Fidelity of the periodical self-reconstruction of wavefield

Abstract The periodical self-reconstruction of the wave function is examined for monochromatic wavefields fulfilling the Helmholtz equation. The effect is possible for an arbitrary signal wavefield with the predetermined wave function due to the pseudosampling of its spatial spectrum in cylindrical coordinates. The simplest description of the effect, based on the decomposition of the wave function into the base of ideal non-diffracting modes carrying infinite energy, is replaced by the model dealing with the pseudo non-diffracting modes. It can be closely related to the experimental realization. The fidelity of the self-reconstruction is examined applying the criterion based on the correlation concept.