Two innovations in diffraction calculations for cylindrically symmetrical systems

Two mathematical innovations are presented that relate to calculating propagation of radiation through cylindrically symmetrical systems using Kirchhoff diffraction theory. The first innovation leads to an efficient means of computing Lommel functions of two arguments (u and nu), typically denoted by U(n)(u, nu) and V(n)(u, nu). This can accelerate computations involving Fresnel diffraction by circular apertures or lenses. The second innovation facilitates calculations of Kirchhoff diffraction integrals without recourse to the Fresnel approximation, yet with greatly improved efficiency like that characteristic of the latter approximation.