New analytical diffraction expressions for the Fresnel–Fraunhofer transition regime

We propose a method to obtain improved expressions for the diffraction of circular apertures in boundary between near and far field. The is based on an analysis center value pattern derived from Fresnel expression. shown be applied both amplitude, phase, complex apertures, compared propagation simulations. show how these new allow use Fraunhofer approximation at numbers least twice as large conventional expressions. This facilitates analytical used much larger shorter distances, with more aperture transmission functions.