The Propagation of Gaussian Beams Going through a ABCD Optical System with an Annular Aperture

The propagation of Gaussian beams is studied, which goes through a paraxial ABCD optical system with an annular aperture. The analytical propagation equation is derived by means of the expansion of the circular domain function into a finite sum of complex Gaussian functions.The propagation equations of Gaussian beams going through circular aperture and circular screen can be regarded as special case in our theoretical model. Numerical caculation examples are given for the focusing of Gaussian beams by an aperture len system. The calculated results are in agreement with those gained by straightforward integral of the Collins formula, but the computing time is greatly reduced.