Radiotelescope Resolution Arcsec

Radio telescope angular resolution

For a circular aperture, the sharpest detail you can resolve before diffraction blurs it follows the Rayleigh criterion, θ (rad) = 1.22 · λ / D. Here λ is the wavelength you are observing and D is the dish diameter. Switch to arcseconds through the small-angle approximation and that same expression turns into θ (arcsec) ≈ 252 · (λ / D), valid as long as λ and D are expressed in the same unit.

Take the 305 m Arecibo dish watching the hydrogen line at 1.420 GHz (λ ≈ 21 cm): it lands at roughly 175 arcsec, and that is exactly why a lone dish usually works alongside an interferometer. With Very Long Baseline Interferometry (VLBI) the array baseline stands in for D, pushing the figure down to microarcseconds. The Event Horizon Telescope did just that to capture the M87* black hole shadow in April 2019 with a 20 µas beam.

Applications

It helps when you want to check a single-dish beam against the angular size of pulsars, maser spots, AGN cores or HII regions. The same number guides the sizing of deep-space communication antennas, and it matters in radio surveys whenever source confusion is what sets your noise floor.

FAQ

Why 1.22 instead of 1? That number traces back to the first zero of the Bessel function J₁, which describes how light diffracts through a circular aperture.

Does atmosphere limit radio resolution? Below 50 GHz the troposphere lets most of the signal through, so what caps your resolution is diffraction and tropospheric phase noise, not seeing.

How can interferometers do better? An interferometer behaves like an aperture as wide as its longest baseline B, so θ ≈ λ/B takes the place of θ ≈ λ/D and the sharpness jumps by orders of magnitude.