Direct calculation of a three-dimensional diffracted field

We present an approach to calculating the complex amplitude of a three-dimensional (3D) diffracted light field in the paraxial approximation based on a 3D Fourier transform. Starting from the Huygens-Fresnel principle, the method is first developed for the computation of the light distribution around the focus of an apertured spherical wave. The method, with modification, is then extended to treat the 3D diffraction of an aperture with an arbitrary transmittance function.