Improvement of the simulation algorithm of flattened Gaussian beams passing through hard-aperture optics

The simulation algorithm of flattened Gaussian beams(FGBs) passing through hard-aperture optics is improved,and an approximate closed-form propagation equation is derived,where a product of Fourier series and complex Gaussian function expansion is adapted to the window function of a hard-edged aperture. Numerical calculation results are compared with those obtained by direct integration of the Collins formula Wen's method.It is shown that the improved algorithm provides more accurate calculation results than the complex Gaussian function expansion,so long as the number of Fourier series is no less than 30.