Hough Transform pattern recognition for track finding at the ATLAS experiment at the LHC

We are exploring Hough Transform (HT) algorithms in FPGAs to identify charged particle trajectories in the ATLAS detector at the HL-LHC. The Inner Detector of the ATLAS experiment measures the trajectories of charged particles in a uniform magnetic field. Our approach is to perform the Hough transformation pattern identification in two steps. The "first-stage" HT uses parameter space in phi0 and q/pT using hits from the semiconductor tracker and identifies those that are consistent with being from the same track. We evaluate adding a second HT step using eta-z0 track coordinate plane, that processes hits identified from roads in the first stage. A working firmware prototype for FPGAs is designed. The performance of this second stage HT is measured as the efficiency and rejection of MC simulations and is presented here, along with an estimation of the resources required of the firmware.