The ability of a telescope to distinguish fine details, limited by aperture size and wavelength.Angular resolution is the ability of an optical system — a telescope, microscope, or camera — to distinguish two closely spaced objects as separate rather than seeing them as a single blurred blob. It is fundamentally limited by the wave nature of light: when light passes through an aperture, it diffracts, creating a central bright spot (the Airy disk) surrounded by faint rings. If two point sources are closer than roughly the radius of that disk, their patterns merge and they become indistinguishable. The smaller the aperture or the longer the wavelength, the worse the resolution.
The diffraction limit was first quantified by Lord Rayleigh in 1879, building on earlier work by Airy on the diffraction pattern of a circular aperture.
The key formula is θ ≈ 1.22 λ / D, where θ is the smallest resolvable angle, λ is the wavelength of light, and D is the aperture diameter. This Rayleigh criterion sets a hard floor: no matter how perfect the optics, diffraction spreads each point source into a finite-sized pattern. To improve resolution, you either increase the aperture (build a bigger telescope) or use shorter wavelengths (e.g., X-rays instead of visible light). In practice, atmospheric turbulence often degrades resolution further, which is why space telescopes and adaptive optics are used.
Angular resolution determines the sharpness of astronomical images, the resolving power of microscopes, and the quality of satellite photography; it also sets the fundamental limit in X-ray microtomography, where the goal is to see tiny internal structures.
The Hubble Space Telescope's 2.4-meter mirror gives it an angular resolution of about 0.05 arcseconds — sharp enough to read a newspaper from 10 kilometers away, yet still limited by diffraction.
| θ | variable | angular resolution — angular resolution radian |
| λ | variable | wavelength of light — wavelength metre |
| D | variable | aperture diameter — diameter metre |
| 1.22 | constant | First zero of the Airy disk for a circular aperture — airy disk constant = 1.22 |
| M_min | variable | Minimum lens mass — mass kilogram |
| sigma_th | variable | Astrometric precision threshold — angular resolution radian |
| D_L | variable | Distance to lens — distance metre |
| D_S | variable | Distance to source — distance metre |
| D_LS | variable | Distance between lens and source — distance metre |
| G | constant | Universal gravitational constant — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| \propto | operator | Indicates proportionality — proportionality |
