Diffraction theory of general nondiffracting beams generated with finite-aperture systems

In this paper, we solve the Fresnel diffraction integral corresponding to the propagation of a general nondiffracting beam generated from an arbitrary finite-aperture system. The solution contains the original infinite-extent nondiffracting beam times a modulating function which does not depend on the nondiffracting beam being generated. The modulating function corresponds to an average taken on a ring of the diffraction pattern of the aperture centered at the point where the performance has to be evaluated. The solution also contains additive functions that become important when the ring has a section lying outside the geometrical projection of the aperture. As an example, we show that the performance of a J0 beam diffracted by a circular aperture may be intuitively understood from the characteristics of the diffraction pattern of a circular aperture.