Approximate propagation equations of flattened gaussian beams passing through a paraxial ABCD system with hard-edge aperture

Abstract The propagation of flattened Gaussian beams through a paraxial optical ABCD system with hard-edge aperture is studied. Approximate closed-form equations of FGBs for the apertured case are derived by means of the expansion of the circ function into a finite sum of complex Gaussian functions. The advantages of the method as compared with the straightforward integration of the Collins formula are discussed and illustrated with numerical examples.