Geometry reconstruction of fluorescence detectors revisited

High-energy cosmic rays with energies exceeding 1017 eV are observed by measurements of the fluorescence light induced by air showers. In the fluorescence technique, the geometry of the shower is reconstructed from the correlation between arrival time and incident angle of the signals detected by the telescope. The calculation of the expected light arrival time used so far in shower reconstruction codes is based on several assumptions. Particularly, it is assumed that fluorescence photons are produced instantaneously during the passage of the shower front and that the fluorescence photons propagate on a straight line with vacuum speed of light towards the telescope.We investigate the validity of these assumptions, how to correct them, and the impact on reconstruction parameters when adopting realistic conditions. Depending on the relative orientation of the shower to the telescope, corrections can reach 100 ns in expected light arrival time, 0.1 grad in arrival direction and 5 g cm-2 in depth of shower maximum. The findings are relevant also for the case of 'hybrid' observations where the shower is registered simultaneously by fluorescence and surface detectors. (authors)