On the basis of expanding a hard-edged aperture function as a finite sum of complex Gaussian functions, an approximate analytical expression for the propagation of an input complex amplitude distribution passing through a general nonsymmetrical apertured double-lens system is derived. Then, the propagation result for two-dimensional flat-topped multi-Gaussian beams is given. It is shown that the apertured Lohmann's symmetrical double-lens system for fractional Fourier transform is a special case of the general apertured doublelens system. The numerical calculation, graphical illustration, and some discussions for the transformation of the two-dimensional flat-topped multi-Gaussian beam in apertured Lohmann's symmetrical double-lens systems are also presented.
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