Intensity distribution of converging spherical waves passing through an annular aperture

Based on the Fresnel diffraction integral,the analytical expression for the field distribution of converging spherical waves passing through an annular aperture is derived and some special cases are discussed.Numerical calculations are performed to show the dependence of intensity distribution on the Fresenl number and obscure ratio.In order to illustrate the valid range of the axial intensity expression and approximation formulae numerical results of both the methods are compared.