= Array factor
The <array factor> describes the <interference> between the elements of a <phased array>, separately from the radiation pattern of each element. For $N$ identical equally spaced elements,
$$
F(\theta)=\sum_{j=0}^{N-1}e^{ij\chi}=e^{i(N-1)\chi/2}\frac{\sin(N\chi/2)}{\sin(\chi/2)},\qquad \chi=\psi-kd\sin\theta.
$$
At $\chi=2\pi m$ the limiting value has magnitude $N$. The total <intensity> is proportional to $|F|^2$ times the single-element <antenna beam pattern>.
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