Fresnel diffraction from polygonal apertures

This study presents for the first time, two complementary analytical techniques for calculating the Fresnel diffraction patterns from a polygonal aperture illuminated by a plane wave. These frameworks are exact, in that they do not involve any further approximation beyond the (paraxial) Fresnel integral. Here, regular polygonal apertures are considered. Results are readily extended to describe near-field diffraction from closed apertures of arbitrary shape. These results are of fundamental importance and have specific applications where standard methods, such as fast Fourier transform (FFT) techniques, fail.