Abstract
Evaluation of the electromagnetic fields diffracted from plane apertures are, in the general case, highly problematic. Fortunately the exploitation of the Fresnel and more restricted Fraunhofer approximations can greatly simplify evaluation. In particular, the use of the fast Fourier transform algorithm when the Fraunhofer approximation is valid greatly increases the speed of computation. However, for specific applications it is often unclear which approximation is appropriate and the degree of accuracy that will be obtained. We build here on earlier work (Shimoji M 1995 Proc. 27th Southeastern Symp. on System Theory (Starkville, MS, March 1995) (Los Alamitos, CA: IEEE Computer Society Press) pp 520–4) that showed that for diffraction from a circular aperture and for a specific phase error, there is a specific curved boundary surface between the Fresnel and Fraunhofer regions. We derive the location of the boundary surface and the magnitude of the errors in field amplitude that can be expected as a result of applying the Fresnel and Fraunhofer approximations. These expressions are exact for a circular aperture and are extended to give the minimum limit on the domain of validity of the Fresnel approximation for plane arbitrary apertures.