. co m p - ph ] 3 1 Ja n 20 02 Implementation of the Hough Transform for 3 D Track Reconstruction in Drift Chambers

This paper is devoted to the method developed in Ref. [1] for 3D reconstruction of the straight tracks in the tracking system consisting of the drift-chamber stereo layers. The method is based on the Hough-transform approach [2] – the discrete case of more general Radon transform [3] – and takes into account both coordinates of the hit wires and drift distances not only for the measurements in one projection, but also in the rotated stereo layers. The proposed method allows one to resolve the right-left ambiguity and provides the accordance between vertical and horizontal projections of the track. Let the straight track of charged particle be detected by the system of drift chambers consisting of the cylindrical tubes placed in such a way that their anode wires stretched along the tube axes are parallel to the vertical coordinate axis Y. In this case the signals from the drift chambers give the information about the track projection onto the horizontal plane XZ. The track projection is described by x(z) = x 0 + t x (z − z 0), where x 0 and t x = tan θ x are the projection offset in z and slope, respectively. The single measurement from the hit wire includes its coordinates x i , z i and measured distance r i from the wire to the track. Assume that error of r i measurement is uniformly distributed within the range [−c, c], where c ≈ (2 ÷ 3)σ is a tuning parameter of the algorithm while σ is a space resolution of the drift chamber. At each value of t x , the Hough image of a single measurement (x i , z i , r i) in the space P x of projection parameters (x 0 , t x) is given by two ranges of possible values of x 0 (see Fig. 1):