We study the reconstruction and particle identification (PID) problem for
Ring Imaging devices providing a good knowledge of the direction of the
Cerenkov photons, as the DIRC system, on which we specialize. We advocate first
the use of the stereographic projection as a tool allowing a suitable
representation of the photon data, as it allows to represent the Cerenkov cone
always as a circle. We set up an algorithm able to perform reliably a fit of
circle arcs of small angular opening, by minimising a true Chi2 expression. The
system we develop for PID relies on this algorithm and on a procedure able to
remove background photons with a high efficiency. We thus show that, even when
the background is large, it is possible to perform an efficient PID by means of
a fit algorithm which finally provides all the circle parameters; these are
connected with the charged track direction and its Cerenkov angle. It is shown
that background effects can be dealt without spoiling significantly the
reconstruction probability distributions.Comment: 67 pages, 23 figure
