  In cluster tomography, we propose measuring the number of clusters $N$
intersected by a line segment of length $\ell$ across a finite sample. As
expected, the leading order of $N(\ell)$ scales as $a\ell$, where $a$ depends
on microscopic details of the system. However, at criticality, there is often
an additional nonlinearity of the form $b\ln(\ell)$, originating from the
endpoints of the line segment. By performing large scale Monte Carlo
simulations of both 2$d$ and 3$d$ percolation, we find that $b$ is universal
and depends only on the angles encountered at the endpoints of the line segment
intersecting the sample. Our findings are further supported by analytic
arguments in 2$d$, building on results in conformal field theory. Being broadly
applicable, cluster tomography can be an efficient tool to detect phase
transitions and to characterize the corresponding universality class in
classical or quantum systems with a relevant cluster structure.
