Diffraction of spherical waves at an annular aperture in the use of the boundary diffraction wave theory: A comparison of different diffraction integral approaches

The integral expression for divergent spherical waves diffracted at an annular aperture is derived based on the theory of the boundary diffraction wave. The expressions for divergent spherical waves diffracted at a circular aperture and a disk, and the axial field are treated as the special cases of our general one. Numerical calculation results for axial and transversal intensity distributions are given to compare our results with the Kirchhoff diffraction integral, first and second Rayleigh diffraction integrals. As expected, our results are in agreement with those in the use of the Kirchhoff diffraction integral, but the computer time is reduced greatly by using the boundary diffraction wave theory. The four diffraction formulae are shown to be consistent for axial and transversal intensity distributions, if the source and observation points are positioned equally from the aperture, or the observation point is located enough far from the aperture. Otherwise, the mean value of the first and second Rayleigh diffraction integrals is equal to the result of the boundary diffraction wave theory.