The scattering and diffraction mechanisms of reflecting and transmitting arrays illuminated by the radiation of a point source for a general near-field focus problem are summa- rized. In particular, the phenomena are interpreted by the ray decompositions of Floquet waves and result in the solutions, analogous to the ordinary UTD-type formulations for the phased ar- ray antennas with a proper parameter mapping. In this approach, the radiations of periodically located current sources are first decomposed into Floquet modes, in which every mode is equiv- alent to the radiation of continuous current sources with additional linear phase impressions. Fast convergence in the radiation computation can be achieved because relatively few modes will propagate to the target zone with the rest being evanescent. The ray decomposition is per- formed by asymptotically evaluating the radiation integral of each Floquet mode and interprets the total fields in terms of rays directly radiated from the aperture and diffracted from aperture truncations.