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Other meanings of Airy disk

Optics

Airy disk

The Airy disk is the diffraction pattern produced by a circular aperture in an optical system, consisting of a bright central spot surrounded by faint concentric rings. It arises from the wave nature of light and sets the fundamental limit to the resolution of any imaging system, such as a microscope or telescope.1

1835
First described by George Biddell Airy
Year
1.22 λ/D
Angular radius of first dark ring
Formula
~84%
Energy in central disk
Fraction
1

Mathematical description

The intensity distribution of the Airy disk is given by the squared modulus of the Fourier transform of a circular aperture, leading to the Airy function I(θ) = I0[2J1(ka sin θ)/(ka sin θ)]2, where J1 is the Bessel function of the first kind, k is the wavenumber, and a is the aperture radius.2 The first zero occurs at an angular radius of 1.22 λ/D, where D is the aperture diameter. This formula is central to the Rayleigh criterion for resolution, which states that two point sources are just resolvable when the peak of one Airy disk falls on the first minimum of the other.3

2

Physical origin and properties

The Airy disk is a consequence of Fraunhofer diffraction, which occurs when light passes through a circular aperture and is observed at a large distance or in the focal plane of a lens. The central bright spot contains about 84% of the total energy, while the remaining energy is distributed among the surrounding rings, whose intensities decrease rapidly. The size of the Airy disk is inversely proportional to the aperture diameter, so larger apertures produce smaller disks and thus higher resolution. This principle is exploited in telescopes and microscopes, where the aperture size is a key design parameter. The Airy disk also sets the diffraction limit for optical storage systems, such as Blu-ray discs, where the spot size determines the data density.

3

Applications and implications

In astronomy, the Airy disk limits the ability of telescopes to resolve close binary stars and planetary details; adaptive optics and interferometry are used to overcome this limit. In microscopy, the Airy disk defines the resolution limit of conventional light microscopes, motivating techniques like confocal microscopy and super-resolution methods such as STED, which circumvent the diffraction barrier. The Airy disk also appears in laser physics, where it describes the far-field profile of a Gaussian beam focused by a circular lens, and in photography, where it affects the sharpness of images at small apertures due to diffraction blur.4

4

Lesser-known aspects

George Biddell Airy first derived the pattern in 1835, but the underlying mathematics was earlier explored by John Herschel and others. The Airy disk is not limited to visible light; it applies to any wave phenomenon, including electron waves in electron microscopes and radio waves in radio telescopes. In the presence of aberrations, the Airy disk becomes distorted, and the Strehl ratio quantifies the degradation. A related concept is the point spread function (PSF), which for a perfect system is the Airy pattern; deconvolution techniques in image processing often assume a PSF of this form. The Airy disk also has a quantum interpretation: it represents the probability distribution of a photon's position in the focal plane, reflecting the uncertainty principle.5

Glossary

Fraunhofer diffraction
Diffraction pattern observed at a large distance from the aperture, where the incident waves are planar.
Rayleigh criterion
A measure of resolution: two point sources are resolvable when the central maximum of one coincides with the first minimum of the other.
Point spread function (PSF)
The response of an imaging system to a point source; for a perfect system, it is the Airy pattern.
Strehl ratio
The ratio of the peak intensity of an aberrated PSF to that of a perfect PSF.

The Airy disk is named after Sir George Biddell Airy, who first described the pattern in 1835.