a visibility \(V_{pq}\). For an array of \(N\) antennas, there are \(N(N-1)/2\) unique antenna pairs or baselines, each sampling one Fourier component of the sky brightness distribution.

The fundamental measurement equation of an array radio telescope—the Radio Interferometric Measurement Equation (RIME)—is:

$$ \mathbf{V}_{pq}(u,v) = \iint \mathbf{B}_p\, \mathbf{E}(l,m)\, e^{-2\pi i(ul + vm)}\, \mathbf{B}_q^{\mathrm{H}} \, dl\, dm $$

Here:

• \(u,v\) are the projected baseline coordinates (in wavelengths) on Earth’s surface
• \(l,m\) are direction cosines on the sky
• \(\mathbf{E}(l,m)\) is the brightness matrix of the source
• \(\mathbf{B}\) is the primary beam or directional sensitivity of each antenna

The visibility \(V_{pq}\) is the Fourier transform of the sky brightness distribution, meaning that an interferometer does not form a direct image but samples the Fourier plane of the sky. When the visibilities are calibrated and inverse-Fourier transformed, they reconstruct the radio image.

The resolution of a telescope describes how closely two points on the sky can be distinguished. For a single dish of diameter \(D\) observing at wavelength \(\lambda\),

$$ \alpha = 1.22 \frac{\lambda}{D} $$

where \(\alpha\) is the angular radius of the central Airy disk. In an array, this resolution depends instead on the longest baseline \(b_{\max}\):

$$ \alpha \approx \frac{\lambda}{b_{\max}} $$

Thus, the greater the separation between antennas, the finer the resolution. For example, the LOFAR array in Europe achieves sub-arcsecond precision using baselines up to 1000 km.

The sensitivity of a radio telescope, measured in janskys (Jy), represents the faintest flux detectable above noise. \(1~\text{Jy} = 10^{-26}~\text{W m}^{-2}\text{ Hz}^{-1}\). Modern instruments like MeerKAT can detect signals of a few microjanskys.

Each antenna pair defines a baseline vector \((u,v)\), corresponding to one point in the Fourier domain. As the Earth rotates, the projected baselines trace elliptical tracks—filling the uv-plane. The pattern of sampled points is the uv-coverage, which determines the quality of the reconstructed image. The inverse Fourier transform of the uv-coverage defines the synthesized beam (the array’s point-spread function), while the field of view is set by the primary beam of a single antenna.

For example, at 21 cm wavelength:

• A 45 m GMRT antenna gives a field of view of about 16 arcminutes
• A 25 km baseline gives a synthesized beam of about 1.7 arcseconds

Hence, the array simultaneously achieves a wide field of view and high angular resolution.