A high performance likelihood reconstruction of gamma-rays for Imaging Atmospheric Cherenkov Telescopes

43 pages, 33 figures, accepted for publication in Astroparticle PhysicsWe present a sophisticated gamma-ray likelihood reconstruction technique for Imaging Atmospheric Cerenkov Telescopes. The technique is based on the comparison of the raw Cherenkov camera pixel images of a photon induced atmospheric particle shower with the predictions from a semi-analytical model. The approach was initiated by the CAT experiment in the 1990's, and has been further developed by a new fit algorithm based on a log-likelihood minimisation using all pixels in the camera, a precise treatment of night sky background noise, the use of stereoscopy and the introduction of first interaction depth as parameter of the model. The reconstruction technique provides a more precise direction and energy reconstruction of the photon induced shower compared to other techniques in use, together with a better gamma efficiency, especially at low energies, as well as an improved background rejection. For data taken with the H.E.S.S. experiment, the reconstruction technique yielded a factor of ~2 better sensitivity compared to the H.E.S.S. standard reconstruction techniques based on second moments of the camera images (Hillas Parameter technique)