Propagation of three-dimensional flattened Gaussian beams through an annular aperture

The propagation properties of three-dimensional flattened Gaussian beams passing through a rectangular annular aperture with a central obscuration have been studied in detail using Collins diffraction integral formula.Numerical calculation results of both Fresnel and Fraunhofer diffractions have shown the dependence of their intensity distributions and power (energy) focusability in the far-field on the obscure ratioe and truncation parameter δ.