Angular resolution#Explanation

The Rayleigh criterion is a heuristic condition for the distance between two light sources, so that they can recognize as separate. By Lord Rayleigh, this minimum distance is equal to the distance from the center of the first minimum of the diffraction pattern. By this reference, the criterion is only applicable, if the resolution is limited by diffraction and the diffraction pattern at all at a minimum. There are more generally applicable criteria.

Diffraction at a slit

If the diffraction-limited resolution is interested in only one direction, such as in optical incremental encoders, the diffraction is to look at the gap. For the single-colored illuminated single slit about results for the more separable angle:

Wherein the approximation of the angles (in radians) is true if the wavelength of the light is much smaller than the nip width.

At a distance from the gap, this results in the following observable half-width:

Diffraction at an aperture

For imaging optics significant is the case of diffraction by a circular aperture, for example the opening of a telescope with diameter d Then for the angular distance of the first minimum

See the Airy disk.

This formal result is close to the empirically found Dawes criterion for visual observations of double stars.

Optical Microscopy

In a microscope is called the Abbe resolution limit, which is determined by the numerical aperture and wavelength. Here normally the resolution from the smallest distance (not above about angles ) of two (point) is described objects. As described above, two (point) objects are Rayleigh still be resolved if the Airy disk of the first object falls with the distance just then on the first minimum of the Airy disk of the second object. Mathematically, this leads to:

The factor 2 comes from the fact that refer here or unlike in the above equations on the half diameter of the lens.