Pearcey integral

In mathematics, the Pearcey integral is defined as[1] The Pearcey integral is a class of canonical diffraction integrals, often used in wave propagation and optical diffraction problems[2] The first numerical evaluation of this integral was performed by Trevor Pearcey using the quadrature formula.

[3][4] In optics, the Pearcey integral can be used to model diffraction effects at a cusp caustic, which corresponds to the boundary between two regions of geometric optics: on one side, each point is contained in three light rays; on the other side, each point is contained in one light ray.

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A plot of the absolute value of the Pearcey integral as a function of its two parameters.
A photograph of a cusp caustic produced by illuminating a flat surface with a laser beam through a droplet of water.
Reflective caustic generated from a circle and parallel rays. On one side, each point is contained in three light rays; on the other side, each point is contained in one light ray.