Construct · 4 fields · 4 citations
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In optics the Airy disk is the bright central core, ringed by faint concentric fringes, that a perfect lens or mirror with a circular aperture forms from a point source, because diffraction at the aperture smears the point into a pattern whose radius sets the smallest detail the system can resolve. The pattern and its ring spacing follow from the Fraunhofer diffraction of a circular aperture, first worked out by George Biddell Airy in 1835 and treated in Born and Wolf's Principles of optics. The referent is the diffraction-limited image of a point, measured by the angular radius to the first dark ring, and it is a different construct from a mathematical special function, a water-wave model, or an elasticity potential that share the Airy name.[1]
In mathematics the Airy function is the pair of special functions that solve the differential equation in which a solution switches from oscillating to exponentially growing or decaying as the independent variable crosses zero, making it the standard local model near a turning point. It arose from Airy's 1838 analysis of the light intensity near an optical caustic and is tabulated in Abramowitz and Stegun's Handbook of mathematical functions. The referent is a formal special function used across asymptotics, quantum mechanics, and wave problems, and it is distinct from the optical diffraction spot, the water-wave theory, or the elasticity potential that also bear the Airy name.[2]
In coastal and ocean engineering Airy wave theory, or linear wave theory, is the first-order description of a surface gravity wave that treats the wave as a sinusoid of small amplitude, giving simple closed forms for the dispersion relation, the orbital motion of water particles, and the energy a wave carries. It descends from Airy's 1841 treatment of tides and waves and is the baseline model in Dean and Dalrymple's Water wave mechanics for engineers and scientists. The referent is an idealised linear water wave, the starting point for coastal design, and it is unrelated to a diffraction spot, a special function, or an elasticity potential beyond the common name.[3]
In solid mechanics the Airy stress function is a single scalar potential whose second derivatives give the in-plane stress components, chosen so that equilibrium is satisfied automatically and the full elasticity problem reduces to one biharmonic equation with the boundary conditions. Airy introduced it in his 1863 On the strains in the interior of beams, and it remains the standard device for solving two-dimensional elasticity problems. The referent is a mathematical potential for plane stress or strain, used to find stresses in beams, plates, and notched bodies, and it is a different construct from the optical diffraction spot, the special function, or the water-wave model that share the Airy name.[4]
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