= Pointing tolerance of a circular receiving aperture
{title2=$\sin\theta_{1/2}\simeq0.5145\lambda/D$}
For a uniformly illuminated circular aperture of diameter D, normalized received <power> is $[2J_1(x)/x]^2$ with $x=\pi D\sin\theta/\lambda$. The first null has $\sin\theta=1.21967\lambda/D$ and the half-power point has $\sin\theta\simeq0.5145\lambda/D$. A pointing tolerance must name the tolerated <power> loss; the first-null angle is not a good low-loss tolerance. These estimates require an ideal aperture pattern and are only approximate for a dish a few <wavelengths> across.
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