Due to the wave nature of light, light passing through apertures is diffracted, and the diffraction increases with decreasing aperture size.

The resulting diffraction pattern of a uniformly illuminated circular aperture has a bright region in the centre, known as the Airy disc or Airy pattern (after its discoverer George Airy) which is surrounded by concentric rings. The diameter of this disc is related to the wavelength of the illuminating light and the size (f-number) of the circular aperture. The angle from the center at which the first minimum occurs is

$\backslash sin\; \backslash theta\; =\; 1.22\; \backslash frac\{\backslash lambda\}\{d\}$

where λ is the wavelength of the light and d is the diameter of the aperture. The Rayleigh criterion for barely resolving two objects is that the centre of the Airy disc for the first object occurs at the first minima of the Airy disc of the second.

The Airy disc is used in astronomy as one of several methods used to determine the quality and alignment of the optical components of a telescope.

Mathematical Details

The intensity of the Fraunhofer diffraction pattern of a circular aperture is given by:

$I(\backslash theta)\; =\; I\_0\; \backslash left\; (\; \backslash frac\{2\; J\_1(ka\; \backslash sin\; \backslash theta)\}\{ka\; \backslash sin\; \backslash theta\}\; \backslash right\; )^2$

where $J\_1$ is a Bessel function of the first kind, $a$ is the radius of the aperture, and $k\; =\; \backslash frac\{2\; \backslash pi\}\{\backslash lambda\}$. The first zero of $J\_1(x)$ is where $x\; =\; 3.83$, so the first zero of the diffraction pattern is where

$\backslash sin\; \backslash theta\; =\; \backslash frac\{3.83\}\{ka\}\; =\; \backslash frac\{3.83\; \backslash lambda\}\{\backslash pi\; d\}\; =\; 1.22\; \backslash frac\{\backslash lambda\}\{d\}$.

See also

• George Biddell Airy
• Fraunhofer diffraction
• Amateur astronomy

External links

• Diffraction Limited Photography understanding how airy discs, lens aperture and pixel size limit the absolute resolution of any camera.

Physical optics

Beugungsscheibchen | Tache d'Airy | Plamka Airy'ego