An efficient formula for the array factor of planar phased arrays with polygonal contour and skewed grid

The far field radiated by a planar array of linearly phased elements can be calculated, in the Kirchoff approximation, by the principle of pattern multiplication (see Stutzman, W.L. and Thiele, G.A., "Antenna theory and design", Wiley and Sons, 1981), i.e. by the product of the element factor and the array factor (AF). A simple and efficient closed-form formula is presented for evaluating the AF of large planar phased arrays with a polygonal rim and skewed grid. The AF is obtained as a superposition of far-field diffraction coefficients from each vertex of the polygonal rim. The analysis is extended to the case of near-zone observation, by resorting to the asymptotic procedure of F. Capolino et al. (see RadioScience, vol.35, no.2, p.579-93, 2000). For pseudocontinuous polygonal curves, the same function can be used without restriction, provided to individualise the right number of vertices and the local lattice directions. In this latter case, however, it is convenient to compensate a priori the singularities on the diffraction cones to avoid the large number of critical directions. Numerical results prove the effectiveness of the presented formulation.