Editing Diffraction-limited system (section)

{{short description|Optical system with resolution performance at the instrument's theoretical limit}}
[[File:Ernst Abbe memorial.JPG|thumb|right|Memorial in Jena, Germany to [[Ernst Karl Abbe]], who approximated the diffraction limit of a microscope as <math>d=\frac{\lambda}{2n\sin{\theta}}</math>, where ''d'' is the resolvable feature size, ''λ'' is the wavelength of light, ''n'' is the index of refraction of the medium being imaged in, and ''θ'' (depicted as ''α'' in the inscription) is the half-angle subtended by the optical objective lens (representing the [[numerical aperture]]).]]
[[File:Diffraction limit diameter vs angular resolution.svg|thumb|Log-log plot of aperture diameter vs angular resolution at the diffraction limit for various light wavelengths compared with various astronomical instruments. For example, the blue star shows that the Hubble Space Telescope is almost diffraction-limited in the visible spectrum at 0.1 arcsecs, whereas the red circle shows that the human eye should have a resolving power of 20 arcsecs in theory, though normally only 60 arcsecs.]]

In [[optics]], any [[Optical instrument|optical instrument or system]]{{spaced ndash}}a [[microscope]], [[telescope]], or [[camera]]{{spaced ndash}}has a principal limit to its [[Optical resolution|resolution]] due to the [[physics]] of [[diffraction]]. An optical instrument is said to be '''diffraction-limited''' if it has reached this limit of resolution performance. Other factors may affect an optical system's performance, such as lens imperfections or [[Optical aberration|aberrations]], but these are caused by errors in the manufacture or [[Paraxial approximation|calculation]] of a lens, whereas the diffraction limit is the maximum resolution possible for a theoretically perfect, or ideal, optical system.<ref>{{cite book |last=Born |first=Max |title=[[Principles of Optics]] |author2=Emil Wolf |publisher=[[Cambridge University Press]] |year=1997 |isbn=0-521-63921-2}}</ref>

The diffraction-limited [[angular resolution]], in radians, of an instrument is proportional to the [[wavelength]] of the light being observed, and inversely proportional to the diameter of its [[Objective (optics)|objective]]'s [[entrance pupil|entrance aperture]]. For telescopes with circular apertures, the size of the smallest feature in an image that is diffraction limited is the size of the [[Airy disk]]. As one decreases the size of the aperture of a telescopic [[lens (optics)|lens]], diffraction proportionately increases. At small apertures, such as [[F-stop|f/22]], most modern lenses are limited only by diffraction and not by aberrations or other imperfections in the construction.

For microscopic instruments, the diffraction-limited [[spatial resolution]] is proportional to the light wavelength, and to the [[numerical aperture]] of either the objective or the object illumination source, whichever is smaller.

In [[astronomy]], a '''diffraction-limited''' observation is one that achieves the resolution of a theoretically ideal objective in the size of instrument used. However, most observations from Earth are [[Astronomical seeing|seeing]]-limited due to [[Atmosphere of Earth|atmospheric]] effects. Optical telescopes on the [[Earth]] work at a much lower resolution than the diffraction limit because of the distortion introduced by the passage of light through several kilometres of [[Turbulence|turbulent]] atmosphere. Advanced observatories have started using [[adaptive optics]] technology, resulting in greater image resolution for faint targets, but it is still difficult to reach the diffraction limit using adaptive optics.

[[Radio telescope]]s are frequently diffraction-limited, because the wavelengths they use (from millimeters to meters) are so long that the atmospheric distortion is negligible. Space-based telescopes (such as [[Hubble Space Telescope|Hubble]], or a number of non-optical telescopes) always work at their diffraction limit, if their design is free of [[optical aberration]].

The beam from a [[laser]] with near-ideal beam propagation properties may be described as being diffraction-limited. A diffraction-limited laser beam, passed through diffraction-limited optics, will remain diffraction-limited, and will have a spatial or angular extent essentially equal to the resolution of the optics at the wavelength of the laser.