The axial intensity of nonparaxial Gaussian beams diffracted by a small aperture

Based on the Rayleigh diffraction integral and without use of the usual approximation,R>λ(λ is wavelength),an exact analytical expression for the axial intensity of nonparaxial Gaussian beams diffracted by a small circular aperture is derived.Then the conventional intensity definition and accurate intensity expression is comparatively studied.It is found that the difference between the two definitions depends on the f-parameter,truncation parameter δ and propagation distance z.