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.

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


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