Rayleigh criterion

The Rayleigh criterion estimates when two point sources are just resolved: the central maximum of one diffraction pattern coincides with the first minimum of the other.

Airy disk: The central bright region in the diffraction pattern formed by a circular aperture. Its first dark ring supplies the minimum used to define resolution.
Wavelength: The spatial period of a wave, measured between corresponding points in successive cycles. The minimum resolvable angle grows in proportion to the light’s wavelength.
Telescope: An instrument that collects and focuses radiation from distant objects. A telescope’s aperture predicts the smallest stellar separation resolved by the criterion.
Abbe diffraction limit: A microscopy resolution limit derived from the spatial frequencies transmitted by an imaging system. It addresses periodic detail and differs from Rayleigh’s two-point-source convention.
Fraunhofer diffraction: The far-field diffraction pattern produced when light propagates from an aperture to a distant observation plane. The criterion compares far-field patterns from two point sources.
Circular aperture: A round opening that limits the light entering an optical system. Its diameter sets the angular scale in the classic Rayleigh formula.
Microscope: An instrument that forms magnified images of small objects using lenses or other optical elements. The criterion estimates the minimum separation between image points in conventional optical microscopy.
Sparrow criterion: A resolution criterion at which the combined intensity profile of two sources loses its central dip. It declares sources resolved at a smaller separation than the Rayleigh criterion.
Point spread function: The image intensity distribution produced by an imaging system from an ideal point source. Two point sources are resolved by comparing their combined point spread functions.
Aperture synthesis: A technique that combines measurements from separated telescopes to emulate a larger aperture. It changes effective aperture geometry beyond the single circular opening assumed by the classic rule.

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