system is a requirement to maintain a close mechanical antenna alignment in order to keep these lobes in the deep nulls of the subarray beam. Each of the three antenna functions will now be determined and the results combined, using Eq. 10, to obtain the composite pattern. Infinite Array of Point Sources (fi) Each subarray is treated as a point source or impulse separated by distances Sx and Sy. Since it is assumed that the array of impulses extends infinitely in all directions, the antenna electric field distribution is given by The Dirac delta notation, 8(Xa - mSx)8(Ya - nSY) expresses an impulse occurring whenever Xa = mSx and Ya = nSY. It can be shown that the multiplication of two delta functions representing the SPS phase centers may be expressed as a infinite series of harmonic cosine functions: Because of the orthogonality property of the cosine terms, the functions exist only when The electric field at a ground grid point is found by taking the Fourier transform (Eq. 7) of the antenna field distribution (Eq. 11) and is given by which, by using the identity and Eq. 12, allows the electric field to be expressed as
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