Combining Radon transform and Electrical Capacitance Tomography for a
$2d+1$ imaging device

This paper describes a coplanar non invasive non destructive capacitive
imaging device. We first introduce a mathematical model for its output, and
discuss some of its theoretical capabilities. We show that the data obtained
from this device can be interpreted as a weighted Radon transform of the
electrical permittivity of the measured object near its surface. Image
reconstructions from experimental data provide good surface resolution as well
as short depth imaging, making the apparatus a $2d+1$ imager. The quality of
the images leads us to expect that excellent results can be delivered by
\emph{ad-hoc} optimized inversion formulas. There are also interesting, yet
unexplored, theoretical questions on imaging that this sensor will allow to
test.