This paper deals with the derivation and physical interpretation of a uniform high-frequency Green's function for a planar right-angle sectoral phased array of dipoles. This high-frequency Green's function represents the basic constituent for the full-wave description of electromagnetic radiation from rectangular periodic arrays and scattering from rectangular periodic structures. The field obtained by direct summation over the contributions from the individual radiators is restructured into a double spectral integral whose high-frequency asymptotic reduction yields a series of propagating and evanescent Floquet waves (FWs) together with corresponding FW-modulated diffracted fields, which arise from FW scattering at the array edges and vertex. Emphasis is given to the analysis and physical interpretation of the vertex diffracted rays. The locally uniform asymptotics governing this phenomenology is physically appealing, numerically accurate, and efficient, owing to the rapid convergence of both the FW series and the series of corresponding FW-modulated diffracted fields away from the array plane. A sample calculation is included to demonstrate the accuracy of the asymptotic algorithm.