Diffraction-limited system

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$Memorial to E.K. Abbe, who first approximated the diffraction limit as .$

Memorial to E.K. Abbe, who first approximated the diffraction limit as $d=\frac{\lambda}{2n\sin{\alpha}}$ .

The resolution of an optical imaging system like a microscope or telescope or camera can be limited by multiple factors like imperfections in the lenses or misalignment. There is however a fundamental maximum to the resolution of any optical system which is due to diffraction. An optical system with the ability to produce images with angular resolution as good as the instrument's theoretical limit is said to be diffraction limited.^[1]

However, through the use of metamaterials, a superlens may be constructed and the diffraction limit is no longer the limit/constraint.

For a given numerical aperture (NA), the resolution of microscopy for flat objects under coherent illumination can be improved using interferometric microscopy. Using the partial images from a holographic recording of the distribution of the complex optical field, the large aperture image can be reconstructed numerically.^[2]

The resolution of a given instrument is proportional to the size of its objective, and inversely proportional to the wavelength of the light being observed. For telescope with circular apertures, the size of the smallest feature in an image that is diffraction limited is the size of the Airy disc.

In astronomy, a diffraction-limited observation is one that is limited only by the optical power of the instrument used. However, most observations from earth are seeing-limited due to 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 turbulent atmosphere. Traditionally, increasing the size of primary mirrors in ground-based telescopes was used to increase the light-gathering ability of the instrument. This allowed weak extra-galaxian objects to be imaged but did not improve resolution.^[3] Techniques such as speckle imaging can be used to obtain diffraction-limited images of bright objects. Some advanced observatories have recently 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.

Radiotelescopes 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 the HST, or a number of non-optical telescopes) always work at their diffraction limit, if their design is free of optical aberration.

[edit] References

^ Max Born, Emil Wolf. Principles of Optics. Cambridge University Press, 1997. ISBN 0521639212
^ Y.Kuznetsova; A.Neumann, S.R.Brueck (2007). "Imaging interferometric microscopy–approaching the linear systems limits of optical resolution". Optics Express 15: 6651-6663.
^ T.S.Fetisova; D.Y.Kuznetsov, V.A.Lipovetski, A.A.Starobinslii, R.P.Olowin. (1993). "Features of the spatial-distribution of rich clusters of galaxies in the Northern and Southern galactic hemispheres.". Astronomy Letters 19: 198-202.