Selection and 3D-Reconstruction of Gamma-Ray-induced Air Showers with a   Stereoscopic System of Atmospheric Cherenkov Telescopes
  A simple 3D-reconstruction method for gamma-ray induced air showers is presented, which takes full advantage of the assets of a system of Atmospheric Cherenkov Telescopes combining stereoscopy and fine-grain imaging like the High Energy Stereoscopic System (H.E.S.S.). The rich information collected by the cameras allows to select electromagnetic showers on the basis of their rotational symmetry with respect to the incident direction, as well as of their relatively small lateral spread. In the framework of a 3D-model of the shower, its main parameters -- incident direction, shower core position on the ground, slant depth of shower maximum, average lateral spread of Cherenkov photon origins (or ``photosphere 3D-width'') and primary energy -- are fitted to the pixel contents of the different images. For gamma-ray showers, the photosphere 3D-width is found to scale with the slant depth of shower maximum, an effect related to the variation of the Cherenkov threshold with the altitude; this property allows to define a dimensionless quantity omega (the ``reduced 3D-width''), which turns out to be an efficient and robust variable to discriminate gamma-rays from primary hadrons. In addition, the omega distribution varies only slowly with the gamma-ray energy and is practically independent of the zenith angle. The performance of the method as applied to H.E.S.S. is presented. Depending on the requirements imposed to reconstructed showers, the angular resolution at zenith varies from 0.04 to 0.1 degrees and the spectral resolution in the same conditions from 15% to 20%. 
M. Lemoine-Goumard, B. Degrange, M. Tluczykont