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Angular resolution

Ignoring blurring of the image by turbulence in the atmosphere (atmospheric seeing) and optical imperfections of the telescope, the angular resolution of an optical telescope is determined by the diameter of the primary mirror or lens gathering the light (also termed its "aperture").

The Rayleigh criterion for the resolution limit α R {\displaystyle \alpha _{R}} (in radians) is given by

where λ {\displaystyle \lambda } is the wavelength and D {\displaystyle D} is the aperture. For visible light (λ {\displaystyle \lambda } = 550 nm) in the small-angle approximation, this equation can be rewritten:

Here, α R {\displaystyle \alpha _{R}} denotes the resolution limit in arcseconds and D {\displaystyle D} is in millimeters.In the ideal case, the two components of a double star system can be discerned even if separated by slightly less than α R {\displaystyle \alpha _{R}}. This is taken into account by the Dawes limit

The equation shows that, all else being equal, the larger the aperture, the better the angular resolution. The resolution is not given by the maximum magnification (or "power") of a telescope. Telescopes marketed by giving high values of the maximum power often deliver poor images.

For large ground-based telescopes, the resolution is limited by atmospheric seeing. This limit can be overcome by placing the telescopes above the atmosphere, e.g., on the summits of high mountains, on balloons and high-flying airplanes, or in space. Resolution limits can also be overcome by adaptive optics, speckle imaging or lucky imaging for ground-based telescopes.

Recently, it has become practical to perform aperture synthesis with arrays of optical telescopes. Very high resolution images can be obtained with groups of widely spaced smaller telescopes, linked together by carefully controlled optical paths, but these interferometers can only be used for imaging bright objects such as stars or measuring the bright cores of active galaxies.