Reconstruction and particle identification for a DIRC system

We study the reconstruction and particle identification (PID) problem for Ring Imaging devices providing a good knowledge of the direction of the Cherenkov 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 Cherenkov 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 χ2 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 Cherenkov angle. It is shown that background effects can be dealt without spoiling significantly the reconstruction probability distributions.