Here we calculate the geometrical factor for the ELENA instrument. ELENA (Emitted Low-Energy Neutral Atoms) is a neutral sensor, part of the SERENA instrument package, for the ESA cornerstone BepiColombo mission to Mercury; it is a new kind of low energetic neutral atoms instrument. It is designed to measure the sputtering emission from planetary surface in the energy range from E ~50eV up to E~5 keV. The instrument FoV is 4.5° by 76°, with nominal resolution of 4.5° by 2°, and nadir pointing. ELENA is a Time-of-Flight (ToF) sensor, based on oscillating shutter (operated at frequencies up to a 100 kHz) and mechanical gratings. The incoming neutral particles directly impinge on the entrance with a definite timing (START) and arrive to a STOP detector at the end of a Time-of-Flight (ToF) chamber. This paper describes both the analytical and the numerical estimation of the geometrical factor for the ELENA sensor. We obtain a geometrical factor of 1.5 10-3 cm2 sr, an angular resolution of 6.5° and a time resolution of 1.5 μs
