On possibilities of the fluorescence detector to measure the shower light curve

Abstract A method to determine the primary energy of very rare big extensive air showers is to measure the fluorescence light flashes induced by them in the atmosphere. From a shower fluorescence image (and its time dependence) it is, in principle, possible to reconstruct the shower cascade curve. The Pierre Auger experiment (in construction) has been using this method (together with measuring the shower charged particles as well) to determine the highest energy part of the cosmic ray spectrum (E J 10 19 eV) and particle arrival directions. Here we analyse which shower parameters affect its image, and, if not taken into account in the reconstruction procedure, may lead to systematic errors in determining its light (cascade) curve, and in consequence, the energy and/or mass of the primary particle. In particular, we analyse the lateral distribution of particles, the thickness and curvature of the shower disk, together with the spherical aberration of the collecting mirror. We show that a non-negligible part of the light flux for showers closer than $15 km to the detector may be hidden in the non-triggered pixels of the camera. For more distant showers this effect is small, but then the atmospheric attenuation has to be known better. We also derive an analytical solution for a spherical mirror focal plane position and the minimal size of the image (spot size) of a parallel light beam