On the Poisson sum formula for analysis of EM radiation/scattering from large finite arrays

A useful procedure, that has been described previously in the literature, employs the Poisson sum formula to represent the solution to the fields of a three-dimensional (3D) large periodically spaced finite planar array problem configuration as a convolution of the infinite planar periodic array solution and the Fourier transform of the equivalent aperture distribution over the finite array. It is shown here that the Poisson sum formula utilized by Felsen and Carin (see J. Opt. Soc. Am. A, vol.11, no.4, p.1291-1306, 1994) and by Felsen and Ribas (see IEEE Trans. Antennas Propagat., vo1.44, no.3, p.375-82, 1996) is exact, hence the use of the less complete Poisson sum formula of Ishimaru (1962), Ishimaru et al. (1985) and Skrivervik et al. (1992, 1993) in finite array problems provides somewhat less accurate results particularly for the wide angle radiation/scattering directions while it provides results in the stronger main beam region that are essentially as accurate as those predicted by the use of the exact Poisson sum formula of Felsen et al.