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Two Innovations in Diffraction Calculations for Cylindrically Symmetrical Systems



Eric L. Shirley, M A. Terraciano


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 v), typically denoted by U_n(u,v) and V_n(u,v), which 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 what is characteristic of that approximation.
Applied Optics
No. 25


aperture, diffraction, efficient, Fresnel approximation, lens, Lommel Functions


Shirley, E. and Terraciano, M. (2001), Two Innovations in Diffraction Calculations for Cylindrically Symmetrical Systems, Applied Optics (Accessed June 22, 2024)


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Created September 1, 2001, Updated February 17, 2017