Exact expressions in terms of Bessel functions are found for some of the diffraction catastrophe integrals that decorate caustics in optics and mechanics. These are the axial and focal-plane sections of the elliptic and hyperbolic umbilic diffraction catastrophes, and symmetric elliptic and hyperbolic unfoldings of the X9 diffraction catastrophes. These representations reveal unexpected relations between the integrals.
|Translated title of the contribution||Axial and focal-plane diffraction catastrophe integrals|
|Pages (from-to)||1 - 13|
|Number of pages||13|
|Journal||Journal of Physics A: Mathematical and Theoretical|
|Publication status||Published - Aug 2010|