Numerical integration of diffraction integrals for a circular aperture

Abstract

Summary It is possible to obtain an accurate irradiance distribution for the diffracted wave field from an aperture by the numerical evaluation of the two-dimensional diffraction integrals using a product-integration method in which Simpson's 1/3 rule is applied twice. The calculations can be done quickly using a standard PC by utilizing matrix operations on complex numbers with Matlab. The diffracted wave field can be calculated from the plane of the aperture to the far field without introducing many of the standard approximations that are used to give Fresnel or Fraunhofer diffraction. The numerical method is used to compare the diffracted irradiance distribution from a circular aperture as predicted by Kirchhoff, Rayleigh-Sommerfeld 1 and Rayleigh-Sommerfeld 2 diffraction integrals.