Airy Functions

doi:10.1117/3.2207310.ch4

Airy Functions

Book: Special Functions for Optical Science and Engineering

Author(s): Vasudevan Lakshminarayanan, L. Srinivasa Varadharajan

Published: 2015

https://doi.org/10.1117/3.2207310.ch4

Author Affiliations +

Abstract

Airy functions are named after the English astronomer George Biddell Airy (1801–1892). Airy’s first mathematical work was on the diffraction phenomenon, namely, the Airy disk - the image of a point object by a telescope - which is familiar to all of us in optics. The name Airy is connected with many physical phenomena and includes, besides the Airy disk, the Airy spiral, an optical phenomenon visible on quartz crystals, and the Airy stress function in elasticity. Airy was very interested in optics and in fact studied the formation of rainbows. A good qualitative summary of the rainbow is given by Adam. In this paper Adam shows how the optical rainbow can be studied at many levels: (i) geometrical optics (rays), (ii) the Airy approximation, (iii) Mie scattering, (iv) complex angular momentum, and (v) catastrophe theory. Airy’s analysis is approximate but applies well to large raindrops that make up the common rainbow (for small drops, catastrophe theory has been used). Details of Airy’s analysis can be found in the chapter on the optics of raindrops in the book by van de Hulst (see also Berry). Airy also analyzed the intensity of light near a caustic wavefront.