  It was proved in \cite{NS1} that obstacles $K$ in $\R^d$ that are finite
disjoint unions of strictly convex domains with $C^3$ boundaries are uniquely
determined by the travelling times of billiard trajectories in their exteriors
and also by their so called scattering length spectra. However the case $d = 2$
is not properly covered in \cite{NS1}. In the present paper we give a separate
different proof of the same result in the case $d = 2$.
