angular resolution

Angular resolution is a measure of the ability of a telescope (optical, radio, etc.) to distinguish spatial detail. "Angular" refers to the measure describing an angle between two distinguishable features of an image with the observer as the vertex of the angle. The physics of diffraction determines a minimum angular resolution of a (circular cross-section) telescope based upon the size of its aperture. A telescope's image of a single point of light in the sky consists not of a dot, but is spread/smeared into a specific pattern: a disk surrounded by rings of light (known as an Airy disk). If the angle between two such points is sufficiently small, their two disks are not distinct from each other. Lord Rayleigh's Rayleigh criterion quantifies a telescope's resolution as the angular distance between two points in the celestial sphere such that within the image, one point's disk's maximum brightness (at the center) coincides with the other point's disk's minimum brightness between the center spot and the first ring surrounding it. The following formula calculates this angle:

           λ
θ = 1.220 ———
           D

θ is the angular resolution (radians), λ is the wavelength, and D is the aperture diameter (using the same distance-unit for the wavelength and aperture, e.g., meters). Another criterion, the Dawes limit aka Dawes criterion, is essentially the same criterion, but specific to optical telescopes, based on a representative wavelength within the optical range (about 460 nm, which is blue):

R = 4.56/D

R is arcseconds and D is in inches (116 is a reasonably-equivalent constant for D in millimeters: 4.56 inches equals 115.824 mm).

With multiple telescopes arranged as an interferometer, smaller angular resolution can be obtained. Also, computer-based analysis on the overlapping Airy disks can sometimes identify and locate individual sources, achieving higher angular resolution than the Rayleigh criterion would imply. The term speckle suppression includes this and other methods of surpassing the Rayleigh criterion. Example angular resolutions (based on Rayleigh criterion):

• 1 arcminute - human eye
• 14 arcseconds - James Clerk Maxwell Telescope (JCMT) with SCUBA
• 0.3 arcseconds - Hale Telescope (5.1 m)
• 0.23 arcseconds - Subaru Telescope (8.3 m)
• 0.05 arcseconds - Hubble Space Telescope (HST) (2.4 m)
• 0.04 arcseconds - Keck Observatory (10 m)
• 0.001 arcseconds - European Southern Observatory Very Large Telescope (ESO VLT) (as optical interferometer, 4 × 8.2 m, 120 m baseline)

Interferometry:

• 0.07 arcseconds for 1 cm wavelength - Very Large Array (36 km baseline)
• 15 milliarcseconds for 1 mm wavelength - Atacama Large Millimeter Array (16 km)
• 0.3 milliarcseconds for 1 cm wavelength - Very Long Baseline Array (8000 km)
• 0.03 milliarcseconds for 1 mm wavelength - Event Horizon Telescope (goal, 10000 km)
• 0.01 milliarcseconds for 1.35 cm wavelength - interferometry using space radio telescope, Spektr-R (350000 km)

(Spektr-R's 10-meter dish limited it to bright radio sources.)