Pearcey integral

In mathematics, the Pearcey[1] integral[2] is defined as[3]

The Pearcey integral is a class of canonical diffraction integrals, often used in wave propagation and optical diffraction problems[4]

In optics, the Pearcey integral can be used to model diffraction effects at a cusp caustic.

A photograph of a cusp caustic produced by illuminating a flat surface with a laser beam through a droplet of water.

Graphs

A plot of the absolute value of the Pearcey integral as a function of its two parameters.
gollark: Idea: genetically engineer Grinch, destroy Christmas forever.
gollark: Russian roulette with orbital lasers?
gollark: It's idiomatic C because if it compiles it runs and it had *no warnings* even with `-Weverything`.
gollark: Well, all programming languages fall into basically 5 categories at most, and I know approximately what those are, so I can* use** any language.
gollark: https://pastebin.com/K1dHumXu

References

  1. https://csiropedia.csiro.au/Pearcey-Trevor/
  2. T. Pearcey, The structure of an electromagnetic field in the neighbourhood of a cusp of a caustic, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 37, 311-317, 1946
  3. Frank W. J. Olver, Daniel W. Lozier, Ronald F. Boisvert, Charles W. Clark, NIST Handbook of Mathematical Functions, p. 777, Cambridge, 2010
  4. R.B.Paris, Hadamard Expansions and Hyperasymptotic Evaluation, p. 207, Encyclopedia of Mathematics and its Applications, 141, Cambridge, 2011


This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.