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A uniform high-frequency formulation of the Green's function is presented, for an arbitrarily contoured finite array of electric dipoles. The planar array is thought of as a sequence of parallel finite linear arrays. Its field is obtained by numerical superposition of the dominant field contributions from each constituent linear array. These contributions are uniformly asymptotically evaluated to yield a field representation in terms of truncated single-indexed conical Floquet waves and tip-diffracted spherical waves. Superimposing the linear array asymptotic contributions leads to a convenient description of the total radiated field at finite distance from the planar array. This is represented as the sum of diffracted fields arising from the actual rim plus conical waves from points located along a curved line on the array surface. The final expression is simple, physically appealing, and more efficient than the element-by-element summation, as demonstrated by numerical examples.