  Charge radii of hadrons are back in the focus since precision spectroscopic
measurements in muonic hydrogen revealed a proton charge radius considerably
smaller than generally accepted ever since R.~Hofstaedter's pioneering
experiments. Recent experimental results also point to an underestimation of
systematic uncertainties in most previous measurements. A new method was thus
proposed by AMBER at CERN using elastic scattering by very high energy muons
using an active hydrogen target. With a simplified setup we may resume elastic
scattering of $\pi$ and K mesons on electrons in inverse kinematics, and, for
the first time, probe antiprotons with few percent precision for their charge
radius. Applying this method also for protons allows a separation of
$G_E^p(Q^2)$ and $G_M^p(Q^2)$ down to $Q^2=10^{-3}(GeV/c)^2$.
