Canonical Integrals for Diffraction Catastrophes
Catastrophe theory was developed in the late 1970s. A catastrophe is a discontinuous change in the behavior of a function that can occur even when its parameters are varied continuously. In diffraction theory, when higher-order catastrophes appear, rapidly oscillating diffraction integrals are required. These integrals represent the light intensity or the quantum-mechanical probability density. When catastrophes occur, classical intensity functions are no longer adequate. The diffraction integrals contain several control parameters (which determine the codimension ) and a set of two-state variables. The curves where intensities accumulate are called caustics.
Examples for four of the seven possible types of catastrophe are:
Pearcey integral (cusp catastrophe)
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