  We study sampling of Fourier Integral Operators $A$ at rates $sh$ with $s$
fixed and $h$ a small parameter. We show that the Nyquist sampling limit of
$Af$ and $f$ are related by the canonical relation of $A$ using semiclassical
analysis. We apply this analysis to the Radon transform in the parallel and the
fan-beam coordinates. We explain and illustrate the optimal sampling rates for
$Af$, the aliasing artifacts, and the effect of averaging (blurring) the data
$Af$. We prove a Weyl type of estimate on the minimal number of sampling points
to recover $f$ stably in terms of the volume of its semiclassical wave front
set.
